# Properties

 Label 2678.2 Level 2678 Weight 2 Dimension 73361 Nonzero newspaces 30 Sturm bound 891072 Trace bound 9

## Defining parameters

 Level: $$N$$ = $$2678 = 2 \cdot 13 \cdot 103$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$30$$ Sturm bound: $$891072$$ Trace bound: $$9$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(2678))$$.

Total New Old
Modular forms 225216 73361 151855
Cusp forms 220321 73361 146960
Eisenstein series 4895 0 4895

## Trace form

 $$73361q + 3q^{2} + 12q^{3} + 3q^{4} + 18q^{5} + 12q^{6} + 16q^{7} - 3q^{8} + 7q^{9} + O(q^{10})$$ $$73361q + 3q^{2} + 12q^{3} + 3q^{4} + 18q^{5} + 12q^{6} + 16q^{7} - 3q^{8} + 7q^{9} - 12q^{10} + 12q^{11} + 4q^{12} - 21q^{13} + 24q^{15} - 5q^{16} + 24q^{17} + 9q^{18} + 4q^{19} + 12q^{20} + 40q^{21} + 36q^{22} + 48q^{23} + 12q^{24} + 63q^{25} + 27q^{26} + 48q^{27} + 16q^{28} + 12q^{29} + 24q^{30} + 16q^{31} + 3q^{32} + 24q^{33} + 6q^{34} - 9q^{36} + 52q^{37} - 12q^{38} + 4q^{39} + 18q^{40} + 24q^{41} + 24q^{42} + 44q^{43} - 12q^{44} + 84q^{45} + 24q^{46} + 48q^{47} + 12q^{48} + 107q^{49} + 39q^{50} + 72q^{51} + 13q^{52} + 90q^{53} + 48q^{54} + 96q^{55} + 112q^{57} + 36q^{58} + 84q^{59} + 24q^{60} + 108q^{61} + 24q^{62} + 64q^{63} - 3q^{64} - 12q^{65} + 48q^{66} + 52q^{67} + 48q^{68} + 48q^{69} + 72q^{70} + 72q^{71} - 9q^{72} + 46q^{73} + 36q^{74} + 76q^{75} + 4q^{76} + 48q^{77} - 12q^{78} + 48q^{79} + 12q^{80} + 115q^{81} + 24q^{82} + 60q^{83} - 28q^{84} - 330q^{85} - 120q^{86} - 288q^{87} + 36q^{88} - 330q^{89} - 702q^{90} - 378q^{91} - 180q^{92} - 656q^{93} - 384q^{94} - 396q^{95} + 12q^{96} - 790q^{97} - 741q^{98} - 768q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(2678))$$

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
2678.2.a $$\chi_{2678}(1, \cdot)$$ 2678.2.a.a 1 1
2678.2.a.b 1
2678.2.a.c 1
2678.2.a.d 1
2678.2.a.e 1
2678.2.a.f 1
2678.2.a.g 1
2678.2.a.h 1
2678.2.a.i 1
2678.2.a.j 1
2678.2.a.k 1
2678.2.a.l 1
2678.2.a.m 1
2678.2.a.n 1
2678.2.a.o 2
2678.2.a.p 3
2678.2.a.q 3
2678.2.a.r 10
2678.2.a.s 10
2678.2.a.t 11
2678.2.a.u 14
2678.2.a.v 15
2678.2.a.w 19
2678.2.d $$\chi_{2678}(207, \cdot)$$ n/a 120 1
2678.2.e $$\chi_{2678}(1797, \cdot)$$ n/a 244 2
2678.2.f $$\chi_{2678}(159, \cdot)$$ n/a 244 2
2678.2.g $$\chi_{2678}(1855, \cdot)$$ n/a 236 2
2678.2.h $$\chi_{2678}(365, \cdot)$$ n/a 208 2
2678.2.i $$\chi_{2678}(411, \cdot)$$ n/a 248 2
2678.2.m $$\chi_{2678}(413, \cdot)$$ n/a 240 2
2678.2.n $$\chi_{2678}(355, \cdot)$$ n/a 244 2
2678.2.o $$\chi_{2678}(1395, \cdot)$$ n/a 244 2
2678.2.v $$\chi_{2678}(571, \cdot)$$ n/a 240 2
2678.2.w $$\chi_{2678}(47, \cdot)$$ n/a 480 4
2678.2.ba $$\chi_{2678}(665, \cdot)$$ n/a 488 4
2678.2.bb $$\chi_{2678}(617, \cdot)$$ n/a 480 4
2678.2.bc $$\chi_{2678}(253, \cdot)$$ n/a 488 4
2678.2.be $$\chi_{2678}(79, \cdot)$$ n/a 1664 16
2678.2.bf $$\chi_{2678}(285, \cdot)$$ n/a 1984 16
2678.2.bi $$\chi_{2678}(105, \cdot)$$ n/a 3328 32
2678.2.bj $$\chi_{2678}(9, \cdot)$$ n/a 3840 32
2678.2.bk $$\chi_{2678}(107, \cdot)$$ n/a 3904 32
2678.2.bl $$\chi_{2678}(29, \cdot)$$ n/a 3904 32
2678.2.bn $$\chi_{2678}(31, \cdot)$$ n/a 3968 32
2678.2.bo $$\chi_{2678}(25, \cdot)$$ n/a 3840 32
2678.2.bv $$\chi_{2678}(17, \cdot)$$ n/a 3904 32
2678.2.bw $$\chi_{2678}(121, \cdot)$$ n/a 3904 32
2678.2.bx $$\chi_{2678}(23, \cdot)$$ n/a 3840 32
2678.2.cb $$\chi_{2678}(45, \cdot)$$ n/a 7808 64
2678.2.cc $$\chi_{2678}(37, \cdot)$$ n/a 7680 64
2678.2.cd $$\chi_{2678}(11, \cdot)$$ n/a 7808 64
2678.2.ch $$\chi_{2678}(5, \cdot)$$ n/a 7680 64

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(2678))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(2678)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(13))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(26))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(103))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(206))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1339))$$$$^{\oplus 2}$$