Space of modular forms of level 95, weight 2, and Character 95.i

• Label: 95.2.i
• Level: $95$
• Weight: $2$
• Character orbit: 95.i
• Rep. character: $\chi_{95}(49,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $16$
• Newform subspaces: $2$
• Sturm bound: $20$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 95 = 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	95.i (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 95 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(20\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(95, [\chi])\).

	Total	New	Old
Modular forms	24	24	0
Cusp forms	16	16	0
Eisenstein series	8	8	0

Trace form

\( 16 q + 6 q^{4} - 12 q^{6} + 2 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(95, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
95.2.i.a	$95$	$2$	95.i	95.i	$6$	$4$	$2$	$0.759$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+\zeta_{12}q^{2}+2\zeta_{12}^{2}q^{4}+(1-\zeta_{12}-\zeta_{12}^{2}+\cdots)q^{5}+\cdots\)
95.2.i.b	$95$	$2$	95.i	95.i	$6$	$12$	$6$	$0.759$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{5}q^{2}+(\beta _{4}-\beta _{5})q^{3}+(-\beta _{2}+\beta _{3}+\cdots)q^{4}+\cdots\)