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Properties

Label 1960.4
Level 1960
Weight 4
Dimension 166999
Nonzero newspaces 36
Sturm bound 903168
Trace bound 12

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Defining parameters

Level: \( N \) = \( 1960 = 2^{3} \cdot 5 \cdot 7^{2} \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 36 \)
Sturm bound: \(903168\)
Trace bound: \(12\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(1960))\).

Total New Old
Modular forms 341568 168163 173405
Cusp forms 335808 166999 168809
Eisenstein series 5760 1164 4596

Trace form

\( 166999 q - 60 q^{2} - 56 q^{3} - 40 q^{4} - 9 q^{5} - 244 q^{6} - 72 q^{7} - 192 q^{8} - 225 q^{9} + O(q^{10}) \) \( 166999 q - 60 q^{2} - 56 q^{3} - 40 q^{4} - 9 q^{5} - 244 q^{6} - 72 q^{7} - 192 q^{8} - 225 q^{9} - 38 q^{10} + 96 q^{11} + 156 q^{12} + 322 q^{13} - 72 q^{14} - 94 q^{15} - 332 q^{16} - 234 q^{17} + 104 q^{18} + 296 q^{19} + 458 q^{20} - 336 q^{21} + 156 q^{22} - 36 q^{23} - 1972 q^{24} - 869 q^{25} - 3380 q^{26} - 2108 q^{27} - 2664 q^{28} + 378 q^{29} - 2314 q^{30} - 3116 q^{31} - 540 q^{32} - 1848 q^{33} + 2328 q^{34} + 396 q^{35} + 5908 q^{36} + 2026 q^{37} + 7372 q^{38} + 4692 q^{39} + 2742 q^{40} + 3150 q^{41} - 2664 q^{42} + 5696 q^{43} - 7004 q^{44} + 3679 q^{45} - 4108 q^{46} + 2692 q^{47} - 660 q^{48} - 972 q^{49} + 404 q^{50} - 8788 q^{51} + 8352 q^{52} - 6854 q^{53} + 14108 q^{54} - 2602 q^{55} + 4404 q^{56} - 5976 q^{57} + 7304 q^{58} - 7792 q^{59} + 2986 q^{60} - 3550 q^{61} + 460 q^{62} - 1248 q^{63} - 7924 q^{64} - 4154 q^{65} - 12116 q^{66} + 8224 q^{67} + 5512 q^{68} + 13064 q^{69} + 924 q^{70} + 17188 q^{71} + 6032 q^{72} - 4202 q^{73} + 6096 q^{74} - 3234 q^{75} - 4388 q^{76} - 3420 q^{77} - 12356 q^{78} - 2980 q^{79} - 11278 q^{80} + 21411 q^{81} - 17472 q^{82} + 5336 q^{83} - 18000 q^{84} + 9586 q^{85} - 23636 q^{86} - 4244 q^{87} - 16988 q^{88} - 6794 q^{89} - 14490 q^{90} - 14520 q^{91} - 18660 q^{92} - 22688 q^{93} - 27108 q^{94} - 21330 q^{95} - 19556 q^{96} + 10350 q^{97} + 10728 q^{98} - 6636 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(1960))\)

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
1960.4.a \(\chi_{1960}(1, \cdot)\) 1960.4.a.a 1 1
1960.4.a.b 1
1960.4.a.c 1
1960.4.a.d 1
1960.4.a.e 1
1960.4.a.f 1
1960.4.a.g 1
1960.4.a.h 1
1960.4.a.i 1
1960.4.a.j 2
1960.4.a.k 2
1960.4.a.l 2
1960.4.a.m 2
1960.4.a.n 2
1960.4.a.o 3
1960.4.a.p 3
1960.4.a.q 3
1960.4.a.r 3
1960.4.a.s 5
1960.4.a.t 5
1960.4.a.u 5
1960.4.a.v 5
1960.4.a.w 6
1960.4.a.x 6
1960.4.a.y 6
1960.4.a.z 6
1960.4.a.ba 6
1960.4.a.bb 6
1960.4.a.bc 8
1960.4.a.bd 8
1960.4.a.be 10
1960.4.a.bf 10
1960.4.b \(\chi_{1960}(981, \cdot)\) n/a 492 1
1960.4.e \(\chi_{1960}(1959, \cdot)\) None 0 1
1960.4.g \(\chi_{1960}(1569, \cdot)\) n/a 184 1
1960.4.h \(\chi_{1960}(1371, \cdot)\) n/a 480 1
1960.4.k \(\chi_{1960}(391, \cdot)\) None 0 1
1960.4.l \(\chi_{1960}(589, \cdot)\) n/a 728 1
1960.4.n \(\chi_{1960}(979, \cdot)\) n/a 712 1
1960.4.q \(\chi_{1960}(361, \cdot)\) n/a 240 2
1960.4.s \(\chi_{1960}(293, \cdot)\) n/a 1424 2
1960.4.t \(\chi_{1960}(687, \cdot)\) None 0 2
1960.4.w \(\chi_{1960}(883, \cdot)\) n/a 1456 2
1960.4.x \(\chi_{1960}(97, \cdot)\) n/a 360 2
1960.4.ba \(\chi_{1960}(19, \cdot)\) n/a 1424 2
1960.4.bc \(\chi_{1960}(31, \cdot)\) None 0 2
1960.4.bf \(\chi_{1960}(949, \cdot)\) n/a 1424 2
1960.4.bg \(\chi_{1960}(569, \cdot)\) n/a 360 2
1960.4.bj \(\chi_{1960}(411, \cdot)\) n/a 960 2
1960.4.bl \(\chi_{1960}(1341, \cdot)\) n/a 960 2
1960.4.bm \(\chi_{1960}(999, \cdot)\) None 0 2
1960.4.bo \(\chi_{1960}(281, \cdot)\) n/a 1008 6
1960.4.bp \(\chi_{1960}(313, \cdot)\) n/a 720 4
1960.4.bs \(\chi_{1960}(67, \cdot)\) n/a 2848 4
1960.4.bt \(\chi_{1960}(263, \cdot)\) None 0 4
1960.4.bw \(\chi_{1960}(117, \cdot)\) n/a 2848 4
1960.4.by \(\chi_{1960}(139, \cdot)\) n/a 6024 6
1960.4.ca \(\chi_{1960}(29, \cdot)\) n/a 6024 6
1960.4.cd \(\chi_{1960}(111, \cdot)\) None 0 6
1960.4.ce \(\chi_{1960}(251, \cdot)\) n/a 4032 6
1960.4.ch \(\chi_{1960}(169, \cdot)\) n/a 1512 6
1960.4.cj \(\chi_{1960}(279, \cdot)\) None 0 6
1960.4.ck \(\chi_{1960}(141, \cdot)\) n/a 4032 6
1960.4.cm \(\chi_{1960}(81, \cdot)\) n/a 2016 12
1960.4.cn \(\chi_{1960}(43, \cdot)\) n/a 12048 12
1960.4.cq \(\chi_{1960}(153, \cdot)\) n/a 3024 12
1960.4.cr \(\chi_{1960}(13, \cdot)\) n/a 12048 12
1960.4.cu \(\chi_{1960}(127, \cdot)\) None 0 12
1960.4.cv \(\chi_{1960}(159, \cdot)\) None 0 12
1960.4.cy \(\chi_{1960}(221, \cdot)\) n/a 8064 12
1960.4.da \(\chi_{1960}(131, \cdot)\) n/a 8064 12
1960.4.db \(\chi_{1960}(9, \cdot)\) n/a 3024 12
1960.4.de \(\chi_{1960}(109, \cdot)\) n/a 12048 12
1960.4.df \(\chi_{1960}(271, \cdot)\) None 0 12
1960.4.dj \(\chi_{1960}(59, \cdot)\) n/a 12048 12
1960.4.dl \(\chi_{1960}(23, \cdot)\) None 0 24
1960.4.dm \(\chi_{1960}(157, \cdot)\) n/a 24096 24
1960.4.dp \(\chi_{1960}(17, \cdot)\) n/a 6048 24
1960.4.dq \(\chi_{1960}(107, \cdot)\) n/a 24096 24

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(1960))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(1960)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 16}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 9}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(70))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(98))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(140))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(196))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(245))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(280))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(392))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(490))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(980))\)\(^{\oplus 2}\)