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

• Label: 91.2.bb
• Level: $91$
• Weight: $2$
• Character orbit: 91.bb
• Rep. character: $\chi_{91}(5,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $32$
• Newform subspaces: $1$
• Sturm bound: $18$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 91 = 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	91.bb (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 91 \)
Character field:			\(\Q(\zeta_{12})\)
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	48	48	0
Cusp forms	32	32	0
Eisenstein series	16	16	0

Trace form

32 * q - 2 * q^2 - 12 * q^3 - 6 * q^5 - 6 * q^7 - 16 * q^8 + 8 * q^9 - 10 * q^11 + 28 * q^14 - 44 * q^15 + 12 * q^16 - 4 * q^18 + 12 * q^19 - 26 * q^21 - 8 * q^22 - 12 * q^24 + 24 * q^26 - 6 * q^28 + 16 * q^29 + 24 * q^31 + 4 * q^32 + 48 * q^33 + 28 * q^35 - 8 * q^37 - 6 * q^39 - 132 * q^40 - 16 * q^42 - 42 * q^44 - 24 * q^45 + 12 * q^46 + 30 * q^47 + 88 * q^50 + 36 * q^52 - 12 * q^53 + 78 * q^54 + 40 * q^57 + 26 * q^58 - 54 * q^59 + 16 * q^60 - 48 * q^61 + 24 * q^63 - 8 * q^65 + 12 * q^66 + 16 * q^67 - 48 * q^68 + 50 * q^70 - 36 * q^71 + 22 * q^72 + 66 * q^73 + 12 * q^74 - 176 * q^78 - 32 * q^79 + 138 * q^80 + 16 * q^81 - 58 * q^84 - 84 * q^85 + 42 * q^86 - 24 * q^87 - 60 * q^89 + 48 * q^92 + 6 * q^93 - 72 * q^94 - 42 * q^96 - 86 * q^98 - 24 * q^99

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.bb.a	$91$	$2$	91.bb	91.ab	$12$	$32$	$8$	$0.727$		None		✓	✓	✓	91.2.bb.a	$4$	$0$	\(-2\)	\(-12\)	\(-6\)	\(-6\)		$\mathrm{SU}(2)[C_{12}]$