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

• Label: 95.11.n
• Level: $95$
• Weight: $11$
• Character orbit: 95.n
• Rep. character: $\chi_{95}(21,\cdot)$
• Character field: $\Q(\zeta_{18})$
• Dimension: $396$
• Newform subspaces: $1$
• Sturm bound: $110$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 95 = 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	95.n (of order \(18\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 19 \)
Character field:			\(\Q(\zeta_{18})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(110\)
Trace bound:			\(0\)

Dimensions

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

	Total	New	Old
Modular forms	612	396	216
Cusp forms	588	396	192
Eisenstein series	24	0	24

Trace form

\( 396 q + 132 q^{3} - 1830 q^{4} + 3066 q^{6} - 95436 q^{9} + O(q^{10}) \)

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.n.a	$95$	$11$	95.n	19.f	$18$	$396$	$66$	$60.359$		None		$2$	$0$	\(0\)	\(132\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{18}]$

Decomposition of \(S_{11}^{\mathrm{old}}(95, [\chi])\) into lower level spaces

\( S_{11}^{\mathrm{old}}(95, [\chi]) \cong \) \(S_{11}^{\mathrm{new}}(19, [\chi])\)\(^{\oplus 2}\)