Swansea magistrates said Robert Riley's online messages were also racially and religiously aggravated and that only a custodial sentence could be imposed.
Riley, from Port Talbot, was sentenced to eight weeks in custody after admitting posting an abusive Twitter message about the death of Leeds schoolteacher Ann Maguire.
The 42-year-old was the second person to be charged with the offence in the wake of the death of Mrs Maguire, who was stabbed to death in her classroom at Corpus Christi Catholic College last month.
Yesterday a third person was arrested in Cardiff and bailed.
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Wales second-row Alun-Wyn Jones believes his side are in "an exciting place" as they target a post-World Cup Six Nations title.
What time’s kick off? How can I watch it? Who’s in the teams? Find out what you need to know here.
Wales Captain Sam Warburton says his team are raring to go as they kick off their Six Nations campaign in Dublin tomorrow.