Space of modular forms of level 76, weight 7, and Character 76.c

• Label: 76.7.c
• Level: $76$
• Weight: $7$
• Character orbit: 76.c
• Rep. character: $\chi_{76}(37,\cdot)$
• Character field: $\Q$
• Dimension: $10$
• Newform subspaces: $2$
• Sturm bound: $70$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 76 = 2^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 7 \)
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:			\(70\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(76, [\chi])\).

	Total	New	Old
Modular forms	63	10	53
Cusp forms	57	10	47
Eisenstein series	6	0	6

Trace form

\( 10 q + 56 q^{5} - 248 q^{7} - 2890 q^{9} + O(q^{10}) \)

Decomposition of \(S_{7}^{\mathrm{new}}(76, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
76.7.c.a	$76$	$7$	76.c	19.b	$2$	$2$	$2$	$17.484$	\(\Q(\sqrt{57}) \)	\(\Q(\sqrt{-19}) \)	✓	$2$	$0$	\(0\)	\(0\)	\(54\)	\(-610\)	$2^{3}$	$\mathrm{U}(1)[D_{2}]$	\(q+(3^{3}+7\beta )q^{5}+(-305+9\beta )q^{7}+3^{6}q^{9}+\cdots\)
76.7.c.b	$76$	$7$	76.c	19.b	$2$	$8$	$8$	$17.484$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(362\)	$2^{8}\cdot 3\cdot 5$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+\beta _{7}q^{5}+(46+\beta _{2}+2\beta _{3}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{7}^{\mathrm{old}}(76, [\chi])\) into lower level spaces

\( S_{7}^{\mathrm{old}}(76, [\chi]) \cong \) \(S_{7}^{\mathrm{new}}(19, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(38, [\chi])\)\(^{\oplus 2}\)