# Properties

 Label 722.2 Level 722 Weight 2 Dimension 5386 Nonzero newspaces 6 Newform subspaces 53 Sturm bound 64980 Trace bound 1

## Defining parameters

 Level: $$N$$ = $$722 = 2 \cdot 19^{2}$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$6$$ Newform subspaces: $$53$$ Sturm bound: $$64980$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(722))$$.

Total New Old
Modular forms 16749 5386 11363
Cusp forms 15742 5386 10356
Eisenstein series 1007 0 1007

## Trace form

 $$5386 q + q^{2} + 4 q^{3} + q^{4} + 6 q^{5} + 4 q^{6} + 8 q^{7} + q^{8} + 13 q^{9} + O(q^{10})$$ $$5386 q + q^{2} + 4 q^{3} + q^{4} + 6 q^{5} + 4 q^{6} + 8 q^{7} + q^{8} + 13 q^{9} + 6 q^{10} + 12 q^{11} - 8 q^{12} - 34 q^{13} - 28 q^{14} - 48 q^{15} + q^{16} - 18 q^{17} - 41 q^{18} - 42 q^{19} - 30 q^{20} - 52 q^{21} - 42 q^{22} - 12 q^{23} + 4 q^{24} - 41 q^{25} - 22 q^{26} - 26 q^{27} - 4 q^{28} - 6 q^{29} + 24 q^{30} - 4 q^{31} + q^{32} - 60 q^{33} + 18 q^{34} - 24 q^{35} + 13 q^{36} + 2 q^{37} - 52 q^{39} + 6 q^{40} + 6 q^{41} + 32 q^{42} - 40 q^{43} - 6 q^{44} - 138 q^{45} - 48 q^{46} - 96 q^{47} - 14 q^{48} - 63 q^{49} - 113 q^{50} - 126 q^{51} + 2 q^{52} - 90 q^{53} - 68 q^{54} - 72 q^{55} - 64 q^{56} - 90 q^{57} - 42 q^{58} - 120 q^{59} - 48 q^{60} - 94 q^{61} - 76 q^{62} - 88 q^{63} - 11 q^{64} - 132 q^{65} - 96 q^{66} - 88 q^{67} - 12 q^{69} - 24 q^{70} - 72 q^{71} - 5 q^{72} + 8 q^{73} + 38 q^{74} + 40 q^{75} + 24 q^{77} - 16 q^{78} - 76 q^{79} + 6 q^{80} - 77 q^{81} - 30 q^{82} - 60 q^{83} - 76 q^{84} - 36 q^{85} - 28 q^{86} - 240 q^{87} + 12 q^{88} - 54 q^{89} - 102 q^{90} - 80 q^{91} - 48 q^{92} - 172 q^{93} - 96 q^{94} - 90 q^{95} + 4 q^{96} - 82 q^{97} - 87 q^{98} - 258 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(722))$$

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
722.2.a $$\chi_{722}(1, \cdot)$$ 722.2.a.a 1 1
722.2.a.b 1
722.2.a.c 1
722.2.a.d 1
722.2.a.e 1
722.2.a.f 1
722.2.a.g 2
722.2.a.h 2
722.2.a.i 2
722.2.a.j 2
722.2.a.k 3
722.2.a.l 3
722.2.a.m 4
722.2.a.n 4
722.2.c $$\chi_{722}(429, \cdot)$$ 722.2.c.a 2 2
722.2.c.b 2
722.2.c.c 2
722.2.c.d 2
722.2.c.e 2
722.2.c.f 2
722.2.c.g 2
722.2.c.h 4
722.2.c.i 4
722.2.c.j 4
722.2.c.k 6
722.2.c.l 6
722.2.c.m 8
722.2.c.n 8
722.2.e $$\chi_{722}(99, \cdot)$$ 722.2.e.a 6 6
722.2.e.b 6
722.2.e.c 6
722.2.e.d 6
722.2.e.e 6
722.2.e.f 6
722.2.e.g 6
722.2.e.h 6
722.2.e.i 6
722.2.e.j 6
722.2.e.k 6
722.2.e.l 6
722.2.e.m 6
722.2.e.n 12
722.2.e.o 12
722.2.e.p 12
722.2.e.q 12
722.2.e.r 24
722.2.e.s 24
722.2.g $$\chi_{722}(39, \cdot)$$ 722.2.g.a 288 18
722.2.g.b 306
722.2.i $$\chi_{722}(7, \cdot)$$ 722.2.i.a 576 36
722.2.i.b 612
722.2.k $$\chi_{722}(5, \cdot)$$ 722.2.k.a 1620 108
722.2.k.b 1728

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(722))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(722)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(19))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(38))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(361))$$$$^{\oplus 2}$$