## Defining parameters

 Level: $$N$$ = $$77 = 7 \cdot 11$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$8$$ Newform subspaces: $$16$$ Sturm bound: $$960$$ Trace bound: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(77))$$.

Total New Old
Modular forms 300 271 29
Cusp forms 181 179 2
Eisenstein series 119 92 27

## Trace form

 $$179q - 23q^{2} - 24q^{3} - 27q^{4} - 26q^{5} - 22q^{6} - 21q^{7} - 45q^{8} - 13q^{9} + O(q^{10})$$ $$179q - 23q^{2} - 24q^{3} - 27q^{4} - 26q^{5} - 22q^{6} - 21q^{7} - 45q^{8} - 13q^{9} - 8q^{10} - 21q^{11} - 28q^{12} - 24q^{13} - 13q^{14} - 34q^{15} + 9q^{16} - 8q^{17} + q^{18} - 10q^{19} + 8q^{20} - 4q^{21} - 23q^{22} - 34q^{23} + 30q^{24} + 9q^{25} + 28q^{26} + 23q^{28} - 30q^{29} + 38q^{30} - 12q^{31} + 17q^{32} + 16q^{33} - 14q^{34} + 14q^{35} + 39q^{36} + 2q^{37} + 30q^{38} + 34q^{39} + 60q^{40} + 28q^{41} + 58q^{42} - 4q^{43} + 43q^{44} + 22q^{45} + 38q^{46} + 2q^{47} + 86q^{48} + 29q^{49} + 17q^{50} + 38q^{51} + 52q^{52} + 36q^{53} + 110q^{54} + 34q^{55} + 45q^{56} + 20q^{57} + 60q^{58} + 20q^{59} - 38q^{60} - 22q^{61} + 34q^{62} - 33q^{63} - 37q^{64} - 44q^{65} - 142q^{66} - 38q^{67} - 76q^{68} - 86q^{69} - 88q^{70} - 102q^{71} - 195q^{72} - 54q^{73} - 24q^{74} - 154q^{75} - 220q^{76} - 41q^{77} - 208q^{78} - 20q^{79} - 136q^{80} - 151q^{81} - 56q^{82} - 24q^{83} - 198q^{84} - 68q^{85} - 102q^{86} - 60q^{87} - 45q^{88} - 60q^{89} - 44q^{90} - 14q^{91} - 8q^{92} + 22q^{93} + 86q^{94} + 60q^{95} - 2q^{96} + 82q^{97} + 97q^{98} + 87q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(77))$$

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
77.2.a $$\chi_{77}(1, \cdot)$$ 77.2.a.a 1 1
77.2.a.b 1
77.2.a.c 1
77.2.a.d 2
77.2.b $$\chi_{77}(76, \cdot)$$ 77.2.b.a 2 1
77.2.b.b 4
77.2.e $$\chi_{77}(23, \cdot)$$ 77.2.e.a 6 2
77.2.e.b 6
77.2.f $$\chi_{77}(15, \cdot)$$ 77.2.f.a 8 4
77.2.f.b 16
77.2.i $$\chi_{77}(10, \cdot)$$ 77.2.i.a 12 2
77.2.l $$\chi_{77}(6, \cdot)$$ 77.2.l.a 8 4
77.2.l.b 16
77.2.m $$\chi_{77}(4, \cdot)$$ 77.2.m.a 8 8
77.2.m.b 40
77.2.n $$\chi_{77}(17, \cdot)$$ 77.2.n.a 48 8

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(77))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(77)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(11))$$$$^{\oplus 2}$$