Space of modular forms of level 91 and weight 4

• Label: 91.4
• Level: 91
• Weight: 4
• Dimension: 900
• Nonzero newspaces: 15
• Newform subspaces: 21
• Sturm bound: 2688
• Trace bound: 3

Defining parameters

Level:	\( N \)	=	\( 91 = 7 \cdot 13 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 15 \)
Newform subspaces:			\( 21 \)
Sturm bound:			\(2688\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(91))\).

	Total	New	Old
Modular forms	1080	1012	68
Cusp forms	936	900	36
Eisenstein series	144	112	32

Trace form

900 * q - 18 * q^2 - 6 * q^3 - 18 * q^4 - 42 * q^5 - 84 * q^6 - 36 * q^7 + 150 * q^8 + 66 * q^9 - 144 * q^10 - 138 * q^11 - 576 * q^12 - 312 * q^13 - 222 * q^14 - 336 * q^15 - 138 * q^16 + 204 * q^17 + 1674 * q^18 + 1182 * q^19 + 1344 * q^20 + 432 * q^21 - 816 * q^22 - 894 * q^23 - 2412 * q^24 - 1176 * q^25 - 1524 * q^26 - 1764 * q^27 - 354 * q^28 + 786 * q^29 + 1260 * q^30 + 870 * q^31 + 1926 * q^32 + 1074 * q^33 + 1644 * q^34 + 96 * q^35 + 282 * q^36 + 540 * q^37 - 2772 * q^38 - 210 * q^39 - 432 * q^40 - 846 * q^41 - 156 * q^42 + 1020 * q^43 - 564 * q^44 + 450 * q^45 - 2220 * q^46 + 114 * q^47 + 1356 * q^48 - 1296 * q^49 + 1002 * q^50 + 678 * q^51 + 888 * q^52 - 1014 * q^53 - 1416 * q^54 - 2436 * q^55 + 522 * q^56 - 4200 * q^57 - 2064 * q^58 - 2838 * q^59 - 3180 * q^60 + 2388 * q^61 + 4056 * q^62 + 2520 * q^63 + 7854 * q^64 + 7548 * q^65 + 8124 * q^66 + 2142 * q^67 - 1752 * q^68 + 564 * q^69 - 1260 * q^70 - 684 * q^71 - 14058 * q^72 - 7758 * q^73 - 17892 * q^74 - 14400 * q^75 - 20148 * q^76 - 10806 * q^77 - 15120 * q^78 - 5262 * q^79 - 14100 * q^80 - 3468 * q^81 - 192 * q^82 - 4980 * q^83 + 14412 * q^84 + 9726 * q^85 + 15420 * q^86 + 24996 * q^87 + 37620 * q^88 + 17970 * q^89 + 44232 * q^90 + 17322 * q^91 + 32952 * q^92 + 23562 * q^93 + 34236 * q^94 + 18174 * q^95 + 24384 * q^96 + 9660 * q^97 + 3474 * q^98 - 6492 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(91))\)

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
91.4.a	\(\chi_{91}(1, \cdot)\)	91.4.a.a	3	1
		91.4.a.b	4
		91.4.a.c	5
		91.4.a.d	6
91.4.c	\(\chi_{91}(64, \cdot)\)	91.4.c.a	22	1
91.4.e	\(\chi_{91}(53, \cdot)\)	91.4.e.a	22	2
		91.4.e.b	26
91.4.f	\(\chi_{91}(22, \cdot)\)	91.4.f.a	2	2
		91.4.f.b	18
		91.4.f.c	20
91.4.g	\(\chi_{91}(9, \cdot)\)	91.4.g.a	52	2
91.4.h	\(\chi_{91}(16, \cdot)\)	91.4.h.a	52	2
91.4.i	\(\chi_{91}(34, \cdot)\)	91.4.i.a	52	2
91.4.k	\(\chi_{91}(4, \cdot)\)	91.4.k.a	52	2
91.4.q	\(\chi_{91}(36, \cdot)\)	91.4.q.a	44	2
91.4.r	\(\chi_{91}(25, \cdot)\)	91.4.r.a	52	2
91.4.u	\(\chi_{91}(30, \cdot)\)	91.4.u.a	52	2
91.4.w	\(\chi_{91}(19, \cdot)\)	91.4.w.a	104	4
91.4.ba	\(\chi_{91}(45, \cdot)\)	91.4.ba.a	104	4
91.4.bb	\(\chi_{91}(5, \cdot)\)	91.4.bb.a	104	4
91.4.bc	\(\chi_{91}(6, \cdot)\)	91.4.bc.a	104	4

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(91))\) into lower level spaces

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