Space of modular forms of level 91 and weight 8

• Label: 91.8
• Level: 91
• Weight: 8
• Dimension: 2172
• Nonzero newspaces: 15
• Newform subspaces: 21
• Sturm bound: 5376
• Trace bound: 3

Defining parameters

Level:	\( N \)	=	\( 91 = 7 \cdot 13 \)
Weight:	\( k \)	=	\( 8 \)
Nonzero newspaces:			\( 15 \)
Newform subspaces:			\( 21 \)
Sturm bound:			\(5376\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(91))\).

	Total	New	Old
Modular forms	2424	2284	140
Cusp forms	2280	2172	108
Eisenstein series	144	112	32

Trace form

2172 * q - 18 * q^2 - 72 * q^3 + 494 * q^4 - 12 * q^5 - 2604 * q^6 + 826 * q^7 - 5610 * q^8 + 12954 * q^9 + 38076 * q^10 - 10428 * q^11 - 109872 * q^12 - 24982 * q^13 - 82158 * q^14 + 93084 * q^15 + 341958 * q^16 + 275178 * q^17 - 408546 * q^18 - 399952 * q^19 - 538056 * q^20 + 58404 * q^21 + 891552 * q^22 + 429240 * q^23 - 60876 * q^24 - 345556 * q^25 - 1113888 * q^26 - 1364616 * q^27 - 494306 * q^28 - 414702 * q^29 + 3270060 * q^30 + 1801508 * q^31 + 1306422 * q^32 - 559356 * q^33 - 1620612 * q^34 - 196464 * q^35 - 88422 * q^36 + 25610 * q^37 - 3866508 * q^38 + 1530312 * q^39 - 6152592 * q^40 - 6437118 * q^41 - 1000380 * q^42 + 4102296 * q^43 + 9310476 * q^44 + 9316710 * q^45 + 14410644 * q^46 + 7197780 * q^47 + 1973964 * q^48 - 589218 * q^49 - 19043058 * q^50 - 15450756 * q^51 - 17807976 * q^52 - 18278268 * q^53 - 12351720 * q^54 + 18037884 * q^55 + 23261658 * q^56 + 18879624 * q^57 + 20094036 * q^58 + 11441484 * q^59 + 19186260 * q^60 + 5163466 * q^61 + 14435544 * q^62 - 10612782 * q^63 - 79301506 * q^64 - 52052502 * q^65 - 38322516 * q^66 + 15906536 * q^67 + 42380880 * q^68 + 13910244 * q^69 + 11581620 * q^70 + 38308812 * q^71 + 88984710 * q^72 + 3763040 * q^73 - 9032112 * q^74 - 6629760 * q^75 + 13095452 * q^76 + 38664768 * q^77 - 108878688 * q^78 - 11427392 * q^79 - 80690580 * q^80 - 50523330 * q^81 - 130393164 * q^82 - 53260080 * q^83 - 136390836 * q^84 + 52040466 * q^85 + 165261804 * q^86 + 90581664 * q^87 + 122261652 * q^88 - 11365644 * q^89 + 30678432 * q^90 + 71169658 * q^91 + 53056440 * q^92 + 127405968 * q^93 + 99927660 * q^94 + 129800664 * q^95 + 102506592 * q^96 - 71943676 * q^97 - 220068606 * q^98 - 278491440 * q^99

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(91))\)

We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list available newforms together with their dimension.

Label	\(\chi\)	Newforms	Dimension	\(\chi\) degree
91.8.a	\(\chi_{91}(1, \cdot)\)	91.8.a.a	1	1
		91.8.a.b	9
		91.8.a.c	10
		91.8.a.d	10
		91.8.a.e	12
91.8.c	\(\chi_{91}(64, \cdot)\)	91.8.c.a	50	1
91.8.e	\(\chi_{91}(53, \cdot)\)	91.8.e.a	54	2
		91.8.e.b	58
91.8.f	\(\chi_{91}(22, \cdot)\)	91.8.f.a	48	2
		91.8.f.b	48
91.8.g	\(\chi_{91}(9, \cdot)\)	91.8.g.a	126	2
91.8.h	\(\chi_{91}(16, \cdot)\)	91.8.h.a	126	2
91.8.i	\(\chi_{91}(34, \cdot)\)	91.8.i.a	124	2
91.8.k	\(\chi_{91}(4, \cdot)\)	91.8.k.a	126	2
91.8.q	\(\chi_{91}(36, \cdot)\)	91.8.q.a	100	2
91.8.r	\(\chi_{91}(25, \cdot)\)	91.8.r.a	128	2
91.8.u	\(\chi_{91}(30, \cdot)\)	91.8.u.a	126	2
91.8.w	\(\chi_{91}(19, \cdot)\)	91.8.w.a	252	4
91.8.ba	\(\chi_{91}(45, \cdot)\)	91.8.ba.a	252	4
91.8.bb	\(\chi_{91}(5, \cdot)\)	91.8.bb.a	256	4
91.8.bc	\(\chi_{91}(6, \cdot)\)	91.8.bc.a	256	4

Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_1(91))\) into lower level spaces

\( S_{8}^{\mathrm{old}}(\Gamma_1(91)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 2}\)