Space of modular forms of level 952 and weight 2

• Label: 952.2
• Level: 952
• Weight: 2
• Dimension: 14500
• Nonzero newspaces: 30
• Newform subspaces: 74
• Sturm bound: 110592
• Trace bound: 17

Defining parameters

Level:	\( N \)	=	\( 952 = 2^{3} \cdot 7 \cdot 17 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 30 \)
Newform subspaces:			\( 74 \)
Sturm bound:			\(110592\)
Trace bound:			\(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(952))\).

	Total	New	Old
Modular forms	28800	15100	13700
Cusp forms	26497	14500	11997
Eisenstein series	2303	600	1703

Trace form

14500 * q - 52 * q^2 - 52 * q^3 - 52 * q^4 - 52 * q^6 - 68 * q^7 - 136 * q^8 - 92 * q^9 - 52 * q^10 - 40 * q^11 - 52 * q^12 + 12 * q^13 - 68 * q^14 - 112 * q^15 - 52 * q^16 - 110 * q^17 - 152 * q^18 - 52 * q^19 - 88 * q^20 - 196 * q^22 - 88 * q^23 - 124 * q^24 - 100 * q^25 - 112 * q^26 - 64 * q^27 - 164 * q^28 + 40 * q^29 - 148 * q^30 - 24 * q^31 - 112 * q^32 - 52 * q^33 - 94 * q^34 - 116 * q^35 - 196 * q^36 + 76 * q^37 - 88 * q^38 - 112 * q^40 - 16 * q^41 + 4 * q^42 - 88 * q^43 - 4 * q^44 + 52 * q^45 + 8 * q^46 - 88 * q^47 - 28 * q^48 - 148 * q^49 - 52 * q^50 - 100 * q^51 - 8 * q^52 - 36 * q^53 - 68 * q^54 - 208 * q^55 - 64 * q^56 - 368 * q^57 - 216 * q^58 - 220 * q^59 - 336 * q^60 - 96 * q^61 - 168 * q^62 - 284 * q^63 - 244 * q^64 - 128 * q^65 - 420 * q^66 - 216 * q^67 - 410 * q^68 - 216 * q^69 - 292 * q^70 - 304 * q^71 - 504 * q^72 - 92 * q^73 - 412 * q^74 - 460 * q^75 - 420 * q^76 - 84 * q^77 - 720 * q^78 - 184 * q^79 - 504 * q^80 - 200 * q^81 - 356 * q^82 - 204 * q^83 - 364 * q^84 + 40 * q^85 - 332 * q^86 - 40 * q^87 - 196 * q^88 - 20 * q^89 - 368 * q^90 + 20 * q^91 - 292 * q^92 + 116 * q^93 - 124 * q^94 + 120 * q^95 - 100 * q^96 - 136 * q^97 - 116 * q^98 + 56 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(952))\)

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
952.2.a	\(\chi_{952}(1, \cdot)\)	952.2.a.a	2	1
		952.2.a.b	2
		952.2.a.c	3
		952.2.a.d	3
		952.2.a.e	3
		952.2.a.f	3
		952.2.a.g	4
		952.2.a.h	4
952.2.b	\(\chi_{952}(477, \cdot)\)	952.2.b.a	2	1
		952.2.b.b	2
		952.2.b.c	2
		952.2.b.d	16
		952.2.b.e	16
		952.2.b.f	28
		952.2.b.g	30
952.2.c	\(\chi_{952}(169, \cdot)\)	952.2.c.a	2	1
		952.2.c.b	4
		952.2.c.c	4
		952.2.c.d	8
		952.2.c.e	10
952.2.h	\(\chi_{952}(951, \cdot)\)	None	0	1
952.2.i	\(\chi_{952}(307, \cdot)\)	952.2.i.a	128	1
952.2.j	\(\chi_{952}(783, \cdot)\)	None	0	1
952.2.k	\(\chi_{952}(475, \cdot)\)	952.2.k.a	8	1
		952.2.k.b	20
		952.2.k.c	112
952.2.p	\(\chi_{952}(645, \cdot)\)	952.2.p.a	108	1
952.2.q	\(\chi_{952}(137, \cdot)\)	952.2.q.a	2	2
		952.2.q.b	2
		952.2.q.c	12
		952.2.q.d	14
		952.2.q.e	14
		952.2.q.f	20
952.2.s	\(\chi_{952}(421, \cdot)\)	952.2.s.a	216	2
952.2.t	\(\chi_{952}(55, \cdot)\)	None	0	2
952.2.w	\(\chi_{952}(225, \cdot)\)	952.2.w.a	24	2
		952.2.w.b	32
952.2.x	\(\chi_{952}(251, \cdot)\)	952.2.x.a	280	2
952.2.z	\(\chi_{952}(373, \cdot)\)	952.2.z.a	4	2
		952.2.z.b	4
		952.2.z.c	272
952.2.be	\(\chi_{952}(103, \cdot)\)	None	0	2
952.2.bf	\(\chi_{952}(339, \cdot)\)	952.2.bf.a	16	2
		952.2.bf.b	264
952.2.bg	\(\chi_{952}(271, \cdot)\)	None	0	2
952.2.bh	\(\chi_{952}(171, \cdot)\)	952.2.bh.a	256	2
952.2.bm	\(\chi_{952}(205, \cdot)\)	952.2.bm.a	4	2
		952.2.bm.b	4
		952.2.bm.c	120
		952.2.bm.d	128
952.2.bn	\(\chi_{952}(305, \cdot)\)	952.2.bn.a	4	2
		952.2.bn.b	12
		952.2.bn.c	20
		952.2.bn.d	36
952.2.bo	\(\chi_{952}(83, \cdot)\)	952.2.bo.a	560	4
952.2.bq	\(\chi_{952}(281, \cdot)\)	952.2.bq.a	48	4
		952.2.bq.b	56
952.2.bs	\(\chi_{952}(111, \cdot)\)	None	0	4
952.2.bu	\(\chi_{952}(253, \cdot)\)	952.2.bu.a	432	4
952.2.bw	\(\chi_{952}(149, \cdot)\)	952.2.bw.a	4	4
		952.2.bw.b	4
		952.2.bw.c	4
		952.2.bw.d	4
		952.2.bw.e	544
952.2.bz	\(\chi_{952}(47, \cdot)\)	None	0	4
952.2.ca	\(\chi_{952}(81, \cdot)\)	952.2.ca.a	8	4
		952.2.ca.b	64
		952.2.ca.c	72
952.2.cd	\(\chi_{952}(115, \cdot)\)	952.2.cd.a	560	4
952.2.ce	\(\chi_{952}(99, \cdot)\)	952.2.ce.a	864	8
952.2.ch	\(\chi_{952}(71, \cdot)\)	None	0	8
952.2.ci	\(\chi_{952}(41, \cdot)\)	952.2.ci.a	144	8
		952.2.ci.b	144
952.2.cl	\(\chi_{952}(125, \cdot)\)	952.2.cl.a	1120	8
952.2.cn	\(\chi_{952}(9, \cdot)\)	952.2.cn.a	144	8
		952.2.cn.b	144
952.2.cp	\(\chi_{952}(19, \cdot)\)	952.2.cp.a	1120	8
952.2.cr	\(\chi_{952}(53, \cdot)\)	952.2.cr.a	1120	8
952.2.ct	\(\chi_{952}(87, \cdot)\)	None	0	8
952.2.cv	\(\chi_{952}(5, \cdot)\)	952.2.cv.a	2240	16
952.2.cw	\(\chi_{952}(73, \cdot)\)	952.2.cw.a	288	16
		952.2.cw.b	288
952.2.cz	\(\chi_{952}(23, \cdot)\)	None	0	16
952.2.da	\(\chi_{952}(11, \cdot)\)	952.2.da.a	2240	16

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(952))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(952)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(34))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(68))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(119))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(136))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(238))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(476))\)\(^{\oplus 2}\)