## Defining parameters

 Level: $$N$$ = $$726 = 2 \cdot 3 \cdot 11^{2}$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$8$$ Newform subspaces: $$61$$ Sturm bound: $$58080$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(726))$$.

Total New Old
Modular forms 15160 3569 11591
Cusp forms 13881 3569 10312
Eisenstein series 1279 0 1279

## Trace form

 $$3569q - q^{2} - q^{3} - q^{4} - 6q^{5} + 9q^{6} + 32q^{7} - q^{8} + 39q^{9} + O(q^{10})$$ $$3569q - q^{2} - q^{3} - q^{4} - 6q^{5} + 9q^{6} + 32q^{7} - q^{8} + 39q^{9} + 34q^{10} + 20q^{11} + 19q^{12} + 26q^{13} + 32q^{14} + 54q^{15} - q^{16} + 62q^{17} + 9q^{18} + 40q^{19} - 6q^{20} + 32q^{21} + 16q^{23} - 11q^{24} + 49q^{25} - 14q^{26} - 61q^{27} - 8q^{28} + 10q^{29} - 66q^{30} + 8q^{31} - q^{32} - 45q^{33} - 18q^{34} - 8q^{35} - 11q^{36} - 38q^{37} - 20q^{38} - 34q^{39} - 6q^{40} - 2q^{41} - 28q^{42} + 76q^{43} + 20q^{44} - 6q^{45} + 56q^{46} + 112q^{47} - q^{48} + 183q^{49} + 49q^{50} + 92q^{51} + 66q^{52} + 66q^{53} + 19q^{54} + 100q^{55} - 8q^{56} - 10q^{57} + 130q^{58} + 60q^{59} + 34q^{60} + 138q^{61} + 88q^{62} + 12q^{63} - q^{64} + 156q^{65} + 60q^{66} + 132q^{67} + 62q^{68} + 36q^{69} + 112q^{70} + 88q^{71} + 39q^{72} + 86q^{73} + 42q^{74} + 59q^{75} + 20q^{76} + 80q^{77} + 66q^{78} + 40q^{79} + 34q^{80} + 79q^{81} - 22q^{82} + 36q^{83} - 8q^{84} + 12q^{85} + 76q^{86} - 30q^{87} + 20q^{88} + 30q^{89} - 26q^{90} - 192q^{91} - 24q^{92} + 28q^{93} - 128q^{94} - q^{96} - 38q^{97} - 57q^{98} - 30q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(726))$$

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
726.2.a $$\chi_{726}(1, \cdot)$$ 726.2.a.a 1 1
726.2.a.b 1
726.2.a.c 1
726.2.a.d 1
726.2.a.e 1
726.2.a.f 1
726.2.a.g 1
726.2.a.h 1
726.2.a.i 1
726.2.a.j 2
726.2.a.k 2
726.2.a.l 2
726.2.a.m 2
726.2.b $$\chi_{726}(725, \cdot)$$ 726.2.b.a 2 1
726.2.b.b 2
726.2.b.c 8
726.2.b.d 8
726.2.b.e 8
726.2.b.f 8
726.2.e $$\chi_{726}(487, \cdot)$$ 726.2.e.a 4 4
726.2.e.b 4
726.2.e.c 4
726.2.e.d 4
726.2.e.e 4
726.2.e.f 4
726.2.e.g 4
726.2.e.h 4
726.2.e.i 4
726.2.e.j 4
726.2.e.k 4
726.2.e.l 4
726.2.e.m 4
726.2.e.n 4
726.2.e.o 4
726.2.e.p 4
726.2.e.q 4
726.2.e.r 4
726.2.h $$\chi_{726}(161, \cdot)$$ 726.2.h.a 8 4
726.2.h.b 8
726.2.h.c 8
726.2.h.d 8
726.2.h.e 8
726.2.h.f 8
726.2.h.g 8
726.2.h.h 8
726.2.h.i 8
726.2.h.j 8
726.2.h.k 32
726.2.h.l 32
726.2.i $$\chi_{726}(67, \cdot)$$ 726.2.i.a 50 10
726.2.i.b 50
726.2.i.c 60
726.2.i.d 60
726.2.l $$\chi_{726}(65, \cdot)$$ 726.2.l.a 220 10
726.2.l.b 220
726.2.m $$\chi_{726}(25, \cdot)$$ 726.2.m.a 200 40
726.2.m.b 200
726.2.m.c 240
726.2.m.d 240
726.2.n $$\chi_{726}(17, \cdot)$$ 726.2.n.a 880 40
726.2.n.b 880

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(726))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(726)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(11))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(22))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(33))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(66))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(121))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(242))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(363))$$$$^{\oplus 2}$$