Space of modular forms of level 114, weight 4, and Character 114.b

• Label: 114.4.b
• Level: $114$
• Weight: $4$
• Character orbit: 114.b
• Rep. character: $\chi_{114}(113,\cdot)$
• Character field: $\Q$
• Dimension: $20$
• Newform subspaces: $2$
• Sturm bound: $80$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 114 = 2 \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	114.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 57 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(80\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(29\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(114, [\chi])\).

	Total	New	Old
Modular forms	64	20	44
Cusp forms	56	20	36
Eisenstein series	8	0	8

Trace form

\( 20 q + 80 q^{4} - 20 q^{6} + 20 q^{7} - 10 q^{9} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(114, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
114.4.b.a	$114$	$4$	114.b	57.d	$2$	$10$	$10$	$6.726$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None		$2$	$0$	\(-20\)	\(5\)	\(0\)	\(10\)	$2^{2}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-2q^{2}+(1-\beta _{1})q^{3}+4q^{4}+(1-\beta _{1}+\cdots)q^{5}+\cdots\)
114.4.b.b	$114$	$4$	114.b	57.d	$2$	$10$	$10$	$6.726$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None		$2$	$0$	\(20\)	\(-5\)	\(0\)	\(10\)	$2^{2}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+2q^{2}-\beta _{3}q^{3}+4q^{4}+(\beta _{3}+\beta _{4})q^{5}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(114, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(114, [\chi]) \cong \)