# Properties

 Label 128.4 Level 128 Weight 4 Dimension 840 Nonzero newspaces 5 Newform subspaces 17 Sturm bound 4096 Trace bound 9

## Defining parameters

 Level: $$N$$ = $$128 = 2^{7}$$ Weight: $$k$$ = $$4$$ Nonzero newspaces: $$5$$ Newform subspaces: $$17$$ Sturm bound: $$4096$$ Trace bound: $$9$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(\Gamma_1(128))$$.

Total New Old
Modular forms 1616 888 728
Cusp forms 1456 840 616
Eisenstein series 160 48 112

## Trace form

 $$840 q - 16 q^{2} - 12 q^{3} - 16 q^{4} - 16 q^{5} - 16 q^{6} - 12 q^{7} - 16 q^{8} - 20 q^{9} + O(q^{10})$$ $$840 q - 16 q^{2} - 12 q^{3} - 16 q^{4} - 16 q^{5} - 16 q^{6} - 12 q^{7} - 16 q^{8} - 20 q^{9} - 16 q^{10} - 12 q^{11} - 16 q^{12} - 16 q^{13} - 16 q^{14} - 16 q^{15} - 16 q^{16} - 24 q^{17} - 16 q^{18} - 12 q^{19} - 16 q^{20} - 124 q^{21} - 16 q^{22} - 340 q^{23} - 16 q^{24} - 196 q^{25} - 16 q^{26} + 252 q^{27} - 16 q^{28} + 384 q^{29} - 16 q^{30} + 736 q^{31} - 16 q^{32} + 896 q^{33} - 16 q^{34} + 444 q^{35} - 16 q^{36} - 16 q^{38} - 612 q^{39} - 16 q^{40} - 964 q^{41} - 16 q^{42} - 820 q^{43} - 16 q^{44} - 300 q^{45} - 16 q^{46} - 16 q^{47} - 16 q^{48} + 1348 q^{49} + 5696 q^{50} + 1368 q^{51} + 6608 q^{52} + 1488 q^{53} + 3440 q^{54} + 276 q^{55} - 800 q^{56} - 1364 q^{57} - 4768 q^{58} - 1388 q^{59} - 9808 q^{60} - 3664 q^{61} - 5872 q^{62} - 2512 q^{63} - 12112 q^{64} - 3920 q^{65} - 10960 q^{66} - 2052 q^{67} - 4144 q^{68} - 2236 q^{69} - 4048 q^{70} - 236 q^{71} + 1280 q^{72} + 1708 q^{73} + 5248 q^{74} + 1696 q^{75} + 11888 q^{76} + 2420 q^{77} + 14096 q^{78} - 16 q^{79} + 10016 q^{80} - 788 q^{81} - 16 q^{82} - 2452 q^{83} - 16 q^{84} + 504 q^{85} - 16 q^{86} + 1276 q^{87} - 16 q^{88} + 3372 q^{89} - 16 q^{90} + 3588 q^{91} - 16 q^{92} + 4256 q^{93} - 16 q^{94} + 6072 q^{95} - 16 q^{96} + 5920 q^{97} - 16 q^{98} + 5408 q^{99} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(\Gamma_1(128))$$

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
128.4.a $$\chi_{128}(1, \cdot)$$ 128.4.a.a 1 1
128.4.a.b 1
128.4.a.c 1
128.4.a.d 1
128.4.a.e 2
128.4.a.f 2
128.4.a.g 2
128.4.a.h 2
128.4.b $$\chi_{128}(65, \cdot)$$ 128.4.b.a 2 1
128.4.b.b 2
128.4.b.c 2
128.4.b.d 2
128.4.b.e 4
128.4.e $$\chi_{128}(33, \cdot)$$ 128.4.e.a 10 2
128.4.e.b 10
128.4.g $$\chi_{128}(17, \cdot)$$ 128.4.g.a 44 4
128.4.i $$\chi_{128}(9, \cdot)$$ None 0 8
128.4.k $$\chi_{128}(5, \cdot)$$ 128.4.k.a 752 16

## Decomposition of $$S_{4}^{\mathrm{old}}(\Gamma_1(128))$$ into lower level spaces

$$S_{4}^{\mathrm{old}}(\Gamma_1(128)) \cong$$ $$S_{4}^{\mathrm{new}}(\Gamma_1(8))$$$$^{\oplus 5}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(16))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(32))$$$$^{\oplus 3}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(64))$$$$^{\oplus 2}$$