## Defining parameters

 Level: $$N$$ = $$1014 = 2 \cdot 3 \cdot 13^{2}$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$12$$ Sturm bound: $$113568$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(1014))$$.

Total New Old
Modular forms 29304 7013 22291
Cusp forms 27481 7013 20468
Eisenstein series 1823 0 1823

## Trace form

 $$7013q - q^{2} - q^{3} - q^{4} - 6q^{5} - q^{6} + 8q^{7} + 11q^{8} + 7q^{9} + O(q^{10})$$ $$7013q - q^{2} - q^{3} - q^{4} - 6q^{5} - q^{6} + 8q^{7} + 11q^{8} + 7q^{9} + 54q^{10} + 36q^{11} + 7q^{12} + 48q^{13} + 40q^{14} + 42q^{15} + 15q^{16} + 42q^{17} + 11q^{18} + 92q^{19} + 6q^{20} + 48q^{21} - 12q^{22} + 24q^{23} - q^{24} + 29q^{25} + 71q^{27} - 8q^{28} + 30q^{29} - 54q^{30} + 16q^{31} - q^{32} - 36q^{33} - 18q^{34} - 49q^{36} - 26q^{37} - 20q^{38} - 44q^{39} - 6q^{40} - 30q^{41} - 80q^{42} + 20q^{43} - 12q^{44} - 114q^{45} - 24q^{46} - q^{48} - 41q^{49} - 19q^{50} + 30q^{51} + 6q^{52} + 90q^{53} + 71q^{54} + 168q^{55} + 40q^{56} + 108q^{57} + 78q^{58} + 132q^{59} + 42q^{60} + 94q^{61} + 112q^{62} + 120q^{63} + 11q^{64} + 102q^{65} + 84q^{66} + 140q^{67} - 6q^{68} + 72q^{69} + 96q^{70} + 24q^{71} + 47q^{72} + 86q^{73} + 118q^{74} + 25q^{75} + 92q^{76} + 192q^{77} + 60q^{78} + 208q^{79} + 6q^{80} - 41q^{81} + 162q^{82} + 60q^{83} + 48q^{84} + 192q^{85} + 52q^{86} + 18q^{87} - 12q^{88} + 150q^{89} + 42q^{90} + 104q^{91} + 72q^{92} + 48q^{93} + 192q^{94} + 72q^{95} - q^{96} + 190q^{97} + 39q^{98} - 84q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(1014))$$

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
1014.2.a $$\chi_{1014}(1, \cdot)$$ 1014.2.a.a 1 1
1014.2.a.b 1
1014.2.a.c 1
1014.2.a.d 1
1014.2.a.e 1
1014.2.a.f 1
1014.2.a.g 1
1014.2.a.h 2
1014.2.a.i 2
1014.2.a.j 2
1014.2.a.k 2
1014.2.a.l 3
1014.2.a.m 3
1014.2.a.n 3
1014.2.a.o 3
1014.2.b $$\chi_{1014}(337, \cdot)$$ 1014.2.b.a 2 1
1014.2.b.b 2
1014.2.b.c 2
1014.2.b.d 4
1014.2.b.e 4
1014.2.b.f 6
1014.2.b.g 6
1014.2.e $$\chi_{1014}(529, \cdot)$$ 1014.2.e.a 2 2
1014.2.e.b 2
1014.2.e.c 2
1014.2.e.d 2
1014.2.e.e 2
1014.2.e.f 2
1014.2.e.g 4
1014.2.e.h 4
1014.2.e.i 4
1014.2.e.j 4
1014.2.e.k 6
1014.2.e.l 6
1014.2.e.m 6
1014.2.e.n 6
1014.2.g $$\chi_{1014}(239, \cdot)$$ 1014.2.g.a 8 2
1014.2.g.b 12
1014.2.g.c 16
1014.2.g.d 16
1014.2.g.e 48
1014.2.i $$\chi_{1014}(361, \cdot)$$ 1014.2.i.a 4 2
1014.2.i.b 4
1014.2.i.c 4
1014.2.i.d 4
1014.2.i.e 4
1014.2.i.f 4
1014.2.i.g 12
1014.2.i.h 12
1014.2.k $$\chi_{1014}(89, \cdot)$$ n/a 208 4
1014.2.m $$\chi_{1014}(79, \cdot)$$ n/a 336 12
1014.2.p $$\chi_{1014}(25, \cdot)$$ n/a 360 12
1014.2.q $$\chi_{1014}(55, \cdot)$$ n/a 720 24
1014.2.r $$\chi_{1014}(5, \cdot)$$ n/a 1488 24
1014.2.u $$\chi_{1014}(43, \cdot)$$ n/a 768 24
1014.2.x $$\chi_{1014}(11, \cdot)$$ n/a 2880 48

"n/a" means that newforms for that character have not been added to the database yet

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(1014))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(1014)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(13))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(26))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(39))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(78))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(169))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(338))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(507))$$$$^{\oplus 2}$$