# Properties

 Label 792.2 Level 792 Weight 2 Dimension 7405 Nonzero newspaces 24 Newform subspaces 89 Sturm bound 69120 Trace bound 16

## Defining parameters

 Level: $$N$$ = $$792 = 2^{3} \cdot 3^{2} \cdot 11$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$24$$ Newform subspaces: $$89$$ Sturm bound: $$69120$$ Trace bound: $$16$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(792))$$.

Total New Old
Modular forms 18240 7729 10511
Cusp forms 16321 7405 8916
Eisenstein series 1919 324 1595

## Trace form

 $$7405 q - 26 q^{2} - 34 q^{3} - 26 q^{4} - 8 q^{5} - 24 q^{6} - 26 q^{7} - 2 q^{8} - 62 q^{9} + O(q^{10})$$ $$7405 q - 26 q^{2} - 34 q^{3} - 26 q^{4} - 8 q^{5} - 24 q^{6} - 26 q^{7} - 2 q^{8} - 62 q^{9} - 42 q^{10} - 13 q^{11} - 52 q^{12} + 4 q^{13} - 2 q^{14} + 8 q^{15} - 10 q^{16} - 30 q^{17} - 40 q^{18} - 61 q^{19} - 50 q^{20} + 24 q^{21} - 44 q^{22} - 34 q^{23} - 88 q^{24} - 64 q^{25} - 86 q^{26} - 40 q^{27} - 106 q^{28} - 22 q^{29} - 132 q^{30} - 8 q^{31} - 96 q^{32} - 73 q^{33} + 8 q^{34} - 72 q^{35} - 140 q^{36} - 12 q^{37} - 56 q^{38} - 112 q^{39} + 20 q^{40} - 20 q^{41} - 140 q^{42} - 40 q^{43} - 2 q^{44} - 4 q^{45} - 52 q^{46} - 84 q^{47} - 80 q^{48} + 74 q^{49} - 16 q^{50} - 48 q^{51} + 72 q^{52} + 88 q^{53} - 16 q^{54} + 16 q^{55} + 44 q^{56} + 58 q^{57} + 73 q^{59} + 92 q^{60} + 76 q^{61} + 98 q^{62} - 24 q^{63} - 50 q^{64} + 128 q^{65} + 64 q^{66} + 110 q^{67} + 138 q^{68} + 36 q^{69} - 8 q^{70} + 94 q^{71} + 164 q^{72} - 42 q^{73} + 140 q^{74} - 68 q^{75} - 42 q^{76} + 138 q^{77} + 68 q^{78} + 138 q^{79} + 52 q^{80} - 62 q^{81} - 230 q^{82} + 21 q^{83} + 88 q^{84} + 44 q^{85} - 70 q^{86} - 76 q^{87} - 204 q^{88} - 134 q^{89} - 12 q^{90} - 28 q^{91} - 218 q^{92} + 20 q^{93} - 198 q^{94} - 78 q^{95} - 196 q^{96} - 147 q^{97} - 332 q^{98} - 70 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(792))$$

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 available newforms together with their dimension.

Label $$\chi$$ Newforms Dimension $$\chi$$ degree
792.2.a $$\chi_{792}(1, \cdot)$$ 792.2.a.a 1 1
792.2.a.b 1
792.2.a.c 1
792.2.a.d 1
792.2.a.e 1
792.2.a.f 1
792.2.a.g 1
792.2.a.h 2
792.2.a.i 2
792.2.a.j 2
792.2.b $$\chi_{792}(593, \cdot)$$ 792.2.b.a 6 1
792.2.b.b 6
792.2.d $$\chi_{792}(287, \cdot)$$ None 0 1
792.2.f $$\chi_{792}(397, \cdot)$$ 792.2.f.a 2 1
792.2.f.b 2
792.2.f.c 2
792.2.f.d 4
792.2.f.e 4
792.2.f.f 6
792.2.f.g 10
792.2.f.h 20
792.2.h $$\chi_{792}(307, \cdot)$$ 792.2.h.a 2 1
792.2.h.b 2
792.2.h.c 2
792.2.h.d 4
792.2.h.e 4
792.2.h.f 8
792.2.h.g 8
792.2.h.h 12
792.2.h.i 16
792.2.k $$\chi_{792}(683, \cdot)$$ 792.2.k.a 40 1
792.2.m $$\chi_{792}(197, \cdot)$$ 792.2.m.a 4 1
792.2.m.b 4
792.2.m.c 40
792.2.o $$\chi_{792}(703, \cdot)$$ None 0 1
792.2.q $$\chi_{792}(265, \cdot)$$ 792.2.q.a 2 2
792.2.q.b 2
792.2.q.c 2
792.2.q.d 4
792.2.q.e 6
792.2.q.f 12
792.2.q.g 16
792.2.q.h 16
792.2.r $$\chi_{792}(289, \cdot)$$ 792.2.r.a 4 4
792.2.r.b 4
792.2.r.c 4
792.2.r.d 4
792.2.r.e 4
792.2.r.f 8
792.2.r.g 8
792.2.r.h 12
792.2.r.i 12
792.2.u $$\chi_{792}(175, \cdot)$$ None 0 2
792.2.w $$\chi_{792}(461, \cdot)$$ 792.2.w.a 280 2
792.2.y $$\chi_{792}(155, \cdot)$$ 792.2.y.a 240 2
792.2.z $$\chi_{792}(43, \cdot)$$ 792.2.z.a 4 2
792.2.z.b 4
792.2.z.c 8
792.2.z.d 8
792.2.z.e 256
792.2.bb $$\chi_{792}(133, \cdot)$$ 792.2.bb.a 4 2
792.2.bb.b 4
792.2.bb.c 8
792.2.bb.d 224
792.2.bd $$\chi_{792}(23, \cdot)$$ None 0 2
792.2.bf $$\chi_{792}(65, \cdot)$$ 792.2.bf.a 36 2
792.2.bf.b 36
792.2.bi $$\chi_{792}(127, \cdot)$$ None 0 4
792.2.bk $$\chi_{792}(413, \cdot)$$ 792.2.bk.a 192 4
792.2.bm $$\chi_{792}(179, \cdot)$$ 792.2.bm.a 192 4
792.2.bp $$\chi_{792}(19, \cdot)$$ 792.2.bp.a 8 4
792.2.bp.b 32
792.2.bp.c 48
792.2.bp.d 48
792.2.bp.e 96
792.2.br $$\chi_{792}(37, \cdot)$$ 792.2.br.a 16 4
792.2.br.b 40
792.2.br.c 80
792.2.br.d 96
792.2.bt $$\chi_{792}(71, \cdot)$$ None 0 4
792.2.bv $$\chi_{792}(17, \cdot)$$ 792.2.bv.a 24 4
792.2.bv.b 24
792.2.bw $$\chi_{792}(25, \cdot)$$ 792.2.bw.a 136 8
792.2.bw.b 152
792.2.by $$\chi_{792}(41, \cdot)$$ 792.2.by.a 144 8
792.2.by.b 144
792.2.ca $$\chi_{792}(47, \cdot)$$ None 0 8
792.2.cc $$\chi_{792}(157, \cdot)$$ 792.2.cc.a 1120 8
792.2.ce $$\chi_{792}(139, \cdot)$$ 792.2.ce.a 16 8
792.2.ce.b 16
792.2.ce.c 16
792.2.ce.d 1072
792.2.cf $$\chi_{792}(59, \cdot)$$ 792.2.cf.a 16 8
792.2.cf.b 16
792.2.cf.c 1088
792.2.ch $$\chi_{792}(29, \cdot)$$ 792.2.ch.a 1120 8
792.2.cj $$\chi_{792}(7, \cdot)$$ None 0 8

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(792))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(792)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 24}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2))$$$$^{\oplus 18}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(3))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(4))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(6))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(8))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(9))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(11))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(12))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(18))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(22))$$$$^{\oplus 9}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(24))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(33))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(36))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(44))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(66))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(72))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(88))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(99))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(132))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(198))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(264))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(396))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(792))$$$$^{\oplus 1}$$