## Defining parameters

 Level: $$N$$ = $$1960 = 2^{3} \cdot 5 \cdot 7^{2}$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$36$$ Sturm bound: $$451584$$ Trace bound: $$12$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(1960))$$.

Total New Old
Modular forms 115776 56443 59333
Cusp forms 110017 55279 54738
Eisenstein series 5759 1164 4595

## Trace form

 $$55279 q - 64 q^{2} - 64 q^{3} - 64 q^{4} - q^{5} - 188 q^{6} - 72 q^{7} - 112 q^{8} - 157 q^{9} + O(q^{10})$$ $$55279 q - 64 q^{2} - 64 q^{3} - 64 q^{4} - q^{5} - 188 q^{6} - 72 q^{7} - 112 q^{8} - 157 q^{9} - 94 q^{10} - 216 q^{11} - 52 q^{12} - 26 q^{13} - 72 q^{14} - 182 q^{15} - 172 q^{16} - 150 q^{17} + 36 q^{18} - 48 q^{19} - 38 q^{20} + 28 q^{22} + 12 q^{23} + 108 q^{24} - 157 q^{25} - 52 q^{26} + 68 q^{27} + 24 q^{28} - 6 q^{29} + 6 q^{30} - 108 q^{31} + 36 q^{32} - 104 q^{33} + 48 q^{34} - 108 q^{35} - 244 q^{36} - 18 q^{37} - 12 q^{38} - 28 q^{39} - 74 q^{40} - 474 q^{41} - 144 q^{42} - 88 q^{43} - 172 q^{44} - 13 q^{45} - 332 q^{46} + 36 q^{47} - 308 q^{48} - 132 q^{49} - 296 q^{50} - 4 q^{51} - 256 q^{52} + 30 q^{53} - 324 q^{54} + 46 q^{55} - 300 q^{56} - 8 q^{57} - 136 q^{58} + 200 q^{59} - 182 q^{60} + 122 q^{61} - 220 q^{62} + 96 q^{63} - 244 q^{64} - 22 q^{65} - 260 q^{66} + 184 q^{67} - 40 q^{68} + 248 q^{69} - 84 q^{70} - 108 q^{71} + 26 q^{73} + 256 q^{74} + 86 q^{75} + 108 q^{76} + 108 q^{77} + 164 q^{78} + 124 q^{79} + 114 q^{80} + 51 q^{81} + 192 q^{82} + 288 q^{83} + 144 q^{84} + 182 q^{85} + 260 q^{86} + 444 q^{87} + 228 q^{88} + 86 q^{89} + 62 q^{90} - 72 q^{91} + 188 q^{92} + 528 q^{93} + 116 q^{94} + 54 q^{95} - 36 q^{96} + 226 q^{97} - 24 q^{98} - 148 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(1960))$$

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 the newforms together with their dimension.

Label $$\chi$$ Newforms Dimension $$\chi$$ degree
1960.2.a $$\chi_{1960}(1, \cdot)$$ 1960.2.a.a 1 1
1960.2.a.b 1
1960.2.a.c 1
1960.2.a.d 1
1960.2.a.e 1
1960.2.a.f 1
1960.2.a.g 1
1960.2.a.h 1
1960.2.a.i 1
1960.2.a.j 1
1960.2.a.k 1
1960.2.a.l 1
1960.2.a.m 1
1960.2.a.n 1
1960.2.a.o 1
1960.2.a.p 2
1960.2.a.q 2
1960.2.a.r 2
1960.2.a.s 2
1960.2.a.t 2
1960.2.a.u 2
1960.2.a.v 3
1960.2.a.w 3
1960.2.a.x 4
1960.2.a.y 4
1960.2.b $$\chi_{1960}(981, \cdot)$$ n/a 164 1
1960.2.e $$\chi_{1960}(1959, \cdot)$$ None 0 1
1960.2.g $$\chi_{1960}(1569, \cdot)$$ 1960.2.g.a 2 1
1960.2.g.b 2
1960.2.g.c 6
1960.2.g.d 8
1960.2.g.e 12
1960.2.g.f 12
1960.2.g.g 20
1960.2.h $$\chi_{1960}(1371, \cdot)$$ n/a 160 1
1960.2.k $$\chi_{1960}(391, \cdot)$$ None 0 1
1960.2.l $$\chi_{1960}(589, \cdot)$$ n/a 236 1
1960.2.n $$\chi_{1960}(979, \cdot)$$ n/a 232 1
1960.2.q $$\chi_{1960}(361, \cdot)$$ 1960.2.q.a 2 2
1960.2.q.b 2
1960.2.q.c 2
1960.2.q.d 2
1960.2.q.e 2
1960.2.q.f 2
1960.2.q.g 2
1960.2.q.h 2
1960.2.q.i 2
1960.2.q.j 2
1960.2.q.k 2
1960.2.q.l 2
1960.2.q.m 2
1960.2.q.n 2
1960.2.q.o 2
1960.2.q.p 4
1960.2.q.q 4
1960.2.q.r 4
1960.2.q.s 4
1960.2.q.t 4
1960.2.q.u 4
1960.2.q.v 4
1960.2.q.w 6
1960.2.q.x 8
1960.2.q.y 8
1960.2.s $$\chi_{1960}(293, \cdot)$$ n/a 464 2
1960.2.t $$\chi_{1960}(687, \cdot)$$ None 0 2
1960.2.w $$\chi_{1960}(883, \cdot)$$ n/a 472 2
1960.2.x $$\chi_{1960}(97, \cdot)$$ n/a 120 2
1960.2.ba $$\chi_{1960}(19, \cdot)$$ n/a 464 2
1960.2.bc $$\chi_{1960}(31, \cdot)$$ None 0 2
1960.2.bf $$\chi_{1960}(949, \cdot)$$ n/a 464 2
1960.2.bg $$\chi_{1960}(569, \cdot)$$ n/a 120 2
1960.2.bj $$\chi_{1960}(411, \cdot)$$ n/a 320 2
1960.2.bl $$\chi_{1960}(1341, \cdot)$$ n/a 320 2
1960.2.bm $$\chi_{1960}(999, \cdot)$$ None 0 2
1960.2.bo $$\chi_{1960}(281, \cdot)$$ n/a 336 6
1960.2.bp $$\chi_{1960}(313, \cdot)$$ n/a 240 4
1960.2.bs $$\chi_{1960}(67, \cdot)$$ n/a 928 4
1960.2.bt $$\chi_{1960}(263, \cdot)$$ None 0 4
1960.2.bw $$\chi_{1960}(117, \cdot)$$ n/a 928 4
1960.2.by $$\chi_{1960}(139, \cdot)$$ n/a 1992 6
1960.2.ca $$\chi_{1960}(29, \cdot)$$ n/a 1992 6
1960.2.cd $$\chi_{1960}(111, \cdot)$$ None 0 6
1960.2.ce $$\chi_{1960}(251, \cdot)$$ n/a 1344 6
1960.2.ch $$\chi_{1960}(169, \cdot)$$ n/a 504 6
1960.2.cj $$\chi_{1960}(279, \cdot)$$ None 0 6
1960.2.ck $$\chi_{1960}(141, \cdot)$$ n/a 1344 6
1960.2.cm $$\chi_{1960}(81, \cdot)$$ n/a 672 12
1960.2.cn $$\chi_{1960}(43, \cdot)$$ n/a 3984 12
1960.2.cq $$\chi_{1960}(153, \cdot)$$ n/a 1008 12
1960.2.cr $$\chi_{1960}(13, \cdot)$$ n/a 3984 12
1960.2.cu $$\chi_{1960}(127, \cdot)$$ None 0 12
1960.2.cv $$\chi_{1960}(159, \cdot)$$ None 0 12
1960.2.cy $$\chi_{1960}(221, \cdot)$$ n/a 2688 12
1960.2.da $$\chi_{1960}(131, \cdot)$$ n/a 2688 12
1960.2.db $$\chi_{1960}(9, \cdot)$$ n/a 1008 12
1960.2.de $$\chi_{1960}(109, \cdot)$$ n/a 3984 12
1960.2.df $$\chi_{1960}(271, \cdot)$$ None 0 12
1960.2.dj $$\chi_{1960}(59, \cdot)$$ n/a 3984 12
1960.2.dl $$\chi_{1960}(23, \cdot)$$ None 0 24
1960.2.dm $$\chi_{1960}(157, \cdot)$$ n/a 7968 24
1960.2.dp $$\chi_{1960}(17, \cdot)$$ n/a 2016 24
1960.2.dq $$\chi_{1960}(107, \cdot)$$ n/a 7968 24

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(1960))$$ into lower level spaces

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