Space of modular forms of level 1040 and weight 2

• Label: 1040.2
• Level: 1040
• Weight: 2
• Dimension: 16136
• Nonzero newspaces: 52
• Sturm bound: 129024
• Trace bound: 13

Defining parameters

Level:	\( N \)	=	\( 1040 = 2^{4} \cdot 5 \cdot 13 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 52 \)
Sturm bound:			\(129024\)
Trace bound:			\(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1040))\).

	Total	New	Old
Modular forms	33600	16732	16868
Cusp forms	30913	16136	14777
Eisenstein series	2687	596	2091

Trace form

16136 * q - 40 * q^2 - 32 * q^3 - 32 * q^4 - 74 * q^5 - 96 * q^6 - 24 * q^7 - 16 * q^8 - 4 * q^9 - 56 * q^10 - 76 * q^11 - 48 * q^12 - 50 * q^13 - 96 * q^14 - 10 * q^15 - 144 * q^16 - 72 * q^17 - 24 * q^18 + 20 * q^19 - 48 * q^20 - 92 * q^21 - 32 * q^22 - 32 * q^24 + 8 * q^25 - 120 * q^26 - 80 * q^27 - 64 * q^28 - 20 * q^29 - 128 * q^30 - 164 * q^31 - 80 * q^32 - 140 * q^33 - 144 * q^34 - 74 * q^35 - 256 * q^36 - 96 * q^37 - 192 * q^38 - 32 * q^39 - 304 * q^40 - 44 * q^41 - 192 * q^42 + 80 * q^43 - 160 * q^44 - 66 * q^45 - 192 * q^46 + 112 * q^47 - 128 * q^48 + 20 * q^49 - 168 * q^50 + 96 * q^51 - 80 * q^52 - 12 * q^53 - 128 * q^54 + 58 * q^55 - 144 * q^56 + 164 * q^57 - 80 * q^58 + 92 * q^59 + 8 * q^60 - 60 * q^61 + 32 * q^62 + 8 * q^63 + 16 * q^64 - 88 * q^65 - 112 * q^66 - 112 * q^67 + 80 * q^68 - 84 * q^69 + 104 * q^70 - 196 * q^71 + 224 * q^72 + 32 * q^73 + 144 * q^74 - 284 * q^75 + 64 * q^76 - 32 * q^77 + 88 * q^78 - 248 * q^79 + 120 * q^80 - 172 * q^81 + 96 * q^82 - 208 * q^83 - 96 * q^84 - 94 * q^85 - 176 * q^86 - 340 * q^87 - 64 * q^88 - 156 * q^89 - 136 * q^90 - 216 * q^91 - 384 * q^92 - 332 * q^93 - 368 * q^94 - 218 * q^95 - 912 * q^96 - 224 * q^97 - 552 * q^98 - 372 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1040))\)

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
1040.2.a	\(\chi_{1040}(1, \cdot)\)	1040.2.a.a	1	1
		1040.2.a.b	1
		1040.2.a.c	1
		1040.2.a.d	1
		1040.2.a.e	1
		1040.2.a.f	1
		1040.2.a.g	1
		1040.2.a.h	2
		1040.2.a.i	2
		1040.2.a.j	2
		1040.2.a.k	2
		1040.2.a.l	2
		1040.2.a.m	2
		1040.2.a.n	2
		1040.2.a.o	3
1040.2.d	\(\chi_{1040}(209, \cdot)\)	1040.2.d.a	2	1
		1040.2.d.b	6
		1040.2.d.c	6
		1040.2.d.d	6
		1040.2.d.e	6
		1040.2.d.f	10
1040.2.e	\(\chi_{1040}(441, \cdot)\)	None	0	1
1040.2.f	\(\chi_{1040}(129, \cdot)\)	1040.2.f.a	2	1
		1040.2.f.b	2
		1040.2.f.c	4
		1040.2.f.d	4
		1040.2.f.e	8
		1040.2.f.f	10
		1040.2.f.g	10
1040.2.g	\(\chi_{1040}(521, \cdot)\)	None	0	1
1040.2.j	\(\chi_{1040}(729, \cdot)\)	None	0	1
1040.2.k	\(\chi_{1040}(961, \cdot)\)	1040.2.k.a	2	1
		1040.2.k.b	6
		1040.2.k.c	6
		1040.2.k.d	6
		1040.2.k.e	8
1040.2.p	\(\chi_{1040}(649, \cdot)\)	None	0	1
1040.2.q	\(\chi_{1040}(81, \cdot)\)	1040.2.q.a	2	2
		1040.2.q.b	2
		1040.2.q.c	2
		1040.2.q.d	2
		1040.2.q.e	2
		1040.2.q.f	2
		1040.2.q.g	2
		1040.2.q.h	2
		1040.2.q.i	2
		1040.2.q.j	2
		1040.2.q.k	2
		1040.2.q.l	4
		1040.2.q.m	4
		1040.2.q.n	4
		1040.2.q.o	4
		1040.2.q.p	4
		1040.2.q.q	6
		1040.2.q.r	8
1040.2.s	\(\chi_{1040}(437, \cdot)\)	n/a	328	2
1040.2.u	\(\chi_{1040}(31, \cdot)\)	1040.2.u.a	24	2
		1040.2.u.b	32
1040.2.v	\(\chi_{1040}(443, \cdot)\)	n/a	288	2
1040.2.y	\(\chi_{1040}(363, \cdot)\)	n/a	328	2
1040.2.z	\(\chi_{1040}(359, \cdot)\)	None	0	2
1040.2.bb	\(\chi_{1040}(333, \cdot)\)	n/a	328	2
1040.2.be	\(\chi_{1040}(389, \cdot)\)	n/a	328	2
1040.2.bg	\(\chi_{1040}(577, \cdot)\)	1040.2.bg.a	2	2
		1040.2.bg.b	2
		1040.2.bg.c	2
		1040.2.bg.d	2
		1040.2.bg.e	2
		1040.2.bg.f	2
		1040.2.bg.g	2
		1040.2.bg.h	2
		1040.2.bg.i	4
		1040.2.bg.j	4
		1040.2.bg.k	4
		1040.2.bg.l	4
		1040.2.bg.m	8
		1040.2.bg.n	8
		1040.2.bg.o	12
		1040.2.bg.p	20
1040.2.bi	\(\chi_{1040}(57, \cdot)\)	None	0	2
1040.2.bj	\(\chi_{1040}(261, \cdot)\)	n/a	192	2
1040.2.bm	\(\chi_{1040}(291, \cdot)\)	n/a	224	2
1040.2.bp	\(\chi_{1040}(287, \cdot)\)	1040.2.bp.a	24	2
		1040.2.bp.b	48
1040.2.bq	\(\chi_{1040}(103, \cdot)\)	None	0	2
1040.2.bs	\(\chi_{1040}(499, \cdot)\)	n/a	328	2
1040.2.bt	\(\chi_{1040}(811, \cdot)\)	n/a	224	2
1040.2.bv	\(\chi_{1040}(207, \cdot)\)	1040.2.bv.a	2	2
		1040.2.bv.b	2
		1040.2.bv.c	24
		1040.2.bv.d	24
		1040.2.bv.e	32
1040.2.bw	\(\chi_{1040}(183, \cdot)\)	None	0	2
1040.2.bz	\(\chi_{1040}(99, \cdot)\)	n/a	328	2
1040.2.cc	\(\chi_{1040}(469, \cdot)\)	n/a	288	2
1040.2.cd	\(\chi_{1040}(177, \cdot)\)	1040.2.cd.a	2	2
		1040.2.cd.b	2
		1040.2.cd.c	2
		1040.2.cd.d	2
		1040.2.cd.e	2
		1040.2.cd.f	2
		1040.2.cd.g	2
		1040.2.cd.h	2
		1040.2.cd.i	4
		1040.2.cd.j	4
		1040.2.cd.k	4
		1040.2.cd.l	4
		1040.2.cd.m	8
		1040.2.cd.n	8
		1040.2.cd.o	12
		1040.2.cd.p	20
1040.2.cf	\(\chi_{1040}(473, \cdot)\)	None	0	2
1040.2.ch	\(\chi_{1040}(181, \cdot)\)	n/a	224	2
1040.2.cj	\(\chi_{1040}(213, \cdot)\)	n/a	328	2
1040.2.cm	\(\chi_{1040}(151, \cdot)\)	None	0	2
1040.2.cn	\(\chi_{1040}(27, \cdot)\)	n/a	288	2
1040.2.cq	\(\chi_{1040}(883, \cdot)\)	n/a	328	2
1040.2.cr	\(\chi_{1040}(239, \cdot)\)	1040.2.cr.a	2	2
		1040.2.cr.b	2
		1040.2.cr.c	24
		1040.2.cr.d	56
1040.2.cu	\(\chi_{1040}(317, \cdot)\)	n/a	328	2
1040.2.cv	\(\chi_{1040}(329, \cdot)\)	None	0	2
1040.2.da	\(\chi_{1040}(641, \cdot)\)	1040.2.da.a	4	2
		1040.2.da.b	8
		1040.2.da.c	8
		1040.2.da.d	8
		1040.2.da.e	12
		1040.2.da.f	16
1040.2.db	\(\chi_{1040}(9, \cdot)\)	None	0	2
1040.2.de	\(\chi_{1040}(601, \cdot)\)	None	0	2
1040.2.df	\(\chi_{1040}(49, \cdot)\)	1040.2.df.a	8	2
		1040.2.df.b	8
		1040.2.df.c	8
		1040.2.df.d	16
		1040.2.df.e	20
		1040.2.df.f	20
1040.2.dg	\(\chi_{1040}(121, \cdot)\)	None	0	2
1040.2.dh	\(\chi_{1040}(289, \cdot)\)	1040.2.dh.a	12	2
		1040.2.dh.b	12
		1040.2.dh.c	12
		1040.2.dh.d	44
1040.2.dk	\(\chi_{1040}(293, \cdot)\)	n/a	656	4
1040.2.dn	\(\chi_{1040}(319, \cdot)\)	n/a	168	4
1040.2.dp	\(\chi_{1040}(3, \cdot)\)	n/a	656	4
1040.2.dq	\(\chi_{1040}(563, \cdot)\)	n/a	656	4
1040.2.ds	\(\chi_{1040}(71, \cdot)\)	None	0	4
1040.2.dv	\(\chi_{1040}(397, \cdot)\)	n/a	656	4
1040.2.dx	\(\chi_{1040}(101, \cdot)\)	n/a	448	4
1040.2.dz	\(\chi_{1040}(137, \cdot)\)	None	0	4
1040.2.eb	\(\chi_{1040}(353, \cdot)\)	n/a	160	4
1040.2.ec	\(\chi_{1040}(29, \cdot)\)	n/a	656	4
1040.2.ee	\(\chi_{1040}(379, \cdot)\)	n/a	656	4
1040.2.eg	\(\chi_{1040}(87, \cdot)\)	None	0	4
1040.2.eh	\(\chi_{1040}(127, \cdot)\)	n/a	168	4
1040.2.ek	\(\chi_{1040}(171, \cdot)\)	n/a	448	4
1040.2.en	\(\chi_{1040}(19, \cdot)\)	n/a	656	4
1040.2.eq	\(\chi_{1040}(23, \cdot)\)	None	0	4
1040.2.er	\(\chi_{1040}(367, \cdot)\)	n/a	168	4
1040.2.et	\(\chi_{1040}(11, \cdot)\)	n/a	448	4
1040.2.ev	\(\chi_{1040}(61, \cdot)\)	n/a	448	4
1040.2.ew	\(\chi_{1040}(457, \cdot)\)	None	0	4
1040.2.ey	\(\chi_{1040}(33, \cdot)\)	n/a	160	4
1040.2.fa	\(\chi_{1040}(69, \cdot)\)	n/a	656	4
1040.2.fd	\(\chi_{1040}(197, \cdot)\)	n/a	656	4
1040.2.ff	\(\chi_{1040}(119, \cdot)\)	None	0	4
1040.2.fh	\(\chi_{1040}(523, \cdot)\)	n/a	656	4
1040.2.fi	\(\chi_{1040}(43, \cdot)\)	n/a	656	4
1040.2.fk	\(\chi_{1040}(111, \cdot)\)	n/a	112	4
1040.2.fm	\(\chi_{1040}(37, \cdot)\)	n/a	656	4

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1040))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1040)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(52))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(65))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(104))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(130))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(208))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(260))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(520))\)\(^{\oplus 2}\)