## Defining parameters

 Level: $$N$$ = $$1078 = 2 \cdot 7^{2} \cdot 11$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$16$$ Sturm bound: $$141120$$ Trace bound: $$4$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(1078))$$.

Total New Old
Modular forms 36480 11095 25385
Cusp forms 34081 11095 22986
Eisenstein series 2399 0 2399

## Trace form

 $$11095 q - 2 q^{2} + 6 q^{4} + 12 q^{5} + 21 q^{6} + 16 q^{7} - 2 q^{8} + 50 q^{9} + O(q^{10})$$ $$11095 q - 2 q^{2} + 6 q^{4} + 12 q^{5} + 21 q^{6} + 16 q^{7} - 2 q^{8} + 50 q^{9} + 22 q^{10} + 22 q^{11} + 10 q^{12} + 22 q^{13} + 12 q^{14} + 78 q^{15} + 6 q^{16} + 80 q^{17} + 27 q^{18} + 63 q^{19} + 12 q^{20} + 52 q^{21} + 12 q^{22} + 68 q^{23} + 21 q^{24} + 82 q^{25} + 64 q^{26} + 141 q^{27} + 16 q^{28} + 76 q^{29} + 78 q^{30} + 78 q^{31} + 3 q^{32} + 103 q^{33} + 32 q^{34} + 84 q^{35} + 35 q^{36} - 8 q^{37} - 22 q^{38} - 2 q^{39} - 62 q^{40} - 20 q^{41} - 108 q^{42} + 2 q^{43} - 15 q^{44} - 214 q^{45} - 184 q^{46} - 80 q^{47} - 28 q^{48} - 236 q^{49} - 66 q^{50} - 175 q^{51} + 4 q^{52} + 14 q^{53} - 148 q^{54} - 68 q^{55} - 72 q^{56} + 61 q^{57} - 44 q^{58} - 7 q^{59} - 16 q^{60} - 90 q^{61} - 94 q^{62} - 108 q^{63} + 6 q^{64} - 92 q^{65} - 372 q^{66} - 30 q^{67} - 40 q^{68} - 298 q^{69} - 96 q^{70} - 256 q^{71} - 198 q^{72} - 144 q^{73} - 152 q^{74} - 557 q^{75} - 62 q^{76} - 96 q^{77} - 360 q^{78} - 118 q^{79} - 98 q^{80} - 795 q^{81} - 145 q^{82} - 319 q^{83} - 68 q^{84} - 322 q^{85} - 239 q^{86} - 548 q^{87} - 98 q^{88} - 172 q^{89} - 234 q^{90} - 160 q^{91} + 78 q^{92} - 446 q^{93} + 84 q^{94} - 106 q^{95} + 16 q^{96} + 83 q^{97} + 96 q^{98} + 118 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(1078))$$

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
1078.2.a $$\chi_{1078}(1, \cdot)$$ 1078.2.a.a 1 1
1078.2.a.b 1
1078.2.a.c 1
1078.2.a.d 1
1078.2.a.e 1
1078.2.a.f 1
1078.2.a.g 1
1078.2.a.h 1
1078.2.a.i 1
1078.2.a.j 1
1078.2.a.k 1
1078.2.a.l 1
1078.2.a.m 1
1078.2.a.n 2
1078.2.a.o 2
1078.2.a.p 2
1078.2.a.q 2
1078.2.a.r 2
1078.2.a.s 2
1078.2.a.t 2
1078.2.a.u 2
1078.2.a.v 2
1078.2.a.w 2
1078.2.a.x 2
1078.2.c $$\chi_{1078}(1077, \cdot)$$ 1078.2.c.a 8 1
1078.2.c.b 16
1078.2.c.c 16
1078.2.e $$\chi_{1078}(67, \cdot)$$ 1078.2.e.a 2 2
1078.2.e.b 2
1078.2.e.c 2
1078.2.e.d 2
1078.2.e.e 2
1078.2.e.f 2
1078.2.e.g 2
1078.2.e.h 2
1078.2.e.i 2
1078.2.e.j 2
1078.2.e.k 2
1078.2.e.l 2
1078.2.e.m 4
1078.2.e.n 4
1078.2.e.o 4
1078.2.e.p 4
1078.2.e.q 4
1078.2.e.r 4
1078.2.e.s 4
1078.2.e.t 4
1078.2.e.u 4
1078.2.e.v 4
1078.2.f $$\chi_{1078}(295, \cdot)$$ n/a 164 4
1078.2.i $$\chi_{1078}(901, \cdot)$$ 1078.2.i.a 16 2
1078.2.i.b 16
1078.2.i.c 16
1078.2.i.d 32
1078.2.j $$\chi_{1078}(155, \cdot)$$ n/a 264 6
1078.2.l $$\chi_{1078}(195, \cdot)$$ n/a 160 4
1078.2.o $$\chi_{1078}(153, \cdot)$$ n/a 336 6
1078.2.q $$\chi_{1078}(361, \cdot)$$ n/a 320 8
1078.2.r $$\chi_{1078}(23, \cdot)$$ n/a 576 12
1078.2.s $$\chi_{1078}(19, \cdot)$$ n/a 320 8
1078.2.v $$\chi_{1078}(15, \cdot)$$ n/a 1344 24
1078.2.w $$\chi_{1078}(87, \cdot)$$ n/a 672 12
1078.2.ba $$\chi_{1078}(13, \cdot)$$ n/a 1344 24
1078.2.bc $$\chi_{1078}(9, \cdot)$$ n/a 2688 48
1078.2.bf $$\chi_{1078}(17, \cdot)$$ n/a 2688 48

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(1078))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(1078)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(11))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(14))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(22))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(49))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(77))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(98))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(154))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(539))$$$$^{\oplus 2}$$