# Properties

 Label 980.2 Level 980 Weight 2 Dimension 14191 Nonzero newspaces 24 Newform subspaces 108 Sturm bound 112896 Trace bound 5

## Defining parameters

 Level: $$N$$ = $$980 = 2^{2} \cdot 5 \cdot 7^{2}$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$24$$ Newform subspaces: $$108$$ Sturm bound: $$112896$$ Trace bound: $$5$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(980))$$.

Total New Old
Modular forms 29424 14775 14649
Cusp forms 27025 14191 12834
Eisenstein series 2399 584 1815

## Trace form

 $$14191 q - 32 q^{2} - 6 q^{3} - 30 q^{4} - 101 q^{5} - 78 q^{6} - 8 q^{7} - 38 q^{8} - 51 q^{9} + O(q^{10})$$ $$14191 q - 32 q^{2} - 6 q^{3} - 30 q^{4} - 101 q^{5} - 78 q^{6} - 8 q^{7} - 38 q^{8} - 51 q^{9} - 21 q^{10} + 12 q^{11} + 30 q^{12} - 20 q^{13} - 12 q^{14} + 14 q^{15} - 50 q^{16} - 72 q^{17} - 12 q^{18} - 43 q^{20} - 194 q^{21} - 102 q^{22} - 6 q^{23} - 66 q^{24} - 33 q^{25} - 122 q^{26} + 36 q^{27} - 84 q^{28} - 6 q^{29} - 51 q^{30} + 72 q^{31} - 22 q^{32} + 120 q^{33} - 42 q^{34} + 51 q^{35} - 90 q^{36} + 108 q^{37} + 54 q^{38} + 206 q^{39} - 19 q^{40} + 14 q^{41} - 6 q^{42} + 90 q^{43} + 54 q^{44} + 116 q^{45} - 30 q^{46} + 138 q^{47} - 60 q^{48} + 76 q^{49} - 110 q^{50} + 168 q^{51} - 118 q^{52} - 24 q^{53} - 234 q^{54} + 21 q^{55} - 132 q^{56} - 216 q^{57} - 226 q^{58} - 36 q^{59} - 303 q^{60} - 244 q^{61} - 234 q^{62} - 60 q^{63} - 282 q^{64} - 210 q^{65} - 390 q^{66} - 162 q^{67} - 294 q^{68} - 264 q^{69} - 225 q^{70} - 108 q^{71} - 450 q^{72} - 124 q^{73} - 330 q^{74} - 192 q^{75} - 366 q^{76} - 90 q^{77} - 438 q^{78} - 132 q^{79} - 350 q^{80} - 357 q^{81} - 404 q^{82} - 162 q^{83} - 588 q^{84} - 270 q^{85} - 540 q^{86} - 300 q^{87} - 600 q^{88} + 66 q^{89} - 576 q^{90} - 136 q^{91} - 348 q^{92} - 312 q^{93} - 516 q^{94} + 34 q^{95} - 888 q^{96} - 196 q^{97} - 648 q^{98} - 96 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(980))$$

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
980.2.a $$\chi_{980}(1, \cdot)$$ 980.2.a.a 1 1
980.2.a.b 1
980.2.a.c 1
980.2.a.d 1
980.2.a.e 1
980.2.a.f 1
980.2.a.g 1
980.2.a.h 1
980.2.a.i 1
980.2.a.j 2
980.2.a.k 2
980.2.c $$\chi_{980}(979, \cdot)$$ 980.2.c.a 8 1
980.2.c.b 8
980.2.c.c 16
980.2.c.d 32
980.2.c.e 48
980.2.e $$\chi_{980}(589, \cdot)$$ 980.2.e.a 2 1
980.2.e.b 2
980.2.e.c 4
980.2.e.d 4
980.2.e.e 4
980.2.e.f 4
980.2.g $$\chi_{980}(391, \cdot)$$ 980.2.g.a 32 1
980.2.g.b 48
980.2.i $$\chi_{980}(361, \cdot)$$ 980.2.i.a 2 2
980.2.i.b 2
980.2.i.c 2
980.2.i.d 2
980.2.i.e 2
980.2.i.f 2
980.2.i.g 2
980.2.i.h 2
980.2.i.i 2
980.2.i.j 2
980.2.i.k 4
980.2.i.l 4
980.2.k $$\chi_{980}(687, \cdot)$$ 980.2.k.a 2 2
980.2.k.b 2
980.2.k.c 2
980.2.k.d 4
980.2.k.e 4
980.2.k.f 4
980.2.k.g 4
980.2.k.h 8
980.2.k.i 32
980.2.k.j 36
980.2.k.k 36
980.2.k.l 36
980.2.k.m 56
980.2.m $$\chi_{980}(97, \cdot)$$ 980.2.m.a 16 2
980.2.m.b 24
980.2.o $$\chi_{980}(31, \cdot)$$ 980.2.o.a 4 2
980.2.o.b 4
980.2.o.c 4
980.2.o.d 4
980.2.o.e 16
980.2.o.f 32
980.2.o.g 96
980.2.q $$\chi_{980}(569, \cdot)$$ 980.2.q.a 4 2
980.2.q.b 4
980.2.q.c 4
980.2.q.d 4
980.2.q.e 4
980.2.q.f 4
980.2.q.g 4
980.2.q.h 4
980.2.q.i 8
980.2.s $$\chi_{980}(19, \cdot)$$ 980.2.s.a 8 2
980.2.s.b 8
980.2.s.c 16
980.2.s.d 32
980.2.s.e 32
980.2.s.f 32
980.2.s.g 96
980.2.u $$\chi_{980}(141, \cdot)$$ 980.2.u.a 54 6
980.2.u.b 66
980.2.v $$\chi_{980}(117, \cdot)$$ 980.2.v.a 16 4
980.2.v.b 16
980.2.v.c 48
980.2.x $$\chi_{980}(67, \cdot)$$ 980.2.x.a 4 4
980.2.x.b 4
980.2.x.c 4
980.2.x.d 4
980.2.x.e 8
980.2.x.f 8
980.2.x.g 8
980.2.x.h 8
980.2.x.i 8
980.2.x.j 64
980.2.x.k 72
980.2.x.l 72
980.2.x.m 72
980.2.x.n 112
980.2.bb $$\chi_{980}(111, \cdot)$$ 980.2.bb.a 672 6
980.2.bd $$\chi_{980}(29, \cdot)$$ 980.2.bd.a 168 6
980.2.bf $$\chi_{980}(139, \cdot)$$ 980.2.bf.a 24 6
980.2.bf.b 960
980.2.bg $$\chi_{980}(81, \cdot)$$ 980.2.bg.a 12 12
980.2.bg.b 84
980.2.bg.c 120
980.2.bi $$\chi_{980}(13, \cdot)$$ 980.2.bi.a 336 12
980.2.bk $$\chi_{980}(43, \cdot)$$ 980.2.bk.a 1968 12
980.2.bl $$\chi_{980}(59, \cdot)$$ 980.2.bl.a 48 12
980.2.bl.b 1920
980.2.bn $$\chi_{980}(9, \cdot)$$ 980.2.bn.a 336 12
980.2.bp $$\chi_{980}(131, \cdot)$$ 980.2.bp.a 1344 12
980.2.bs $$\chi_{980}(23, \cdot)$$ 980.2.bs.a 3936 24
980.2.bu $$\chi_{980}(17, \cdot)$$ 980.2.bu.a 672 24

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(980))$$ into lower level spaces

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