Space of modular forms of level 95, weight 7, and Character 95.d

• Label: 95.7.d
• Level: $95$
• Weight: $7$
• Character orbit: 95.d
• Rep. character: $\chi_{95}(94,\cdot)$
• Character field: $\Q$
• Dimension: $58$
• Newform subspaces: $4$
• Sturm bound: $70$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 95 = 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	95.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 95 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(70\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(95, [\chi])\).

	Total	New	Old
Modular forms	62	62	0
Cusp forms	58	58	0
Eisenstein series	4	4	0

Trace form

\( 58 q + 1920 q^{4} + 54 q^{5} - 584 q^{6} + 13118 q^{9} + O(q^{10}) \)

Decomposition of \(S_{7}^{\mathrm{new}}(95, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
95.7.d.a	$95$	$7$	95.d	95.d	$2$	$2$	$2$	$21.855$	\(\Q(\sqrt{-19}) \)	\(\Q(\sqrt{-19}) \)		$4$	$0$	\(0\)	\(0\)	\(-54\)	\(0\)	$2^{3}$	$\mathrm{U}(1)[D_{2}]$	\(q-2^{6}q^{4}+(-3^{3}+7\beta )q^{5}+18\beta q^{7}+\cdots\)
95.7.d.b	$95$	$7$	95.d	95.d	$2$	$4$	$4$	$21.855$	4.4.462080.1	\(\Q(\sqrt{-95}) \)	✓	$4$	$0$	\(0\)	\(0\)	\(-500\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+(-2\beta _{1}+3\beta _{2})q^{2}+(3\beta _{1}-11\beta _{2}+\cdots)q^{3}+\cdots\)
95.7.d.c	$95$	$7$	95.d	95.d	$2$	$4$	$4$	$21.855$	4.4.7600.1	\(\Q(\sqrt{-95}) \)	✓	$4$	$0$	\(0\)	\(0\)	\(500\)	\(0\)	$2^{2}$	$\mathrm{U}(1)[D_{2}]$	\(q+(-2\beta _{1}-3\beta _{2})q^{2}+(-3\beta _{1}-11\beta _{2}+\cdots)q^{3}+\cdots\)
95.7.d.d	$95$	$7$	95.d	95.d	$2$	$48$	$48$	$21.855$		None		$4$	$0$	\(0\)	\(0\)	\(108\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$