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

• Label: 114.4.h
• Level: $114$
• Weight: $4$
• Character orbit: 114.h
• Rep. character: $\chi_{114}(65,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $40$
• 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.h (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 57 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(80\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(5\)

Dimensions

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

	Total	New	Old
Modular forms	128	40	88
Cusp forms	112	40	72
Eisenstein series	16	0	16

Trace form

\( 40 q - 3 q^{3} - 80 q^{4} - 10 q^{6} - 20 q^{7} - 5 q^{9} + O(q^{10}) \)

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.h.a	$114$	$4$	114.h	57.f	$6$	$20$	$10$	$6.726$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		$2$	$0$	\(-20\)	\(-4\)	\(0\)	\(-10\)	$2^{4}\cdot 3^{8}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-2-2\beta _{2})q^{2}+(-\beta _{1}+\beta _{3})q^{3}+\cdots\)
114.4.h.b	$114$	$4$	114.h	57.f	$6$	$20$	$10$	$6.726$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		$2$	$0$	\(20\)	\(1\)	\(0\)	\(-10\)	$2^{4}\cdot 3^{8}$	$\mathrm{SU}(2)[C_{6}]$	\(q-2\beta _{1}q^{2}-\beta _{5}q^{3}+(-4-4\beta _{1})q^{4}+\cdots\)

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

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