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

• Label: 91.4.ba
• Level: $91$
• Weight: $4$
• Character orbit: 91.ba
• Rep. character: $\chi_{91}(45,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $104$
• Newform subspaces: $1$
• Sturm bound: $37$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 91 = 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	91.ba (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 91 \)
Character field:			\(\Q(\zeta_{12})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(37\)
Trace bound:			\(0\)

Dimensions

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

	Total	New	Old
Modular forms	120	120	0
Cusp forms	104	104	0
Eisenstein series	16	16	0

Trace form

104 * q - 2 * q^2 - 6 * q^3 - 6 * q^5 - 48 * q^6 - 56 * q^7 + 8 * q^8 + 398 * q^9 - 6 * q^10 - 50 * q^11 - 192 * q^12 + 160 * q^14 - 2 * q^15 - 1284 * q^16 - 12 * q^17 + 2 * q^18 + 558 * q^19 + 432 * q^20 + 66 * q^21 - 60 * q^22 + 918 * q^24 - 756 * q^26 + 706 * q^28 + 80 * q^29 - 822 * q^30 + 174 * q^31 - 78 * q^32 + 1698 * q^33 - 48 * q^34 + 506 * q^35 - 1386 * q^36 - 618 * q^37 - 802 * q^39 - 2352 * q^40 + 1044 * q^41 - 190 * q^42 + 156 * q^43 - 226 * q^44 - 6 * q^45 - 1732 * q^46 - 6 * q^47 + 60 * q^48 + 1974 * q^49 + 186 * q^50 - 684 * q^51 + 1962 * q^52 - 136 * q^53 - 318 * q^54 - 1188 * q^55 + 666 * q^56 + 814 * q^57 + 2318 * q^58 - 2070 * q^59 + 6554 * q^60 - 906 * q^61 - 2088 * q^62 - 5536 * q^63 - 486 * q^65 + 3450 * q^66 + 446 * q^67 + 1848 * q^69 - 2124 * q^70 + 2340 * q^71 + 2542 * q^72 - 3174 * q^73 - 5932 * q^74 - 4212 * q^75 + 816 * q^76 + 6338 * q^78 - 692 * q^79 - 10890 * q^80 + 1096 * q^81 + 858 * q^82 - 1980 * q^83 - 1964 * q^84 + 1822 * q^85 + 810 * q^86 + 8418 * q^88 + 6186 * q^89 + 8424 * q^90 - 5824 * q^91 - 1484 * q^92 - 2898 * q^93 + 14454 * q^94 + 6090 * q^96 + 180 * q^97 + 352 * q^98 - 3704 * 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.ba.a	$91$	$4$	91.ba	91.aa	$12$	$104$	$26$	$5.369$		None		✓	✓	✓	91.4.w.a	$2$	$0$	\(-2\)	\(-6\)	\(-6\)	\(-56\)		$\mathrm{SU}(2)[C_{12}]$