Space of modular forms of level 91 and weight 2

• Label: 91.2
• Level: 91
• Weight: 2
• Dimension: 261
• Nonzero newspaces: 15
• Newform subspaces: 26
• Sturm bound: 1344
• Trace bound: 5

Defining parameters

Level:	\( N \)	=	\( 91 = 7 \cdot 13 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 15 \)
Newform subspaces:			\( 26 \)
Sturm bound:			\(1344\)
Trace bound:			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(91))\).

	Total	New	Old
Modular forms	408	373	35
Cusp forms	265	261	4
Eisenstein series	143	112	31

Trace form

261 * q - 27 * q^2 - 28 * q^3 - 31 * q^4 - 30 * q^5 - 36 * q^6 - 29 * q^7 - 57 * q^8 - 21 * q^9 - 12 * q^10 - 24 * q^11 - 13 * q^13 - 51 * q^14 - 60 * q^15 - 15 * q^16 - 24 * q^17 + 3 * q^18 - 4 * q^19 - 8 * q^21 - 36 * q^22 - 24 * q^23 + 36 * q^24 - 13 * q^25 - 3 * q^26 - 16 * q^27 + 13 * q^28 - 36 * q^29 + 48 * q^30 - 4 * q^31 + 45 * q^32 + 12 * q^33 + 18 * q^34 + 6 * q^35 + 17 * q^36 - 28 * q^37 - 12 * q^39 + 6 * q^40 + 24 * q^41 + 48 * q^42 - 12 * q^43 + 48 * q^44 + 48 * q^45 + 72 * q^46 + 12 * q^47 + 68 * q^48 + 27 * q^49 + 33 * q^50 + 60 * q^51 + 51 * q^52 - 6 * q^53 + 60 * q^54 + 36 * q^55 + 69 * q^56 + 8 * q^57 + 36 * q^58 + 132 * q^60 + 28 * q^61 + 48 * q^62 + 55 * q^63 + 59 * q^64 + 60 * q^65 + 72 * q^66 + 20 * q^67 + 96 * q^68 + 36 * q^69 + 90 * q^70 - 12 * q^71 - 63 * q^72 + 26 * q^73 + 36 * q^74 + 12 * q^75 - 76 * q^76 - 60 * q^77 - 12 * q^78 - 152 * q^79 - 108 * q^80 - 93 * q^81 - 216 * q^82 - 60 * q^83 - 176 * q^84 - 198 * q^85 - 48 * q^86 - 120 * q^87 - 288 * q^88 - 66 * q^89 - 210 * q^90 - 101 * q^91 - 288 * q^92 - 40 * q^93 - 240 * q^94 - 72 * q^95 - 216 * q^96 - 178 * q^97 - 75 * q^98 - 132 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(91))\)

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
91.2.a	\(\chi_{91}(1, \cdot)\)	91.2.a.a	1	1
		91.2.a.b	1
		91.2.a.c	2
		91.2.a.d	3
91.2.c	\(\chi_{91}(64, \cdot)\)	91.2.c.a	6	1
91.2.e	\(\chi_{91}(53, \cdot)\)	91.2.e.a	2	2
		91.2.e.b	4
		91.2.e.c	10
91.2.f	\(\chi_{91}(22, \cdot)\)	91.2.f.a	4	2
		91.2.f.b	4
		91.2.f.c	8
91.2.g	\(\chi_{91}(9, \cdot)\)	91.2.g.a	2	2
		91.2.g.b	12
91.2.h	\(\chi_{91}(16, \cdot)\)	91.2.h.a	2	2
		91.2.h.b	12
91.2.i	\(\chi_{91}(34, \cdot)\)	91.2.i.a	12	2
91.2.k	\(\chi_{91}(4, \cdot)\)	91.2.k.a	2	2
		91.2.k.b	12
91.2.q	\(\chi_{91}(36, \cdot)\)	91.2.q.a	12	2
91.2.r	\(\chi_{91}(25, \cdot)\)	91.2.r.a	16	2
91.2.u	\(\chi_{91}(30, \cdot)\)	91.2.u.a	2	2
		91.2.u.b	12
91.2.w	\(\chi_{91}(19, \cdot)\)	91.2.w.a	28	4
91.2.ba	\(\chi_{91}(45, \cdot)\)	91.2.ba.a	28	4
91.2.bb	\(\chi_{91}(5, \cdot)\)	91.2.bb.a	32	4
91.2.bc	\(\chi_{91}(6, \cdot)\)	91.2.bc.a	32	4

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(91))\) into lower level spaces

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