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

• Label: 91.2.h
• Level: $91$
• Weight: $2$
• Character orbit: 91.h
• Rep. character: $\chi_{91}(16,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $14$
• Newform subspaces: $2$
• Sturm bound: $18$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 91 = 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	91.h (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 91 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 2 \)
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	22	22	0
Cusp forms	14	14	0
Eisenstein series	8	8	0

Trace form

14 * q - 2 * q^2 + 4 * q^3 + 6 * q^4 - 2 * q^5 - 6 * q^6 + q^7 - 12 * q^8 - 3 * q^9 + q^10 + 7 * q^11 + 2 * q^12 - 4 * q^13 + 2 * q^14 + 7 * q^15 - 18 * q^16 - 14 * q^17 - 3 * q^18 + 2 * q^20 + 6 * q^21 - 2 * q^22 + 2 * q^23 - 20 * q^24 + 3 * q^25 - 18 * q^26 - 26 * q^27 - 5 * q^28 - 4 * q^29 + 4 * q^30 + 13 * q^31 - 6 * q^32 + 7 * q^33 + 28 * q^34 + 5 * q^35 - 15 * q^36 + 30 * q^37 - 16 * q^38 - 5 * q^39 + 4 * q^40 - 11 * q^41 + 65 * q^42 - 4 * q^43 + 18 * q^44 + 50 * q^45 - 32 * q^46 - 2 * q^47 + 18 * q^48 - q^49 + 2 * q^50 - 26 * q^51 + 43 * q^52 - 5 * q^53 + 18 * q^54 + 18 * q^55 - 3 * q^56 + 48 * q^57 - 15 * q^58 - 34 * q^59 + 11 * q^60 + 8 * q^61 + 2 * q^62 - 34 * q^63 - 16 * q^64 - 20 * q^65 + 9 * q^66 - 8 * q^67 - 54 * q^68 + 23 * q^69 - 54 * q^70 - 7 * q^71 + 43 * q^72 - 17 * q^73 + 10 * q^74 - 18 * q^75 - 10 * q^76 + 26 * q^77 + 31 * q^78 + 10 * q^79 - 4 * q^80 - 15 * q^81 - 2 * q^82 - 54 * q^83 - 61 * q^84 + 5 * q^85 - 74 * q^87 - 9 * q^88 + 4 * q^89 + 20 * q^90 - 39 * q^91 + 54 * q^92 - 4 * q^93 + 44 * q^94 + 6 * q^95 + 34 * q^96 - 30 * q^97 + 22 * q^98 - 56 * 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.h.a	$91$	$2$	91.h	91.h	$3$	$2$	$1$	$0.727$	\(\Q(\sqrt{-3}) \)	None		✓			91.2.g.a	$2$	$0$	\(2\)	\(3\)	\(-3\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+q^{2}+3\zeta_{6}q^{3}-q^{4}-3\zeta_{6}q^{5}+3\zeta_{6}q^{6}+\cdots\)
91.2.h.b	$91$	$2$	91.h	91.h	$3$	$12$	$6$	$0.727$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		✓	✓		91.2.g.b	$2$	$0$	\(-4\)	\(1\)	\(1\)	\(-3\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(\beta _{3}+\beta _{5}-\beta _{11})q^{2}+\beta _{11}q^{3}+(1+\cdots)q^{4}+\cdots\)