Properties

 Label 384.3 Level 384 Weight 3 Dimension 3408 Nonzero newspaces 10 Newform subspaces 26 Sturm bound 24576 Trace bound 25

Defining parameters

 Level: $$N$$ = $$384 = 2^{7} \cdot 3$$ Weight: $$k$$ = $$3$$ Nonzero newspaces: $$10$$ Newform subspaces: $$26$$ Sturm bound: $$24576$$ Trace bound: $$25$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(\Gamma_1(384))$$.

Total New Old
Modular forms 8512 3504 5008
Cusp forms 7872 3408 4464
Eisenstein series 640 96 544

Trace form

 $$3408 q - 12 q^{3} - 32 q^{4} - 16 q^{6} - 24 q^{7} - 20 q^{9} + O(q^{10})$$ $$3408 q - 12 q^{3} - 32 q^{4} - 16 q^{6} - 24 q^{7} - 20 q^{9} - 32 q^{10} - 16 q^{12} - 32 q^{13} - 16 q^{15} - 32 q^{16} - 16 q^{18} - 24 q^{19} - 52 q^{21} - 32 q^{22} - 128 q^{23} - 16 q^{24} - 232 q^{25} - 108 q^{27} - 32 q^{28} - 64 q^{29} - 16 q^{30} - 16 q^{31} + 32 q^{33} - 32 q^{34} + 192 q^{35} - 16 q^{36} + 160 q^{37} + 180 q^{39} - 32 q^{40} + 320 q^{41} - 16 q^{42} + 168 q^{43} + 84 q^{45} - 32 q^{46} - 16 q^{48} + 344 q^{49} + 1248 q^{50} + 216 q^{51} + 2080 q^{52} + 640 q^{53} + 272 q^{54} + 488 q^{55} + 1568 q^{56} + 364 q^{57} + 1408 q^{58} + 256 q^{59} + 560 q^{60} + 224 q^{61} + 192 q^{62} + 8 q^{63} - 416 q^{64} - 256 q^{65} - 592 q^{66} - 344 q^{67} - 960 q^{68} - 364 q^{69} - 2720 q^{70} - 512 q^{71} - 16 q^{72} - 1320 q^{73} - 2464 q^{74} - 296 q^{75} - 3360 q^{76} - 896 q^{77} - 1456 q^{78} - 544 q^{79} - 1632 q^{80} + 424 q^{81} - 32 q^{82} - 16 q^{84} - 432 q^{85} + 436 q^{87} - 32 q^{88} - 16 q^{90} - 24 q^{91} + 80 q^{93} - 32 q^{94} - 16 q^{96} - 64 q^{97} - 268 q^{99} + O(q^{100})$$

Decomposition of $$S_{3}^{\mathrm{new}}(\Gamma_1(384))$$

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
384.3.b $$\chi_{384}(319, \cdot)$$ 384.3.b.a 4 1
384.3.b.b 4
384.3.b.c 8
384.3.e $$\chi_{384}(257, \cdot)$$ 384.3.e.a 8 1
384.3.e.b 8
384.3.e.c 8
384.3.e.d 8
384.3.g $$\chi_{384}(127, \cdot)$$ 384.3.g.a 8 1
384.3.g.b 8
384.3.h $$\chi_{384}(65, \cdot)$$ 384.3.h.a 2 1
384.3.h.b 2
384.3.h.c 2
384.3.h.d 2
384.3.h.e 4
384.3.h.f 4
384.3.h.g 16
384.3.i $$\chi_{384}(161, \cdot)$$ 384.3.i.a 8 2
384.3.i.b 8
384.3.i.c 20
384.3.i.d 20
384.3.l $$\chi_{384}(31, \cdot)$$ 384.3.l.a 16 2
384.3.l.b 16
384.3.m $$\chi_{384}(79, \cdot)$$ 384.3.m.a 64 4
384.3.p $$\chi_{384}(17, \cdot)$$ 384.3.p.a 120 4
384.3.q $$\chi_{384}(41, \cdot)$$ None 0 8
384.3.t $$\chi_{384}(7, \cdot)$$ None 0 8
384.3.u $$\chi_{384}(19, \cdot)$$ 384.3.u.a 1024 16
384.3.x $$\chi_{384}(5, \cdot)$$ 384.3.x.a 2016 16

Decomposition of $$S_{3}^{\mathrm{old}}(\Gamma_1(384))$$ into lower level spaces

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