Space of modular forms of level 91, weight 2, and Character 91.c

• Label: 91.2.c
• Level: $91$
• Weight: $2$
• Character orbit: 91.c
• Rep. character: $\chi_{91}(64,\cdot)$
• Character field: $\Q$
• Dimension: $6$
• Newform subspaces: $1$
• Sturm bound: $18$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 91 = 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	91.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 13 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(18\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(91, [\chi])\).

	Total	New	Old
Modular forms	10	6	4
Cusp forms	6	6	0
Eisenstein series	4	0	4

Trace form

6 * q - 4 * q^4 - 2 * q^9 - 20 * q^12 + 8 * q^13 - 4 * q^14 + 8 * q^16 - 8 * q^17 + 24 * q^22 + 6 * q^23 + 8 * q^25 + 12 * q^26 - 12 * q^27 - 14 * q^29 + 16 * q^30 - 6 * q^35 + 4 * q^36 - 4 * q^38 - 8 * q^39 - 20 * q^40 - 4 * q^42 - 26 * q^43 + 8 * q^48 - 6 * q^49 + 8 * q^51 - 20 * q^52 + 2 * q^53 + 12 * q^55 + 12 * q^56 + 28 * q^61 + 16 * q^62 - 8 * q^64 - 6 * q^65 + 28 * q^66 + 20 * q^68 - 4 * q^69 - 24 * q^74 + 44 * q^75 + 16 * q^77 + 16 * q^78 + 26 * q^79 - 26 * q^81 - 56 * q^82 - 40 * q^87 - 40 * q^88 - 12 * q^90 - 2 * q^91 - 36 * q^92 + 20 * q^94 + 58 * q^95

Decomposition of \(S_{2}^{\mathrm{new}}(91, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
91.2.c.a	$91$	$2$	91.c	13.b	$2$	$6$	$6$	$0.727$	6.0.350464.1	None		✓	✓	✓	91.2.c.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta _{3}+\beta _{4})q^{2}+\beta _{1}q^{3}+(-1-\beta _{1}+\cdots)q^{4}+\cdots\)