# Properties

 Label 384.5 Level 384 Weight 5 Dimension 6864 Nonzero newspaces 10 Sturm bound 40960 Trace bound 25

## Defining parameters

 Level: $$N$$ = $$384 = 2^{7} \cdot 3$$ Weight: $$k$$ = $$5$$ Nonzero newspaces: $$10$$ Sturm bound: $$40960$$ Trace bound: $$25$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{5}(\Gamma_1(384))$$.

Total New Old
Modular forms 16704 6960 9744
Cusp forms 16064 6864 9200
Eisenstein series 640 96 544

## Trace form

 $$6864 q - 12 q^{3} - 32 q^{4} - 16 q^{6} - 24 q^{7} - 20 q^{9} + O(q^{10})$$ $$6864 q - 12 q^{3} - 32 q^{4} - 16 q^{6} - 24 q^{7} - 20 q^{9} - 32 q^{10} - 16 q^{12} - 32 q^{13} - 16 q^{15} - 32 q^{16} - 16 q^{18} - 24 q^{19} - 340 q^{21} - 32 q^{22} - 2304 q^{23} - 16 q^{24} + 2648 q^{25} + 3636 q^{27} - 32 q^{28} + 3456 q^{29} - 16 q^{30} - 16 q^{31} - 4000 q^{33} - 32 q^{34} - 10368 q^{35} - 16 q^{36} - 7328 q^{37} - 2700 q^{39} - 32 q^{40} + 5760 q^{41} - 16 q^{42} + 11112 q^{43} + 2484 q^{45} - 32 q^{46} - 16 q^{48} + 19160 q^{49} + 86112 q^{50} + 8376 q^{51} + 35872 q^{52} - 3840 q^{53} - 7792 q^{54} - 23576 q^{55} - 98784 q^{56} - 29972 q^{57} - 131072 q^{58} - 26112 q^{59} - 63952 q^{60} - 30240 q^{61} - 23616 q^{62} + 8 q^{63} + 48736 q^{64} + 32256 q^{65} + 70832 q^{66} + 37736 q^{67} + 106560 q^{68} + 39476 q^{69} + 244576 q^{70} + 39936 q^{71} - 16 q^{72} + 58840 q^{73} + 66528 q^{74} + 4792 q^{75} - 56608 q^{76} - 37632 q^{77} - 99376 q^{78} - 50208 q^{79} - 210528 q^{80} + 15208 q^{81} - 32 q^{82} - 16 q^{84} - 10032 q^{85} - 49292 q^{87} - 32 q^{88} - 16 q^{90} - 24 q^{91} - 17488 q^{93} - 32 q^{94} - 16 q^{96} - 64 q^{97} + 46580 q^{99} + O(q^{100})$$

## Decomposition of $$S_{5}^{\mathrm{new}}(\Gamma_1(384))$$

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
384.5.b $$\chi_{384}(319, \cdot)$$ 384.5.b.a 4 1
384.5.b.b 4
384.5.b.c 8
384.5.b.d 16
384.5.e $$\chi_{384}(257, \cdot)$$ 384.5.e.a 16 1
384.5.e.b 16
384.5.e.c 16
384.5.e.d 16
384.5.g $$\chi_{384}(127, \cdot)$$ 384.5.g.a 16 1
384.5.g.b 16
384.5.h $$\chi_{384}(65, \cdot)$$ 384.5.h.a 2 1
384.5.h.b 2
384.5.h.c 2
384.5.h.d 2
384.5.h.e 4
384.5.h.f 4
384.5.h.g 16
384.5.h.h 32
384.5.i $$\chi_{384}(161, \cdot)$$ n/a 120 2
384.5.l $$\chi_{384}(31, \cdot)$$ 384.5.l.a 32 2
384.5.l.b 32
384.5.m $$\chi_{384}(79, \cdot)$$ n/a 128 4
384.5.p $$\chi_{384}(17, \cdot)$$ n/a 248 4
384.5.q $$\chi_{384}(41, \cdot)$$ None 0 8
384.5.t $$\chi_{384}(7, \cdot)$$ None 0 8
384.5.u $$\chi_{384}(19, \cdot)$$ n/a 2048 16
384.5.x $$\chi_{384}(5, \cdot)$$ n/a 4064 16

"n/a" means that newforms for that character have not been added to the database yet

## Decomposition of $$S_{5}^{\mathrm{old}}(\Gamma_1(384))$$ into lower level spaces

$$S_{5}^{\mathrm{old}}(\Gamma_1(384)) \cong$$ $$S_{5}^{\mathrm{new}}(\Gamma_1(4))$$$$^{\oplus 12}$$$$\oplus$$$$S_{5}^{\mathrm{new}}(\Gamma_1(6))$$$$^{\oplus 7}$$$$\oplus$$$$S_{5}^{\mathrm{new}}(\Gamma_1(8))$$$$^{\oplus 10}$$$$\oplus$$$$S_{5}^{\mathrm{new}}(\Gamma_1(12))$$$$^{\oplus 6}$$$$\oplus$$$$S_{5}^{\mathrm{new}}(\Gamma_1(16))$$$$^{\oplus 8}$$$$\oplus$$$$S_{5}^{\mathrm{new}}(\Gamma_1(24))$$$$^{\oplus 5}$$$$\oplus$$$$S_{5}^{\mathrm{new}}(\Gamma_1(32))$$$$^{\oplus 6}$$$$\oplus$$$$S_{5}^{\mathrm{new}}(\Gamma_1(48))$$$$^{\oplus 4}$$$$\oplus$$$$S_{5}^{\mathrm{new}}(\Gamma_1(64))$$$$^{\oplus 4}$$$$\oplus$$$$S_{5}^{\mathrm{new}}(\Gamma_1(96))$$$$^{\oplus 3}$$$$\oplus$$$$S_{5}^{\mathrm{new}}(\Gamma_1(128))$$$$^{\oplus 2}$$$$\oplus$$$$S_{5}^{\mathrm{new}}(\Gamma_1(192))$$$$^{\oplus 2}$$