# Properties

 Label 828.2 Level 828 Weight 2 Dimension 8554 Nonzero newspaces 16 Newform subspaces 43 Sturm bound 76032 Trace bound 5

## Defining parameters

 Level: $$N$$ = $$828 = 2^{2} \cdot 3^{2} \cdot 23$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$16$$ Newform subspaces: $$43$$ Sturm bound: $$76032$$ Trace bound: $$5$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(828))$$.

Total New Old
Modular forms 19888 8934 10954
Cusp forms 18129 8554 9575
Eisenstein series 1759 380 1379

## Trace form

 $$8554 q - 27 q^{2} - 23 q^{4} - 48 q^{5} - 38 q^{6} + 6 q^{7} - 33 q^{8} - 64 q^{9} + O(q^{10})$$ $$8554 q - 27 q^{2} - 23 q^{4} - 48 q^{5} - 38 q^{6} + 6 q^{7} - 33 q^{8} - 64 q^{9} - 91 q^{10} + 6 q^{11} - 56 q^{12} - 52 q^{13} - 57 q^{14} - 18 q^{15} - 47 q^{16} - 101 q^{17} - 80 q^{18} - 11 q^{19} - 69 q^{20} - 82 q^{21} - 28 q^{22} - 25 q^{23} - 94 q^{24} - 70 q^{25} - 33 q^{26} - 75 q^{28} - 83 q^{29} - 8 q^{30} + 7 q^{31} + 33 q^{32} - 118 q^{33} + 15 q^{34} + 34 q^{35} + 22 q^{36} - 134 q^{37} + 76 q^{38} + 6 q^{39} + 51 q^{40} - 86 q^{41} - 8 q^{42} + 26 q^{43} + 44 q^{44} - 118 q^{45} - 23 q^{46} + 26 q^{47} - 86 q^{48} - 38 q^{49} + 2 q^{50} + 13 q^{52} - 20 q^{53} - 122 q^{54} + 74 q^{55} - 14 q^{56} - 34 q^{57} - 42 q^{58} + 148 q^{59} - 56 q^{60} + 56 q^{61} - 33 q^{62} + 116 q^{63} - 119 q^{64} + 219 q^{65} + 4 q^{66} + 84 q^{67} - 36 q^{68} + 61 q^{69} - 54 q^{70} + 213 q^{71} - 2 q^{72} - 16 q^{73} + 16 q^{74} + 178 q^{75} - 82 q^{76} + 241 q^{77} - 20 q^{78} + 184 q^{79} - 132 q^{80} + 24 q^{81} - 193 q^{82} + 103 q^{83} - 104 q^{84} + 134 q^{85} - 185 q^{86} + 18 q^{87} - 79 q^{88} - 24 q^{89} - 100 q^{90} + 56 q^{91} - 156 q^{92} - 266 q^{93} - 74 q^{94} + 9 q^{95} - 68 q^{96} - 79 q^{97} - 121 q^{98} - 18 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(828))$$

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
828.2.a $$\chi_{828}(1, \cdot)$$ 828.2.a.a 1 1
828.2.a.b 1
828.2.a.c 1
828.2.a.d 1
828.2.a.e 2
828.2.a.f 2
828.2.c $$\chi_{828}(323, \cdot)$$ 828.2.c.a 2 1
828.2.c.b 2
828.2.c.c 8
828.2.c.d 8
828.2.c.e 12
828.2.c.f 12
828.2.e $$\chi_{828}(91, \cdot)$$ 828.2.e.a 4 1
828.2.e.b 6
828.2.e.c 8
828.2.e.d 8
828.2.e.e 8
828.2.e.f 24
828.2.g $$\chi_{828}(413, \cdot)$$ 828.2.g.a 8 1
828.2.i $$\chi_{828}(277, \cdot)$$ 828.2.i.a 6 2
828.2.i.b 10
828.2.i.c 12
828.2.i.d 16
828.2.k $$\chi_{828}(137, \cdot)$$ 828.2.k.a 48 2
828.2.m $$\chi_{828}(367, \cdot)$$ 828.2.m.a 8 2
828.2.m.b 12
828.2.m.c 12
828.2.m.d 248
828.2.o $$\chi_{828}(47, \cdot)$$ 828.2.o.a 132 2
828.2.o.b 132
828.2.q $$\chi_{828}(73, \cdot)$$ 828.2.q.a 20 10
828.2.q.b 20
828.2.q.c 20
828.2.q.d 40
828.2.s $$\chi_{828}(17, \cdot)$$ 828.2.s.a 80 10
828.2.u $$\chi_{828}(19, \cdot)$$ 828.2.u.a 100 10
828.2.u.b 240
828.2.u.c 240
828.2.w $$\chi_{828}(35, \cdot)$$ 828.2.w.a 480 10
828.2.y $$\chi_{828}(13, \cdot)$$ 828.2.y.a 480 20
828.2.ba $$\chi_{828}(59, \cdot)$$ 828.2.ba.a 2800 20
828.2.bc $$\chi_{828}(7, \cdot)$$ 828.2.bc.a 2800 20
828.2.be $$\chi_{828}(5, \cdot)$$ 828.2.be.a 480 20

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(828))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(828)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(18))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(23))$$$$^{\oplus 9}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(36))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(46))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(69))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(92))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(138))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(207))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(276))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(414))$$$$^{\oplus 2}$$