## Defining parameters

 Level: $$N$$ = $$242 = 2 \cdot 11^{2}$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$4$$ Newform subspaces: $$17$$ Sturm bound: $$7260$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(242))$$.

Total New Old
Modular forms 1975 596 1379
Cusp forms 1656 596 1060
Eisenstein series 319 0 319

## Trace form

 $$596q + q^{2} + 4q^{3} + q^{4} + 6q^{5} - 6q^{6} - 12q^{7} + q^{8} - 27q^{9} + O(q^{10})$$ $$596q + q^{2} + 4q^{3} + q^{4} + 6q^{5} - 6q^{6} - 12q^{7} + q^{8} - 27q^{9} - 14q^{10} - 10q^{11} - 16q^{12} - 6q^{13} - 12q^{14} - 36q^{15} + q^{16} - 22q^{17} + 3q^{18} - 10q^{19} + 6q^{20} - 8q^{21} - 16q^{23} - 6q^{24} - 49q^{25} - 26q^{26} - 50q^{27} - 12q^{28} - 50q^{29} - 36q^{30} - 28q^{31} - 9q^{32} - 55q^{33} - 22q^{34} - 72q^{35} + 3q^{36} - 2q^{37} - 40q^{38} - 44q^{39} - 14q^{40} - 38q^{41} - 28q^{42} - 56q^{43} - 15q^{44} - 22q^{45} - 16q^{46} - 32q^{47} + 4q^{48} - 63q^{49} - 9q^{50} - 58q^{51} - 26q^{52} - 46q^{53} - 40q^{54} - 70q^{55} + 8q^{56} - 90q^{57} - 50q^{58} - 70q^{59} - 16q^{60} - 78q^{61} - 28q^{62} - 136q^{63} + q^{64} - 116q^{65} - 60q^{66} - 112q^{67} - 22q^{68} - 124q^{69} - 32q^{70} - 88q^{71} - 27q^{72} - 46q^{73} - 2q^{74} - 106q^{75} - 80q^{77} - 24q^{78} - 20q^{79} - 14q^{80} - 149q^{81} - 28q^{82} - 46q^{83} - 48q^{84} - 112q^{85} - 86q^{86} - 80q^{87} - 10q^{88} - 70q^{89} - 102q^{90} - 88q^{91} - 36q^{92} - 132q^{93} - 72q^{94} - 100q^{95} + 4q^{96} - 92q^{97} - 33q^{98} - 130q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(242))$$

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
242.2.a $$\chi_{242}(1, \cdot)$$ 242.2.a.a 1 1
242.2.a.b 1
242.2.a.c 2
242.2.a.d 2
242.2.a.e 2
242.2.a.f 2
242.2.c $$\chi_{242}(3, \cdot)$$ 242.2.c.a 4 4
242.2.c.b 4
242.2.c.c 4
242.2.c.d 4
242.2.c.e 4
242.2.c.f 8
242.2.c.g 8
242.2.e $$\chi_{242}(23, \cdot)$$ 242.2.e.a 50 10
242.2.e.b 60
242.2.g $$\chi_{242}(5, \cdot)$$ 242.2.g.a 200 40
242.2.g.b 240

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(242))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(242)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(11))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(22))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(121))$$$$^{\oplus 2}$$