# Properties

 Label 1014.2 Level 1014 Weight 2 Dimension 7013 Nonzero newspaces 12 Sturm bound 113568 Trace bound 1

## 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

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

## 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

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