Space of modular forms of level 91, weight 4, and Character 91.e

• Label: 91.4.e
• Level: $91$
• Weight: $4$
• Character orbit: 91.e
• Rep. character: $\chi_{91}(53,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $48$
• Newform subspaces: $2$
• Sturm bound: $37$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 91 = 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	91.e (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 7 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(37\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(91, [\chi])\).

	Total	New	Old
Modular forms	60	48	12
Cusp forms	52	48	4
Eisenstein series	8	0	8

Trace form

48 * q + 2 * q^2 - 106 * q^4 + 12 * q^5 - 32 * q^6 + 8 * q^7 + 120 * q^8 - 188 * q^9 + 18 * q^10 + 8 * q^11 - 110 * q^12 - 52 * q^13 + 180 * q^14 - 314 * q^16 - 178 * q^17 + 160 * q^18 + 152 * q^19 + 472 * q^20 + 284 * q^21 - 384 * q^22 - 260 * q^23 - 308 * q^24 - 636 * q^25 + 156 * q^26 + 828 * q^27 - 910 * q^28 - 500 * q^29 + 392 * q^30 + 560 * q^31 + 292 * q^32 + 108 * q^33 + 224 * q^34 + 544 * q^35 + 2216 * q^36 - 376 * q^37 + 156 * q^38 - 48 * q^40 - 2488 * q^41 - 2056 * q^42 + 1912 * q^43 - 130 * q^44 + 832 * q^45 - 1168 * q^46 + 1204 * q^47 + 1756 * q^48 - 278 * q^49 - 664 * q^50 + 246 * q^51 + 312 * q^52 - 566 * q^53 - 602 * q^54 + 2464 * q^55 - 2618 * q^56 + 432 * q^57 - 1458 * q^58 + 1572 * q^59 - 2536 * q^60 + 310 * q^61 + 288 * q^62 + 1776 * q^63 + 3520 * q^64 - 208 * q^65 + 678 * q^66 + 2000 * q^67 - 2212 * q^68 + 2504 * q^69 - 438 * q^70 - 2064 * q^71 - 3002 * q^72 - 1888 * q^73 - 2066 * q^74 - 2308 * q^75 - 2712 * q^76 + 1148 * q^77 - 1820 * q^78 + 436 * q^79 + 794 * q^80 - 4112 * q^81 - 2156 * q^82 - 4880 * q^83 + 8414 * q^84 - 1992 * q^85 + 226 * q^86 + 1404 * q^87 + 1590 * q^88 + 1252 * q^89 + 7732 * q^90 + 624 * q^91 - 580 * q^92 + 1560 * q^93 + 820 * q^94 + 5108 * q^95 - 3394 * q^96 + 1304 * q^97 + 5014 * q^98 - 5752 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(91, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
91.4.e.a	$91$	$4$	91.e	7.c	$3$	$22$	$11$	$5.369$		None		✓			91.4.e.a	$2$	$0$	\(7\)	\(0\)	\(-2\)	\(28\)		$\mathrm{SU}(2)[C_{3}]$
91.4.e.b	$91$	$4$	91.e	7.c	$3$	$26$	$13$	$5.369$		None		✓	✓		91.4.e.b	$2$	$0$	\(-5\)	\(0\)	\(14\)	\(-20\)		$\mathrm{SU}(2)[C_{3}]$

Decomposition of \(S_{4}^{\mathrm{old}}(91, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(91, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 2}\)