# Properties

 Label 644.2 Level 644 Weight 2 Dimension 6848 Nonzero newspaces 16 Newform subspaces 27 Sturm bound 50688 Trace bound 5

## Defining parameters

 Level: $$N$$ = $$644 = 2^{2} \cdot 7 \cdot 23$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$16$$ Newform subspaces: $$27$$ Sturm bound: $$50688$$ Trace bound: $$5$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(644))$$.

Total New Old
Modular forms 13332 7264 6068
Cusp forms 12013 6848 5165
Eisenstein series 1319 416 903

## Trace form

 $$6848 q - 38 q^{2} + 2 q^{3} - 38 q^{4} - 70 q^{5} - 44 q^{6} + 8 q^{7} - 104 q^{8} - 80 q^{9} + O(q^{10})$$ $$6848 q - 38 q^{2} + 2 q^{3} - 38 q^{4} - 70 q^{5} - 44 q^{6} + 8 q^{7} - 104 q^{8} - 80 q^{9} - 56 q^{10} - 6 q^{11} - 68 q^{12} - 96 q^{13} - 73 q^{14} + 10 q^{15} - 62 q^{16} - 48 q^{17} - 50 q^{18} + 20 q^{19} - 44 q^{20} - 87 q^{21} - 96 q^{22} + 47 q^{23} - 64 q^{24} - 48 q^{25} - 20 q^{26} + 86 q^{27} - q^{28} - 198 q^{29} - 32 q^{30} + 8 q^{31} - 38 q^{32} - 84 q^{33} - 88 q^{34} - 52 q^{35} - 238 q^{36} - 190 q^{37} - 190 q^{38} - 84 q^{39} - 244 q^{40} - 156 q^{41} - 189 q^{42} - 72 q^{43} - 234 q^{44} - 276 q^{45} - 232 q^{46} - 106 q^{47} - 220 q^{48} - 144 q^{49} - 270 q^{50} - 82 q^{51} - 264 q^{52} - 90 q^{53} - 184 q^{54} - 8 q^{55} - 128 q^{56} - 166 q^{57} - 142 q^{58} + 62 q^{59} - 64 q^{60} + 34 q^{61} - 44 q^{62} + 75 q^{63} - 128 q^{64} + 54 q^{65} + 34 q^{66} + 30 q^{67} - 66 q^{68} + 16 q^{69} - 122 q^{70} + 110 q^{71} - 80 q^{72} - 106 q^{73} + 2 q^{74} + 118 q^{75} + 66 q^{76} - 185 q^{77} + 62 q^{78} + 18 q^{79} + 202 q^{80} - 334 q^{81} + 64 q^{82} - 26 q^{83} + 99 q^{84} - 544 q^{85} + 212 q^{86} - 144 q^{87} + 96 q^{88} - 298 q^{89} + 330 q^{90} - 28 q^{91} + 94 q^{92} - 730 q^{93} + 170 q^{94} - 72 q^{95} + 422 q^{96} - 114 q^{97} - 14 q^{98} - 46 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(644))$$

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
644.2.a $$\chi_{644}(1, \cdot)$$ 644.2.a.a 1 1
644.2.a.b 1
644.2.a.c 5
644.2.a.d 5
644.2.c $$\chi_{644}(183, \cdot)$$ 644.2.c.a 36 1
644.2.c.b 36
644.2.d $$\chi_{644}(321, \cdot)$$ 644.2.d.a 16 1
644.2.f $$\chi_{644}(139, \cdot)$$ 644.2.f.a 4 1
644.2.f.b 4
644.2.f.c 80
644.2.i $$\chi_{644}(93, \cdot)$$ 644.2.i.a 14 2
644.2.i.b 14
644.2.k $$\chi_{644}(47, \cdot)$$ 644.2.k.a 176 2
644.2.m $$\chi_{644}(45, \cdot)$$ 644.2.m.a 32 2
644.2.p $$\chi_{644}(275, \cdot)$$ 644.2.p.a 184 2
644.2.q $$\chi_{644}(29, \cdot)$$ 644.2.q.a 60 10
644.2.q.b 60
644.2.t $$\chi_{644}(27, \cdot)$$ 644.2.t.a 20 10
644.2.t.b 20
644.2.t.c 880
644.2.v $$\chi_{644}(97, \cdot)$$ 644.2.v.a 160 10
644.2.w $$\chi_{644}(15, \cdot)$$ 644.2.w.a 360 10
644.2.w.b 360
644.2.y $$\chi_{644}(9, \cdot)$$ 644.2.y.a 320 20
644.2.z $$\chi_{644}(11, \cdot)$$ 644.2.z.a 1840 20
644.2.bc $$\chi_{644}(5, \cdot)$$ 644.2.bc.a 320 20
644.2.be $$\chi_{644}(3, \cdot)$$ 644.2.be.a 1840 20

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(644))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(644)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(14))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(23))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(28))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(46))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(92))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(161))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(322))$$$$^{\oplus 2}$$