Space of modular forms of level 95, weight 11, and Character 95.d

• Label: 95.11.d
• Level: $95$
• Weight: $11$
• Character orbit: 95.d
• Rep. character: $\chi_{95}(94,\cdot)$
• Character field: $\Q$
• Dimension: $98$
• Newform subspaces: $4$
• Sturm bound: $110$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 95 = 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 11 \)
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:			\(110\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{11}(95, [\chi])\).

	Total	New	Old
Modular forms	102	102	0
Cusp forms	98	98	0
Eisenstein series	4	4	0

Trace form

\( 98 q + 50368 q^{4} + 1109 q^{5} + 760 q^{6} + 1850198 q^{9} + O(q^{10}) \)

Decomposition of \(S_{11}^{\mathrm{new}}(95, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
95.11.d.a	$95$	$11$	95.d	95.d	$2$	$2$	$2$	$60.359$	\(\Q(\sqrt{-19}) \)	\(\Q(\sqrt{-19}) \)		$4$	$0$	\(0\)	\(0\)	\(3951\)	\(0\)	$11$	$\mathrm{U}(1)[D_{2}]$	\(q-2^{10}q^{4}+(2026+101\beta )q^{5}+(177+\cdots)q^{7}+\cdots\)
95.11.d.b	$95$	$11$	95.d	95.d	$2$	$4$	$4$	$60.359$	4.4.462080.1	\(\Q(\sqrt{-95}) \)	✓	$4$	$0$	\(0\)	\(0\)	\(-12500\)	\(0\)	$5$	$\mathrm{U}(1)[D_{2}]$	\(q+(\beta _{1}+12\beta _{2})q^{2}+(-23\beta _{1}+43\beta _{2}+\cdots)q^{3}+\cdots\)
95.11.d.c	$95$	$11$	95.d	95.d	$2$	$4$	$4$	$60.359$	4.4.7600.1	\(\Q(\sqrt{-95}) \)	✓	$4$	$0$	\(0\)	\(0\)	\(12500\)	\(0\)	$2^{2}\cdot 5^{2}\cdot 11$	$\mathrm{U}(1)[D_{2}]$	\(q+(\beta _{1}+2\beta _{2})q^{2}+(-6\beta _{1}+17\beta _{2})q^{3}+\cdots\)
95.11.d.d	$95$	$11$	95.d	95.d	$2$	$88$	$88$	$60.359$		None		$4$	$0$	\(0\)	\(0\)	\(-2842\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$