# Properties

 Label 20.3 Level 20 Weight 3 Dimension 10 Nonzero newspaces 3 Newform subspaces 5 Sturm bound 72 Trace bound 2

## Defining parameters

 Level: $$N$$ = $$20 = 2^{2} \cdot 5$$ Weight: $$k$$ = $$3$$ Nonzero newspaces: $$3$$ Newform subspaces: $$5$$ Sturm bound: $$72$$ Trace bound: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(\Gamma_1(20))$$.

Total New Old
Modular forms 34 14 20
Cusp forms 14 10 4
Eisenstein series 20 4 16

## Trace form

 $$10 q - 2 q^{2} + 2 q^{3} - 4 q^{4} - 10 q^{5} - 16 q^{6} - 14 q^{7} - 8 q^{8} - 8 q^{9} + O(q^{10})$$ $$10 q - 2 q^{2} + 2 q^{3} - 4 q^{4} - 10 q^{5} - 16 q^{6} - 14 q^{7} - 8 q^{8} - 8 q^{9} + 6 q^{10} + 20 q^{11} + 40 q^{12} + 2 q^{13} + 56 q^{14} + 2 q^{15} + 48 q^{16} - 22 q^{17} + 22 q^{18} - 44 q^{20} - 20 q^{21} - 80 q^{22} - 46 q^{23} - 144 q^{24} + 42 q^{25} - 108 q^{26} + 32 q^{27} - 40 q^{28} + 32 q^{29} + 40 q^{30} - 28 q^{31} + 128 q^{32} + 100 q^{33} + 156 q^{34} + 98 q^{35} + 92 q^{36} + 82 q^{37} + 80 q^{38} - 24 q^{40} - 52 q^{41} - 120 q^{42} - 30 q^{43} - 80 q^{44} - 220 q^{45} - 136 q^{46} - 78 q^{47} - 168 q^{49} + 86 q^{50} + 4 q^{51} + 56 q^{52} - 190 q^{53} + 112 q^{54} - 60 q^{55} + 144 q^{56} - 16 q^{57} - 36 q^{58} + 40 q^{60} + 140 q^{61} - 80 q^{62} + 98 q^{63} - 64 q^{64} + 250 q^{65} + 80 q^{66} - 14 q^{67} - 136 q^{68} + 472 q^{69} - 80 q^{70} + 196 q^{71} - 72 q^{72} + 362 q^{73} - 204 q^{74} - 62 q^{75} + 100 q^{77} - 80 q^{78} - 144 q^{80} - 366 q^{81} + 116 q^{82} - 126 q^{83} + 32 q^{84} - 302 q^{85} + 224 q^{86} - 16 q^{87} + 160 q^{88} - 528 q^{89} - 114 q^{90} - 252 q^{91} - 120 q^{92} - 428 q^{93} - 104 q^{94} + 64 q^{95} - 256 q^{96} - 198 q^{97} + 102 q^{98} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(\Gamma_1(20))$$

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 available newforms together with their dimension.

Label $$\chi$$ Newforms Dimension $$\chi$$ degree
20.3.b $$\chi_{20}(11, \cdot)$$ 20.3.b.a 4 1
20.3.d $$\chi_{20}(19, \cdot)$$ 20.3.d.a 1 1
20.3.d.b 1
20.3.d.c 2
20.3.f $$\chi_{20}(13, \cdot)$$ 20.3.f.a 2 2

## Decomposition of $$S_{3}^{\mathrm{old}}(\Gamma_1(20))$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(\Gamma_1(20)) \cong$$ $$S_{3}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 6}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(2))$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(4))$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(5))$$$$^{\oplus 3}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(10))$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(20))$$$$^{\oplus 1}$$