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

• Label: 91.2.f
• Level: $91$
• Weight: $2$
• Character orbit: 91.f
• Rep. character: $\chi_{91}(22,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $16$
• Newform subspaces: $3$
• Sturm bound: $18$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 91 = 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	91.f (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 13 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(18\)
Trace bound:			\(2\)
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 - 8 * q^5 + 6 * q^6 - 10 * q^9 - 2 * q^10 - 2 * q^11 + 4 * q^12 - 2 * q^13 + 8 * q^14 - 2 * q^15 - 22 * q^16 + 10 * q^17 + 36 * q^18 - 8 * q^19 - 10 * q^20 - 4 * q^21 - 2 * q^22 - 4 * q^23 + 28 * q^24 - 4 * q^25 - 12 * q^26 - 36 * q^27 + 2 * q^29 + 16 * q^30 - 4 * q^31 + 18 * q^32 + 22 * q^33 - 8 * q^34 - 10 * q^35 + 8 * q^36 + 16 * q^37 - 52 * q^38 + 12 * q^39 - 8 * q^40 + 16 * q^41 - 4 * q^42 - 18 * q^43 + 24 * q^44 - 10 * q^45 - 20 * q^46 + 28 * q^47 + 26 * q^48 - 8 * q^49 - 46 * q^50 - 20 * q^51 + 78 * q^52 + 16 * q^53 + 6 * q^55 - 12 * q^56 - 20 * q^57 - 6 * q^58 - 10 * q^59 - 76 * q^60 + 24 * q^61 - 4 * q^62 + 4 * q^63 + 40 * q^64 + 10 * q^65 + 12 * q^66 + 20 * q^67 + 66 * q^68 - 4 * q^69 + 48 * q^70 + 8 * q^71 - 26 * q^72 - 16 * q^73 - 32 * q^74 + 14 * q^75 - 18 * q^76 + 8 * q^77 - 74 * q^78 + 8 * q^79 - 34 * q^80 - 28 * q^81 + 28 * q^82 + 12 * q^83 + 22 * q^84 + 2 * q^85 + 48 * q^86 + 10 * q^87 - 30 * q^88 - 32 * q^89 + 116 * q^90 + 2 * q^91 - 24 * q^92 - 18 * q^93 - 52 * q^94 - 18 * q^95 - 212 * q^96 - 26 * q^97 - 2 * q^98 + 76 * 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.f.a	$91$	$2$	91.f	13.c	$3$	$4$	$2$	$0.727$	\(\Q(\sqrt{-3}, \sqrt{5})\)	None		✓			91.2.f.a	$2$	$0$	\(-3\)	\(3\)	\(6\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1-\beta _{1}-\beta _{3})q^{2}+(1+\beta _{1}+\beta _{3})q^{3}+\cdots\)
91.2.f.b	$91$	$2$	91.f	13.c	$3$	$4$	$2$	$0.727$	\(\Q(\zeta_{12})\)	None		✓			91.2.f.b	$2$	$0$	\(0\)	\(-2\)	\(0\)	\(-2\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta_{2} q^{2}+(-\beta_{2}-\beta_1)q^{3}+(\beta_1-1)q^{4}+\cdots\)
91.2.f.c	$91$	$2$	91.f	13.c	$3$	$8$	$4$	$0.727$	8.0.\(\cdots\).1	None		✓	✓		91.2.f.c	$2$	$0$	\(1\)	\(-1\)	\(-14\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{1}q^{2}-\beta _{5}q^{3}+(-1+\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)