# Properties

 Label 1980.2 Level 1980 Weight 2 Dimension 42676 Nonzero newspaces 48 Sturm bound 414720 Trace bound 24

## Defining parameters

 Level: $$N$$ = $$1980 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 11$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$48$$ Sturm bound: $$414720$$ Trace bound: $$24$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(1980))$$.

Total New Old
Modular forms 106880 43644 63236
Cusp forms 100481 42676 57805
Eisenstein series 6399 968 5431

## Trace form

 $$42676 q - 30 q^{2} - 42 q^{4} - 82 q^{5} - 100 q^{6} - 6 q^{7} - 30 q^{8} - 104 q^{9} + O(q^{10})$$ $$42676 q - 30 q^{2} - 42 q^{4} - 82 q^{5} - 100 q^{6} - 6 q^{7} - 30 q^{8} - 104 q^{9} - 128 q^{10} - 12 q^{11} - 40 q^{12} - 94 q^{13} + 32 q^{14} - 6 q^{15} - 70 q^{16} - 54 q^{17} + 64 q^{18} - 54 q^{19} + 46 q^{20} - 188 q^{21} - 48 q^{22} - 2 q^{23} + 44 q^{24} - 112 q^{25} - 4 q^{26} - 12 q^{27} - 28 q^{28} - 26 q^{29} - 44 q^{31} + 20 q^{32} - 102 q^{33} + 64 q^{34} + 27 q^{35} - 156 q^{36} - 256 q^{37} + 40 q^{39} + 74 q^{40} - 130 q^{41} - 32 q^{42} - 76 q^{43} + 40 q^{44} - 28 q^{45} - 140 q^{46} + 70 q^{47} + 28 q^{48} - 8 q^{49} - 62 q^{50} + 116 q^{51} + 124 q^{52} + 158 q^{53} + 188 q^{54} + 16 q^{55} + 24 q^{56} + 280 q^{57} + 180 q^{58} + 256 q^{59} - 12 q^{60} + 102 q^{61} + 220 q^{62} + 156 q^{63} + 150 q^{64} + 104 q^{65} + 52 q^{66} + 190 q^{67} + 92 q^{68} + 12 q^{69} + 86 q^{70} + 112 q^{71} - 16 q^{72} - 90 q^{73} + 176 q^{74} - 118 q^{75} + 272 q^{76} + 200 q^{77} - 184 q^{78} + 90 q^{79} - 94 q^{80} - 272 q^{81} + 282 q^{82} - 18 q^{83} - 100 q^{84} + 43 q^{85} - 114 q^{86} - 60 q^{87} + 172 q^{88} - 126 q^{89} - 336 q^{90} - 226 q^{91} + 108 q^{92} + 124 q^{93} + 256 q^{94} - 7 q^{95} - 388 q^{96} + 68 q^{97} - 92 q^{98} + 226 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(1980))$$

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
1980.2.a $$\chi_{1980}(1, \cdot)$$ 1980.2.a.a 1 1
1980.2.a.b 1
1980.2.a.c 1
1980.2.a.d 1
1980.2.a.e 1
1980.2.a.f 1
1980.2.a.g 2
1980.2.a.h 2
1980.2.a.i 2
1980.2.a.j 2
1980.2.a.k 2
1980.2.a.l 2
1980.2.c $$\chi_{1980}(1189, \cdot)$$ 1980.2.c.a 2 1
1980.2.c.b 2
1980.2.c.c 2
1980.2.c.d 2
1980.2.c.e 2
1980.2.c.f 4
1980.2.c.g 4
1980.2.c.h 4
1980.2.c.i 4
1980.2.d $$\chi_{1980}(1781, \cdot)$$ 1980.2.d.a 16 1
1980.2.f $$\chi_{1980}(1871, \cdot)$$ 1980.2.f.a 40 1
1980.2.f.b 40
1980.2.i $$\chi_{1980}(1099, \cdot)$$ n/a 176 1
1980.2.k $$\chi_{1980}(1891, \cdot)$$ n/a 120 1
1980.2.l $$\chi_{1980}(1079, \cdot)$$ n/a 120 1
1980.2.n $$\chi_{1980}(989, \cdot)$$ 1980.2.n.a 24 1
1980.2.q $$\chi_{1980}(661, \cdot)$$ 1980.2.q.a 2 2
1980.2.q.b 2
1980.2.q.c 2
1980.2.q.d 4
1980.2.q.e 14
1980.2.q.f 16
1980.2.q.g 18
1980.2.q.h 22
1980.2.r $$\chi_{1980}(1187, \cdot)$$ n/a 288 2
1980.2.u $$\chi_{1980}(1277, \cdot)$$ 1980.2.u.a 20 2
1980.2.u.b 20
1980.2.v $$\chi_{1980}(1387, \cdot)$$ n/a 300 2
1980.2.y $$\chi_{1980}(1297, \cdot)$$ 1980.2.y.a 4 2
1980.2.y.b 8
1980.2.y.c 24
1980.2.y.d 24
1980.2.z $$\chi_{1980}(181, \cdot)$$ 1980.2.z.a 8 4
1980.2.z.b 8
1980.2.z.c 8
1980.2.z.d 8
1980.2.z.e 8
1980.2.z.f 8
1980.2.z.g 16
1980.2.z.h 16
1980.2.ba $$\chi_{1980}(329, \cdot)$$ n/a 144 2
1980.2.be $$\chi_{1980}(571, \cdot)$$ n/a 576 2
1980.2.bf $$\chi_{1980}(419, \cdot)$$ n/a 720 2
1980.2.bh $$\chi_{1980}(551, \cdot)$$ n/a 480 2
1980.2.bk $$\chi_{1980}(439, \cdot)$$ n/a 848 2
1980.2.bm $$\chi_{1980}(529, \cdot)$$ n/a 120 2
1980.2.bn $$\chi_{1980}(461, \cdot)$$ 1980.2.bn.a 96 2
1980.2.br $$\chi_{1980}(629, \cdot)$$ 1980.2.br.a 96 4
1980.2.bt $$\chi_{1980}(179, \cdot)$$ n/a 576 4
1980.2.bu $$\chi_{1980}(271, \cdot)$$ n/a 480 4
1980.2.bw $$\chi_{1980}(19, \cdot)$$ n/a 704 4
1980.2.bz $$\chi_{1980}(71, \cdot)$$ n/a 384 4
1980.2.cb $$\chi_{1980}(161, \cdot)$$ 1980.2.cb.a 64 4
1980.2.cc $$\chi_{1980}(289, \cdot)$$ n/a 120 4
1980.2.ce $$\chi_{1980}(353, \cdot)$$ n/a 240 4
1980.2.ch $$\chi_{1980}(263, \cdot)$$ n/a 1696 4
1980.2.ci $$\chi_{1980}(373, \cdot)$$ n/a 288 4
1980.2.cl $$\chi_{1980}(67, \cdot)$$ n/a 1440 4
1980.2.cm $$\chi_{1980}(301, \cdot)$$ n/a 384 8
1980.2.cn $$\chi_{1980}(73, \cdot)$$ n/a 240 8
1980.2.cq $$\chi_{1980}(163, \cdot)$$ n/a 1408 8
1980.2.cr $$\chi_{1980}(53, \cdot)$$ n/a 192 8
1980.2.cu $$\chi_{1980}(107, \cdot)$$ n/a 1152 8
1980.2.cw $$\chi_{1980}(41, \cdot)$$ n/a 384 8
1980.2.cx $$\chi_{1980}(49, \cdot)$$ n/a 576 8
1980.2.cz $$\chi_{1980}(79, \cdot)$$ n/a 3392 8
1980.2.dc $$\chi_{1980}(191, \cdot)$$ n/a 2304 8
1980.2.de $$\chi_{1980}(59, \cdot)$$ n/a 3392 8
1980.2.df $$\chi_{1980}(151, \cdot)$$ n/a 2304 8
1980.2.dj $$\chi_{1980}(29, \cdot)$$ n/a 576 8
1980.2.dk $$\chi_{1980}(103, \cdot)$$ n/a 6784 16
1980.2.dn $$\chi_{1980}(13, \cdot)$$ n/a 1152 16
1980.2.do $$\chi_{1980}(83, \cdot)$$ n/a 6784 16
1980.2.dr $$\chi_{1980}(113, \cdot)$$ n/a 1152 16

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(1980))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(1980)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(11))$$$$^{\oplus 18}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(15))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(18))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(20))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(22))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(30))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(33))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(36))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(44))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(45))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(55))$$$$^{\oplus 9}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(60))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(66))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(90))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(99))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(110))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(132))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(165))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(180))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(198))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(220))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(330))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(396))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(495))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(660))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(990))$$$$^{\oplus 2}$$