## Defining parameters

 Level: $$N$$ = $$1792 = 2^{8} \cdot 7$$ Weight: $$k$$ = $$3$$ Nonzero newspaces: $$24$$ Sturm bound: $$589824$$ Trace bound: $$193$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(\Gamma_1(1792))$$.

Total New Old
Modular forms 198720 106504 92216
Cusp forms 194496 105464 89032
Eisenstein series 4224 1040 3184

## Trace form

 $$105464q - 128q^{2} - 96q^{3} - 128q^{4} - 128q^{5} - 128q^{6} - 120q^{7} - 320q^{8} - 160q^{9} + O(q^{10})$$ $$105464q - 128q^{2} - 96q^{3} - 128q^{4} - 128q^{5} - 128q^{6} - 120q^{7} - 320q^{8} - 160q^{9} - 128q^{10} - 96q^{11} - 128q^{12} - 128q^{13} - 160q^{14} - 240q^{15} - 128q^{16} - 192q^{17} - 128q^{18} - 96q^{19} - 128q^{20} - 160q^{21} - 320q^{22} - 96q^{23} - 128q^{24} - 160q^{25} - 128q^{26} - 96q^{27} - 160q^{28} - 320q^{29} - 128q^{30} - 112q^{31} - 128q^{32} - 224q^{33} - 128q^{34} - 120q^{35} - 320q^{36} - 128q^{37} - 128q^{38} - 96q^{39} - 128q^{40} - 160q^{41} - 160q^{42} - 240q^{43} - 128q^{44} - 272q^{45} - 128q^{46} - 96q^{47} - 128q^{48} - 240q^{49} - 320q^{50} - 864q^{51} - 128q^{52} - 768q^{53} - 128q^{54} - 1120q^{55} - 160q^{56} - 1168q^{57} - 128q^{58} - 608q^{59} - 128q^{60} - 384q^{61} - 128q^{62} - 112q^{63} - 320q^{64} - 32q^{65} - 128q^{66} + 544q^{67} - 128q^{68} + 640q^{69} - 160q^{70} + 784q^{71} - 128q^{72} + 1120q^{73} - 128q^{74} + 1440q^{75} - 128q^{76} + 288q^{77} - 320q^{78} + 928q^{79} - 128q^{80} + 456q^{81} - 128q^{82} - 96q^{83} - 160q^{84} + 80q^{85} - 128q^{86} - 96q^{87} - 128q^{88} - 160q^{89} - 128q^{90} - 120q^{91} - 320q^{92} + 160q^{93} - 128q^{94} - 112q^{95} - 128q^{96} - 224q^{97} - 160q^{98} - 96q^{99} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(\Gamma_1(1792))$$

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
1792.3.c $$\chi_{1792}(769, \cdot)$$ n/a 124 1
1792.3.d $$\chi_{1792}(1023, \cdot)$$ 1792.3.d.a 4 1
1792.3.d.b 4
1792.3.d.c 4
1792.3.d.d 6
1792.3.d.e 6
1792.3.d.f 8
1792.3.d.g 8
1792.3.d.h 12
1792.3.d.i 12
1792.3.d.j 16
1792.3.d.k 16
1792.3.g $$\chi_{1792}(127, \cdot)$$ 1792.3.g.a 4 1
1792.3.g.b 4
1792.3.g.c 4
1792.3.g.d 8
1792.3.g.e 8
1792.3.g.f 8
1792.3.g.g 12
1792.3.g.h 24
1792.3.g.i 24
1792.3.h $$\chi_{1792}(1665, \cdot)$$ n/a 124 1
1792.3.k $$\chi_{1792}(575, \cdot)$$ n/a 192 2
1792.3.l $$\chi_{1792}(321, \cdot)$$ n/a 256 2
1792.3.n $$\chi_{1792}(129, \cdot)$$ n/a 248 2
1792.3.o $$\chi_{1792}(639, \cdot)$$ n/a 248 2
1792.3.r $$\chi_{1792}(767, \cdot)$$ n/a 248 2
1792.3.s $$\chi_{1792}(257, \cdot)$$ n/a 248 2
1792.3.v $$\chi_{1792}(97, \cdot)$$ n/a 496 4
1792.3.w $$\chi_{1792}(351, \cdot)$$ n/a 384 4
1792.3.y $$\chi_{1792}(191, \cdot)$$ n/a 512 4
1792.3.bb $$\chi_{1792}(577, \cdot)$$ n/a 512 4
1792.3.be $$\chi_{1792}(15, \cdot)$$ n/a 768 8
1792.3.bf $$\chi_{1792}(209, \cdot)$$ n/a 1008 8
1792.3.bg $$\chi_{1792}(33, \cdot)$$ n/a 992 8
1792.3.bj $$\chi_{1792}(95, \cdot)$$ n/a 992 8
1792.3.bl $$\chi_{1792}(71, \cdot)$$ None 0 16
1792.3.bm $$\chi_{1792}(41, \cdot)$$ None 0 16
1792.3.bo $$\chi_{1792}(17, \cdot)$$ n/a 2016 16
1792.3.bp $$\chi_{1792}(79, \cdot)$$ n/a 2016 16
1792.3.bt $$\chi_{1792}(13, \cdot)$$ n/a 16320 32
1792.3.bu $$\chi_{1792}(43, \cdot)$$ n/a 12288 32
1792.3.bw $$\chi_{1792}(23, \cdot)$$ None 0 32
1792.3.bz $$\chi_{1792}(73, \cdot)$$ None 0 32
1792.3.ca $$\chi_{1792}(5, \cdot)$$ n/a 32640 64
1792.3.cd $$\chi_{1792}(11, \cdot)$$ n/a 32640 64

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

## Decomposition of $$S_{3}^{\mathrm{old}}(\Gamma_1(1792))$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(\Gamma_1(1792)) \cong$$ $$S_{3}^{\mathrm{new}}(\Gamma_1(7))$$$$^{\oplus 9}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(8))$$$$^{\oplus 12}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(14))$$$$^{\oplus 8}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(16))$$$$^{\oplus 10}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(28))$$$$^{\oplus 7}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(32))$$$$^{\oplus 8}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(56))$$$$^{\oplus 6}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(64))$$$$^{\oplus 6}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(112))$$$$^{\oplus 5}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(128))$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(224))$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(256))$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(448))$$$$^{\oplus 3}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(896))$$$$^{\oplus 2}$$