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Properties

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

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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

\( 16136 q - 40 q^{2} - 32 q^{3} - 32 q^{4} - 74 q^{5} - 96 q^{6} - 24 q^{7} - 16 q^{8} - 4 q^{9} + O(q^{10}) \) \( 16136 q - 40 q^{2} - 32 q^{3} - 32 q^{4} - 74 q^{5} - 96 q^{6} - 24 q^{7} - 16 q^{8} - 4 q^{9} - 56 q^{10} - 76 q^{11} - 48 q^{12} - 50 q^{13} - 96 q^{14} - 10 q^{15} - 144 q^{16} - 72 q^{17} - 24 q^{18} + 20 q^{19} - 48 q^{20} - 92 q^{21} - 32 q^{22} - 32 q^{24} + 8 q^{25} - 120 q^{26} - 80 q^{27} - 64 q^{28} - 20 q^{29} - 128 q^{30} - 164 q^{31} - 80 q^{32} - 140 q^{33} - 144 q^{34} - 74 q^{35} - 256 q^{36} - 96 q^{37} - 192 q^{38} - 32 q^{39} - 304 q^{40} - 44 q^{41} - 192 q^{42} + 80 q^{43} - 160 q^{44} - 66 q^{45} - 192 q^{46} + 112 q^{47} - 128 q^{48} + 20 q^{49} - 168 q^{50} + 96 q^{51} - 80 q^{52} - 12 q^{53} - 128 q^{54} + 58 q^{55} - 144 q^{56} + 164 q^{57} - 80 q^{58} + 92 q^{59} + 8 q^{60} - 60 q^{61} + 32 q^{62} + 8 q^{63} + 16 q^{64} - 88 q^{65} - 112 q^{66} - 112 q^{67} + 80 q^{68} - 84 q^{69} + 104 q^{70} - 196 q^{71} + 224 q^{72} + 32 q^{73} + 144 q^{74} - 284 q^{75} + 64 q^{76} - 32 q^{77} + 88 q^{78} - 248 q^{79} + 120 q^{80} - 172 q^{81} + 96 q^{82} - 208 q^{83} - 96 q^{84} - 94 q^{85} - 176 q^{86} - 340 q^{87} - 64 q^{88} - 156 q^{89} - 136 q^{90} - 216 q^{91} - 384 q^{92} - 332 q^{93} - 368 q^{94} - 218 q^{95} - 912 q^{96} - 224 q^{97} - 552 q^{98} - 372 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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 the 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

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