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

• Label: 91.2.e
• Level: $91$
• Weight: $2$
• Character orbit: 91.e
• Rep. character: $\chi_{91}(53,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $16$
• Newform subspaces: $3$
• Sturm bound: $18$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 91 = 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	91.e (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 7 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(18\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

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

Trace form

16 * q - 2 * q^2 - 10 * q^4 - 2 * q^5 - 6 * q^7 - 4 * q^9 + 10 * q^10 - 2 * q^11 + 10 * q^12 + 4 * q^13 - 10 * q^14 - 20 * q^15 - 22 * q^16 + 4 * q^17 - 8 * q^19 + 32 * q^20 + 2 * q^21 + 28 * q^22 + 8 * q^23 - 20 * q^24 - 4 * q^25 - 6 * q^26 + 30 * q^28 - 16 * q^29 - 2 * q^30 - 4 * q^31 - 12 * q^32 - 8 * q^33 - 32 * q^34 - 4 * q^35 + 32 * q^36 - 8 * q^37 + 26 * q^38 - 8 * q^40 + 28 * q^41 + 32 * q^42 - 24 * q^43 + 6 * q^44 + 32 * q^45 - 20 * q^46 - 2 * q^47 - 76 * q^48 - 20 * q^49 + 8 * q^50 + 28 * q^51 - 6 * q^52 - 8 * q^53 - 18 * q^54 - 32 * q^57 + 42 * q^58 - 10 * q^59 + 44 * q^60 + 12 * q^61 - 76 * q^62 + 40 * q^63 + 40 * q^64 - 2 * q^65 - 6 * q^66 - 4 * q^67 + 18 * q^68 + 56 * q^69 + 54 * q^70 + 20 * q^71 + 22 * q^72 - 22 * q^73 + 34 * q^74 + 20 * q^75 + 48 * q^76 - 52 * q^77 - 20 * q^78 - 4 * q^79 - 70 * q^80 + 32 * q^81 - 44 * q^82 + 12 * q^83 - 98 * q^84 - 4 * q^85 - 54 * q^86 + 28 * q^87 - 24 * q^88 + 4 * q^89 - 88 * q^90 + 8 * q^91 - 12 * q^92 - 18 * q^93 - 46 * q^94 + 12 * q^95 + 22 * q^96 - 68 * q^97 + 34 * q^98 + 16 * 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.e.a	$91$	$2$	91.e	7.c	$3$	$2$	$1$	$0.727$	\(\Q(\sqrt{-3}) \)	None		✓			91.2.e.a	$2$	$0$	\(-1\)	\(0\)	\(0\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{4}+(2-3\zeta_{6})q^{7}+\cdots\)
91.2.e.b	$91$	$2$	91.e	7.c	$3$	$4$	$2$	$0.727$	\(\Q(\sqrt{-3}, \sqrt{5})\)	None		✓			91.2.e.b	$2$	$0$	\(3\)	\(0\)	\(0\)	\(-8\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1+\beta _{1}+\beta _{3})q^{2}+(-2\beta _{1}-2\beta _{2}+\cdots)q^{3}+\cdots\)
91.2.e.c	$91$	$2$	91.e	7.c	$3$	$10$	$5$	$0.727$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None		✓	✓		91.2.e.c	$2$	$0$	\(-4\)	\(0\)	\(-2\)	\(1\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(\beta _{1}-\beta _{7})q^{2}+(-\beta _{4}+\beta _{9})q^{3}+(-2+\cdots)q^{4}+\cdots\)