Space of modular forms of level 1, weight 124, and trivial character

• Label: 1.124.a
• Level: $1$
• Weight: $124$
• Character orbit: 1.a
• Rep. character: $\chi_{1}(1,\cdot)$
• Character field: $\Q$
• Dimension: $10$
• Newform subspaces: $1$
• Sturm bound: $10$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 1 \)
Weight:	\( k \)	\(=\)	\( 124 \)
Character orbit:	\([\chi]\)	\(=\)	1.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(10\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{124}(\Gamma_0(1))\).

	Total	New	Old
Modular forms	11	11	0
Cusp forms	10	10	0
Eisenstein series	1	1	0

Trace form

\( 10 q + 2202364291733634600 q^{2} + 134125909579478648360089344600 q^{3} + 57084626888206052159227531786235721280 q^{4} + 113311323144401441139520857445630379551020 q^{5} + 1704428975203488447105127830499670347572029831520 q^{6} - 588489927154562089895546247825497341684043299210000 q^{7} + 31510915218929096051805568530239002377664910158953331200 q^{8} + 110622019190242888335688316416186156626673662860821573119570 q^{9} + O(q^{10}) \)

Decomposition of \(S_{124}^{\mathrm{new}}(\Gamma_0(1))\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1.124.a.a	$1$	$124$	1.a	1.a	$1$	$10$	$10$	$95.808$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	$1$	$0$	\(22\!\cdots\!00\)	\(13\!\cdots\!00\)	\(11\!\cdots\!20\)	\(-58\!\cdots\!00\)	$+$	$2^{178}\cdot 3^{70}\cdot 5^{22}\cdot 7^{9}\cdot 11^{6}\cdot 13^{2}\cdot 17\cdot 31^{2}\cdot 41^{3}$	$\mathrm{SU}(2)$	\(q+(220236429173363460-\beta _{1})q^{2}+\cdots\)