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

• Label: 91.2.u
• Level: $91$
• Weight: $2$
• Character orbit: 91.u
• Rep. character: $\chi_{91}(30,\cdot)$
• Character field: $\Q(\zeta_{6})$
• 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.u (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 91 \)
Character field:			\(\Q(\zeta_{6})\)
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 - 3 * q^2 + 4 * q^3 + 5 * q^4 - 6 * q^6 - 2 * q^7 - 2 * q^9 - 18 * q^10 - 2 * q^12 - 4 * q^13 + 10 * q^14 - 9 * q^15 - 3 * q^16 + 11 * q^17 + 3 * q^18 - 6 * q^20 - 16 * q^21 - 6 * q^22 + 3 * q^23 - 7 * q^25 - 12 * q^26 + 22 * q^27 + 26 * q^28 - 4 * q^29 - 28 * q^30 - 15 * q^31 + 9 * q^32 + 27 * q^35 - 15 * q^36 + 15 * q^37 + 16 * q^38 + q^39 - 4 * q^40 - 15 * q^41 - 14 * q^42 + 24 * q^44 - 3 * q^45 - 30 * q^46 + 14 * q^48 + 20 * q^49 + 24 * q^50 + 10 * q^51 + 52 * q^52 + q^53 - 9 * q^54 - 24 * q^55 + 3 * q^56 + 21 * q^59 + 33 * q^60 + 4 * q^61 + 38 * q^62 - 44 * q^63 + 6 * q^65 - 43 * q^66 - 5 * q^68 + 7 * q^69 - 18 * q^70 + 33 * q^71 - 57 * q^73 - 33 * q^74 + 3 * q^75 - 42 * q^76 - 10 * q^77 + 47 * q^78 - 30 * q^79 - 26 * q^81 + 8 * q^82 + 4 * q^84 - 3 * q^85 + 90 * q^86 + 13 * q^87 + 10 * q^88 + 36 * q^89 - 12 * q^90 - 17 * q^91 - 66 * q^92 - 84 * q^93 + 28 * q^94 + 5 * q^95 - 12 * q^96 - 12 * q^97 - 45 * q^98

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.u.a	$91$	$2$	91.u	91.u	$6$	$2$	$1$	$0.727$	\(\Q(\sqrt{-3}) \)	None		✓			91.2.k.a	$2$	$1$	\(-3\)	\(-2\)	\(-3\)	\(-5\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-2+\zeta_{6})q^{2}-q^{3}+(1-\zeta_{6})q^{4}+\cdots\)
91.2.u.b	$91$	$2$	91.u	91.u	$6$	$12$	$6$	$0.727$	12.0.\(\cdots\).1	None		✓	✓		91.2.k.b	$2$	$0$	\(0\)	\(6\)	\(3\)	\(3\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{10}q^{2}+(1-\beta _{1}+\beta _{3}+\beta _{8})q^{3}+\cdots\)