## Defining parameters

 Level: $$N$$ = $$1792 = 2^{8} \cdot 7$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$24$$ Sturm bound: $$393216$$ Trace bound: $$193$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(1792))$$.

Total New Old
Modular forms 100416 53512 46904
Cusp forms 96193 52472 43721
Eisenstein series 4223 1040 3183

## Trace form

 $$52472q - 128q^{2} - 96q^{3} - 128q^{4} - 128q^{5} - 128q^{6} - 120q^{7} - 320q^{8} - 160q^{9} + O(q^{10})$$ $$52472q - 128q^{2} - 96q^{3} - 128q^{4} - 128q^{5} - 128q^{6} - 120q^{7} - 320q^{8} - 160q^{9} - 128q^{10} - 96q^{11} - 128q^{12} - 128q^{13} - 160q^{14} - 240q^{15} - 128q^{16} - 192q^{17} - 128q^{18} - 96q^{19} - 128q^{20} - 160q^{21} - 320q^{22} - 96q^{23} - 128q^{24} - 160q^{25} - 128q^{26} - 96q^{27} - 160q^{28} - 320q^{29} - 128q^{30} - 80q^{31} - 128q^{32} - 224q^{33} - 128q^{34} - 120q^{35} - 320q^{36} - 128q^{37} - 128q^{38} - 96q^{39} - 128q^{40} - 160q^{41} - 160q^{42} - 240q^{43} - 128q^{44} - 80q^{45} - 128q^{46} - 96q^{47} - 128q^{48} - 240q^{49} - 320q^{50} - 32q^{51} - 128q^{52} - 64q^{53} - 128q^{54} + 32q^{55} - 160q^{56} - 272q^{57} - 128q^{58} + 32q^{59} - 128q^{60} - 128q^{62} - 48q^{63} - 320q^{64} - 160q^{65} - 128q^{66} + 64q^{67} - 128q^{68} - 160q^{70} - 112q^{71} - 128q^{72} - 32q^{73} - 128q^{74} + 32q^{75} - 128q^{76} - 128q^{77} - 320q^{78} - 32q^{79} - 128q^{80} - 120q^{81} - 128q^{82} - 96q^{83} - 160q^{84} - 240q^{85} - 128q^{86} - 96q^{87} - 128q^{88} - 160q^{89} - 128q^{90} - 120q^{91} - 320q^{92} - 224q^{93} - 128q^{94} - 80q^{95} - 128q^{96} - 224q^{97} - 160q^{98} - 192q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(1792))$$

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
1792.2.a $$\chi_{1792}(1, \cdot)$$ 1792.2.a.a 1 1
1792.2.a.b 1
1792.2.a.c 1
1792.2.a.d 1
1792.2.a.e 1
1792.2.a.f 1
1792.2.a.g 1
1792.2.a.h 1
1792.2.a.i 2
1792.2.a.j 2
1792.2.a.k 2
1792.2.a.l 2
1792.2.a.m 2
1792.2.a.n 2
1792.2.a.o 2
1792.2.a.p 2
1792.2.a.q 2
1792.2.a.r 2
1792.2.a.s 2
1792.2.a.t 2
1792.2.a.u 4
1792.2.a.v 4
1792.2.a.w 4
1792.2.a.x 4
1792.2.b $$\chi_{1792}(897, \cdot)$$ 1792.2.b.a 2 1
1792.2.b.b 2
1792.2.b.c 2
1792.2.b.d 2
1792.2.b.e 2
1792.2.b.f 2
1792.2.b.g 2
1792.2.b.h 2
1792.2.b.i 2
1792.2.b.j 2
1792.2.b.k 4
1792.2.b.l 4
1792.2.b.m 4
1792.2.b.n 4
1792.2.b.o 6
1792.2.b.p 6
1792.2.e $$\chi_{1792}(895, \cdot)$$ 1792.2.e.a 4 1
1792.2.e.b 4
1792.2.e.c 4
1792.2.e.d 8
1792.2.e.e 8
1792.2.e.f 8
1792.2.e.g 8
1792.2.e.h 8
1792.2.e.i 8
1792.2.f $$\chi_{1792}(1791, \cdot)$$ 1792.2.f.a 4 1
1792.2.f.b 4
1792.2.f.c 4
1792.2.f.d 4
1792.2.f.e 4
1792.2.f.f 4
1792.2.f.g 4
1792.2.f.h 4
1792.2.f.i 4
1792.2.f.j 8
1792.2.f.k 8
1792.2.f.l 8
1792.2.i $$\chi_{1792}(513, \cdot)$$ n/a 120 2
1792.2.j $$\chi_{1792}(447, \cdot)$$ n/a 128 2
1792.2.m $$\chi_{1792}(449, \cdot)$$ 1792.2.m.a 8 2
1792.2.m.b 8
1792.2.m.c 8
1792.2.m.d 8
1792.2.m.e 16
1792.2.m.f 16
1792.2.m.g 16
1792.2.m.h 16
1792.2.p $$\chi_{1792}(255, \cdot)$$ n/a 120 2
1792.2.q $$\chi_{1792}(383, \cdot)$$ n/a 120 2
1792.2.t $$\chi_{1792}(641, \cdot)$$ n/a 120 2
1792.2.u $$\chi_{1792}(225, \cdot)$$ n/a 192 4
1792.2.x $$\chi_{1792}(223, \cdot)$$ n/a 240 4
1792.2.z $$\chi_{1792}(703, \cdot)$$ n/a 256 4
1792.2.ba $$\chi_{1792}(65, \cdot)$$ n/a 256 4
1792.2.bc $$\chi_{1792}(113, \cdot)$$ n/a 384 8
1792.2.bd $$\chi_{1792}(111, \cdot)$$ n/a 496 8
1792.2.bh $$\chi_{1792}(289, \cdot)$$ n/a 480 8
1792.2.bi $$\chi_{1792}(31, \cdot)$$ n/a 480 8
1792.2.bk $$\chi_{1792}(55, \cdot)$$ None 0 16
1792.2.bn $$\chi_{1792}(57, \cdot)$$ None 0 16
1792.2.bq $$\chi_{1792}(47, \cdot)$$ n/a 992 16
1792.2.br $$\chi_{1792}(81, \cdot)$$ n/a 992 16
1792.2.bs $$\chi_{1792}(29, \cdot)$$ n/a 6144 32
1792.2.bv $$\chi_{1792}(27, \cdot)$$ n/a 8128 32
1792.2.bx $$\chi_{1792}(87, \cdot)$$ None 0 32
1792.2.by $$\chi_{1792}(9, \cdot)$$ None 0 32
1792.2.cb $$\chi_{1792}(37, \cdot)$$ n/a 16256 64
1792.2.cc $$\chi_{1792}(3, \cdot)$$ n/a 16256 64

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(1792))$$ into lower level spaces

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