# Properties

 Label 80.3 Level 80 Weight 3 Dimension 184 Nonzero newspaces 7 Newform subspaces 11 Sturm bound 1152 Trace bound 3

## Defining parameters

 Level: $$N$$ = $$80 = 2^{4} \cdot 5$$ Weight: $$k$$ = $$3$$ Nonzero newspaces: $$7$$ Newform subspaces: $$11$$ Sturm bound: $$1152$$ Trace bound: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(\Gamma_1(80))$$.

Total New Old
Modular forms 440 212 228
Cusp forms 328 184 144
Eisenstein series 112 28 84

## Trace form

 $$184 q - 4 q^{2} - 2 q^{3} + 8 q^{4} - 2 q^{5} + 2 q^{7} - 16 q^{8} - 18 q^{9} + O(q^{10})$$ $$184 q - 4 q^{2} - 2 q^{3} + 8 q^{4} - 2 q^{5} + 2 q^{7} - 16 q^{8} - 18 q^{9} - 44 q^{10} + 24 q^{11} - 112 q^{12} - 2 q^{13} - 32 q^{14} + 42 q^{15} + 64 q^{16} + 66 q^{17} + 140 q^{18} - 68 q^{19} + 76 q^{20} - 12 q^{21} + 96 q^{22} - 174 q^{23} - 104 q^{24} - 36 q^{25} - 208 q^{26} - 248 q^{27} - 248 q^{28} - 176 q^{29} - 348 q^{30} - 76 q^{31} - 304 q^{32} - 220 q^{33} - 176 q^{34} + 46 q^{35} - 104 q^{36} - 42 q^{37} - 144 q^{38} + 376 q^{39} + 32 q^{40} + 24 q^{41} + 280 q^{42} + 286 q^{43} + 232 q^{44} + 268 q^{45} + 376 q^{46} + 234 q^{47} + 616 q^{48} + 458 q^{49} + 336 q^{50} - 36 q^{51} + 208 q^{52} - 90 q^{53} + 216 q^{54} - 112 q^{55} + 320 q^{56} + 80 q^{57} + 344 q^{58} - 420 q^{59} + 280 q^{60} - 68 q^{61} + 280 q^{62} - 622 q^{63} + 224 q^{64} - 218 q^{65} + 424 q^{66} - 466 q^{67} + 384 q^{68} - 256 q^{69} + 656 q^{70} - 420 q^{71} + 728 q^{72} + 18 q^{73} + 616 q^{74} - 470 q^{75} + 552 q^{76} + 268 q^{77} + 280 q^{78} - 320 q^{80} - 176 q^{81} - 824 q^{82} - 50 q^{83} - 1232 q^{84} + 446 q^{85} - 1000 q^{86} + 496 q^{87} - 784 q^{88} + 276 q^{89} - 1168 q^{90} + 956 q^{91} - 736 q^{92} + 564 q^{93} - 944 q^{94} + 1000 q^{95} - 944 q^{96} - 134 q^{97} - 876 q^{98} + 1092 q^{99} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(\Gamma_1(80))$$

We only show spaces with odd 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
80.3.b $$\chi_{80}(31, \cdot)$$ 80.3.b.a 4 1
80.3.e $$\chi_{80}(39, \cdot)$$ None 0 1
80.3.g $$\chi_{80}(71, \cdot)$$ None 0 1
80.3.h $$\chi_{80}(79, \cdot)$$ 80.3.h.a 2 1
80.3.h.b 4
80.3.i $$\chi_{80}(13, \cdot)$$ 80.3.i.a 44 2
80.3.k $$\chi_{80}(19, \cdot)$$ 80.3.k.a 44 2
80.3.m $$\chi_{80}(57, \cdot)$$ None 0 2
80.3.p $$\chi_{80}(17, \cdot)$$ 80.3.p.a 2 2
80.3.p.b 2
80.3.p.c 2
80.3.p.d 4
80.3.r $$\chi_{80}(11, \cdot)$$ 80.3.r.a 32 2
80.3.t $$\chi_{80}(53, \cdot)$$ 80.3.t.a 44 2

## Decomposition of $$S_{3}^{\mathrm{old}}(\Gamma_1(80))$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(\Gamma_1(80)) \cong$$ $$S_{3}^{\mathrm{new}}(\Gamma_1(8))$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(10))$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(16))$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(20))$$$$^{\oplus 3}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(40))$$$$^{\oplus 2}$$