# Properties

 Label 100.3 Level 100 Weight 3 Dimension 302 Nonzero newspaces 6 Newform subspaces 14 Sturm bound 1800 Trace bound 2

## Defining parameters

 Level: $$N$$ = $$100 = 2^{2} \cdot 5^{2}$$ Weight: $$k$$ = $$3$$ Nonzero newspaces: $$6$$ Newform subspaces: $$14$$ Sturm bound: $$1800$$ Trace bound: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(\Gamma_1(100))$$.

Total New Old
Modular forms 670 344 326
Cusp forms 530 302 228
Eisenstein series 140 42 98

## Trace form

 $$302q - 6q^{2} - 4q^{3} - 2q^{4} - 10q^{5} + 14q^{6} + 28q^{7} + 6q^{8} - 4q^{9} + O(q^{10})$$ $$302q - 6q^{2} - 4q^{3} - 2q^{4} - 10q^{5} + 14q^{6} + 28q^{7} + 6q^{8} - 4q^{9} - 16q^{10} - 40q^{11} - 90q^{12} - 24q^{13} - 122q^{14} - 2q^{15} - 114q^{16} + 94q^{17} - 54q^{18} + 100q^{19} + 34q^{20} + 64q^{21} + 150q^{22} + 112q^{23} + 268q^{24} - 92q^{25} + 188q^{26} - 154q^{27} + 70q^{28} - 184q^{29} - 50q^{30} - 84q^{31} - 266q^{32} - 400q^{33} - 322q^{34} - 208q^{35} - 330q^{36} - 244q^{37} - 500q^{38} - 400q^{39} - 436q^{40} - 92q^{41} - 470q^{42} - 180q^{43} - 200q^{44} - 120q^{45} + 74q^{46} + 76q^{47} - 140q^{48} + 296q^{49} - 6q^{50} + 112q^{51} + 148q^{52} + 540q^{53} + 416q^{54} + 300q^{55} + 114q^{56} + 652q^{57} + 692q^{58} + 550q^{59} + 1050q^{60} + 184q^{61} + 800q^{62} + 914q^{63} + 568q^{64} + 260q^{65} + 110q^{66} + 308q^{67} + 262q^{68} - 614q^{69} + 70q^{70} - 272q^{71} + 224q^{72} - 704q^{73} + 388q^{74} - 18q^{75} + 100q^{76} - 460q^{77} + 240q^{78} - 200q^{79} + 134q^{80} - 232q^{81} + 438q^{82} - 698q^{83} + 1126q^{84} - 1208q^{85} + 314q^{86} - 1098q^{87} + 990q^{88} - 1064q^{89} + 1454q^{90} - 156q^{91} + 930q^{92} - 74q^{93} + 998q^{94} - 224q^{95} + 794q^{96} - 64q^{97} - 114q^{98} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(\Gamma_1(100))$$

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
100.3.b $$\chi_{100}(51, \cdot)$$ 100.3.b.a 1 1
100.3.b.b 1
100.3.b.c 2
100.3.b.d 4
100.3.b.e 4
100.3.b.f 4
100.3.d $$\chi_{100}(99, \cdot)$$ 100.3.d.a 8 1
100.3.d.b 8
100.3.f $$\chi_{100}(57, \cdot)$$ 100.3.f.a 2 2
100.3.f.b 4
100.3.h $$\chi_{100}(19, \cdot)$$ 100.3.h.a 8 4
100.3.h.b 104
100.3.j $$\chi_{100}(11, \cdot)$$ 100.3.j.a 112 4
100.3.k $$\chi_{100}(13, \cdot)$$ 100.3.k.a 40 8

## Decomposition of $$S_{3}^{\mathrm{old}}(\Gamma_1(100))$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(\Gamma_1(100)) \cong$$ $$S_{3}^{\mathrm{new}}(\Gamma_1(10))$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(20))$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(25))$$$$^{\oplus 3}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(50))$$$$^{\oplus 2}$$