# Properties

 Label 121.2 Level 121 Weight 2 Dimension 524 Nonzero newspaces 4 Newform subspaces 11 Sturm bound 2420 Trace bound 1

## Defining parameters

 Level: $$N$$ = $$121 = 11^{2}$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$4$$ Newform subspaces: $$11$$ Sturm bound: $$2420$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(121))$$.

Total New Old
Modular forms 685 665 20
Cusp forms 526 524 2
Eisenstein series 159 141 18

## Trace form

 $$524q - 48q^{2} - 49q^{3} - 52q^{4} - 51q^{5} - 47q^{6} - 43q^{7} - 40q^{8} - 38q^{9} + O(q^{10})$$ $$524q - 48q^{2} - 49q^{3} - 52q^{4} - 51q^{5} - 47q^{6} - 43q^{7} - 40q^{8} - 38q^{9} - 33q^{10} - 45q^{11} - 73q^{12} - 49q^{13} - 39q^{14} - 29q^{15} - 16q^{16} - 33q^{17} - 24q^{18} - 35q^{19} - 17q^{20} - 27q^{21} - 20q^{22} - 79q^{23} + 5q^{24} - 16q^{25} + 3q^{26} - 25q^{27} + 9q^{28} - 25q^{29} + 13q^{30} - 37q^{31} - 8q^{32} - 10q^{33} - 59q^{34} - 3q^{35} + 44q^{36} - 23q^{37} + 5q^{38} + 9q^{39} + 35q^{40} + 3q^{41} + 49q^{42} + q^{43} + 20q^{44} - 23q^{45} + 13q^{46} - 23q^{47} + 61q^{48} + 8q^{49} + 22q^{50} + 13q^{51} + 27q^{52} + 11q^{53} + 85q^{54} + 10q^{55} + 15q^{56} + 25q^{57} + 35q^{58} - 5q^{59} + 117q^{60} - 17q^{61} + 69q^{62} + 41q^{63} + 88q^{64} + 21q^{65} + 75q^{66} - 23q^{67} + 79q^{68} + 39q^{69} + 81q^{70} + 23q^{71} + 140q^{72} + 11q^{73} + 71q^{74} + 61q^{75} + 85q^{76} + 35q^{77} + 47q^{78} + 45q^{79} + 139q^{80} + 64q^{81} + 39q^{82} + 41q^{83} + 161q^{84} + 57q^{85} + 53q^{86} + 65q^{87} + 110q^{88} - 45q^{89} + 171q^{90} + 73q^{91} + 117q^{92} + 87q^{93} + 121q^{94} + 65q^{95} + 213q^{96} + 57q^{97} + 104q^{98} + 90q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(121))$$

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
121.2.a $$\chi_{121}(1, \cdot)$$ 121.2.a.a 1 1
121.2.a.b 1
121.2.a.c 1
121.2.a.d 1
121.2.c $$\chi_{121}(3, \cdot)$$ 121.2.c.a 4 4
121.2.c.b 4
121.2.c.c 4
121.2.c.d 4
121.2.c.e 4
121.2.e $$\chi_{121}(12, \cdot)$$ 121.2.e.a 100 10
121.2.g $$\chi_{121}(4, \cdot)$$ 121.2.g.a 400 40

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(121))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(121)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(11))$$$$^{\oplus 2}$$