## Defining parameters

 Level: $$N$$ = $$91 = 7 \cdot 13$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$15$$ Newform subspaces: $$26$$ Sturm bound: $$1344$$ Trace bound: $$5$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(91))$$.

Total New Old
Modular forms 408 373 35
Cusp forms 265 261 4
Eisenstein series 143 112 31

## Trace form

 $$261 q - 27 q^{2} - 28 q^{3} - 31 q^{4} - 30 q^{5} - 36 q^{6} - 29 q^{7} - 57 q^{8} - 21 q^{9} + O(q^{10})$$ $$261 q - 27 q^{2} - 28 q^{3} - 31 q^{4} - 30 q^{5} - 36 q^{6} - 29 q^{7} - 57 q^{8} - 21 q^{9} - 12 q^{10} - 24 q^{11} - 13 q^{13} - 51 q^{14} - 60 q^{15} - 15 q^{16} - 24 q^{17} + 3 q^{18} - 4 q^{19} - 8 q^{21} - 36 q^{22} - 24 q^{23} + 36 q^{24} - 13 q^{25} - 3 q^{26} - 16 q^{27} + 13 q^{28} - 36 q^{29} + 48 q^{30} - 4 q^{31} + 45 q^{32} + 12 q^{33} + 18 q^{34} + 6 q^{35} + 17 q^{36} - 28 q^{37} - 12 q^{39} + 6 q^{40} + 24 q^{41} + 48 q^{42} - 12 q^{43} + 48 q^{44} + 48 q^{45} + 72 q^{46} + 12 q^{47} + 68 q^{48} + 27 q^{49} + 33 q^{50} + 60 q^{51} + 51 q^{52} - 6 q^{53} + 60 q^{54} + 36 q^{55} + 69 q^{56} + 8 q^{57} + 36 q^{58} + 132 q^{60} + 28 q^{61} + 48 q^{62} + 55 q^{63} + 59 q^{64} + 60 q^{65} + 72 q^{66} + 20 q^{67} + 96 q^{68} + 36 q^{69} + 90 q^{70} - 12 q^{71} - 63 q^{72} + 26 q^{73} + 36 q^{74} + 12 q^{75} - 76 q^{76} - 60 q^{77} - 12 q^{78} - 152 q^{79} - 108 q^{80} - 93 q^{81} - 216 q^{82} - 60 q^{83} - 176 q^{84} - 198 q^{85} - 48 q^{86} - 120 q^{87} - 288 q^{88} - 66 q^{89} - 210 q^{90} - 101 q^{91} - 288 q^{92} - 40 q^{93} - 240 q^{94} - 72 q^{95} - 216 q^{96} - 178 q^{97} - 75 q^{98} - 132 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(91))$$

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
91.2.a $$\chi_{91}(1, \cdot)$$ 91.2.a.a 1 1
91.2.a.b 1
91.2.a.c 2
91.2.a.d 3
91.2.c $$\chi_{91}(64, \cdot)$$ 91.2.c.a 6 1
91.2.e $$\chi_{91}(53, \cdot)$$ 91.2.e.a 2 2
91.2.e.b 4
91.2.e.c 10
91.2.f $$\chi_{91}(22, \cdot)$$ 91.2.f.a 4 2
91.2.f.b 4
91.2.f.c 8
91.2.g $$\chi_{91}(9, \cdot)$$ 91.2.g.a 2 2
91.2.g.b 12
91.2.h $$\chi_{91}(16, \cdot)$$ 91.2.h.a 2 2
91.2.h.b 12
91.2.i $$\chi_{91}(34, \cdot)$$ 91.2.i.a 12 2
91.2.k $$\chi_{91}(4, \cdot)$$ 91.2.k.a 2 2
91.2.k.b 12
91.2.q $$\chi_{91}(36, \cdot)$$ 91.2.q.a 12 2
91.2.r $$\chi_{91}(25, \cdot)$$ 91.2.r.a 16 2
91.2.u $$\chi_{91}(30, \cdot)$$ 91.2.u.a 2 2
91.2.u.b 12
91.2.w $$\chi_{91}(19, \cdot)$$ 91.2.w.a 28 4
91.2.ba $$\chi_{91}(45, \cdot)$$ 91.2.ba.a 28 4
91.2.bb $$\chi_{91}(5, \cdot)$$ 91.2.bb.a 32 4
91.2.bc $$\chi_{91}(6, \cdot)$$ 91.2.bc.a 32 4

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(91))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(91)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(13))$$$$^{\oplus 2}$$