Space of modular forms of level 76, weight 9, and Character 76.c

• Label: 76.9.c
• Level: $76$
• Weight: $9$
• Character orbit: 76.c
• Rep. character: $\chi_{76}(37,\cdot)$
• Character field: $\Q$
• Dimension: $14$
• Newform subspaces: $2$
• Sturm bound: $90$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 76 = 2^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	76.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 19 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(90\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(76, [\chi])\).

	Total	New	Old
Modular forms	83	14	69
Cusp forms	77	14	63
Eisenstein series	6	0	6

Trace form

\( 14 q - 279 q^{5} + 1207 q^{7} - 33088 q^{9} + O(q^{10}) \)

Decomposition of \(S_{9}^{\mathrm{new}}(76, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
76.9.c.a	$76$	$9$	76.c	19.b	$2$	$2$	$2$	$30.961$	\(\Q(\sqrt{57}) \)	\(\Q(\sqrt{-19}) \)	✓	$2$	$0$	\(0\)	\(0\)	\(289\)	\(-527\)	$3$	$\mathrm{U}(1)[D_{2}]$	\(q+(191+93\beta )q^{5}+(-3^{4}+365\beta )q^{7}+\cdots\)
76.9.c.b	$76$	$9$	76.c	19.b	$2$	$12$	$12$	$30.961$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(-568\)	\(1734\)	$2^{19}\cdot 3^{4}\cdot 7$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+(-47+\beta _{3})q^{5}+(12^{2}-\beta _{5}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{9}^{\mathrm{old}}(76, [\chi])\) into lower level spaces

\( S_{9}^{\mathrm{old}}(76, [\chi]) \cong \) \(S_{9}^{\mathrm{new}}(19, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(38, [\chi])\)\(^{\oplus 2}\)