## Defining parameters

 Level: $$N$$ = $$241$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$16$$ Newform subspaces: $$17$$ Sturm bound: $$9680$$ Trace bound: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(241))$$.

Total New Old
Modular forms 2540 2540 0
Cusp forms 2301 2301 0
Eisenstein series 239 239 0

## Trace form

 $$2301q - 117q^{2} - 116q^{3} - 113q^{4} - 114q^{5} - 108q^{6} - 112q^{7} - 105q^{8} - 107q^{9} + O(q^{10})$$ $$2301q - 117q^{2} - 116q^{3} - 113q^{4} - 114q^{5} - 108q^{6} - 112q^{7} - 105q^{8} - 107q^{9} - 102q^{10} - 108q^{11} - 92q^{12} - 106q^{13} - 96q^{14} - 96q^{15} - 89q^{16} - 102q^{17} - 81q^{18} - 100q^{19} - 78q^{20} - 88q^{21} - 84q^{22} - 96q^{23} - 60q^{24} - 89q^{25} - 78q^{26} - 80q^{27} - 64q^{28} - 90q^{29} - 48q^{30} - 88q^{31} - 57q^{32} - 72q^{33} - 66q^{34} - 72q^{35} - 29q^{36} - 82q^{37} - 60q^{38} - 64q^{39} - 30q^{40} - 78q^{41} - 24q^{42} - 76q^{43} - 36q^{44} - 42q^{45} - 48q^{46} - 72q^{47} + 4q^{48} - 63q^{49} - 27q^{50} - 48q^{51} - 22q^{52} - 66q^{53} - 48q^{55} - 40q^{57} - 30q^{58} - 60q^{59} + 48q^{60} - 58q^{61} - 24q^{62} - 16q^{63} + 7q^{64} - 36q^{65} + 24q^{66} - 52q^{67} + 6q^{68} - 24q^{69} + 24q^{70} - 48q^{71} + 75q^{72} - 46q^{73} - 6q^{74} + 4q^{75} + 20q^{76} - 24q^{77} + 48q^{78} - 40q^{79} + 66q^{80} + q^{81} + 6q^{82} - 36q^{83} + 104q^{84} - 12q^{85} + 12q^{86} + 60q^{88} - 30q^{89} + 114q^{90} - 8q^{91} + 48q^{92} + 8q^{93} + 24q^{94} + 132q^{96} - 22q^{97} + 51q^{98} + 36q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(241))$$

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
241.2.a $$\chi_{241}(1, \cdot)$$ 241.2.a.a 7 1
241.2.a.b 12
241.2.b $$\chi_{241}(240, \cdot)$$ 241.2.b.a 18 1
241.2.c $$\chi_{241}(15, \cdot)$$ 241.2.c.a 38 2
241.2.d $$\chi_{241}(64, \cdot)$$ 241.2.d.a 36 2
241.2.e $$\chi_{241}(87, \cdot)$$ 241.2.e.a 72 4
241.2.f $$\chi_{241}(16, \cdot)$$ 241.2.f.a 38 2
241.2.g $$\chi_{241}(8, \cdot)$$ 241.2.g.a 76 4
241.2.h $$\chi_{241}(36, \cdot)$$ 241.2.h.a 72 4
241.2.i $$\chi_{241}(4, \cdot)$$ 241.2.i.a 76 4
241.2.j $$\chi_{241}(24, \cdot)$$ 241.2.j.a 152 8
241.2.l $$\chi_{241}(6, \cdot)$$ 241.2.l.a 144 8
241.2.m $$\chi_{241}(2, \cdot)$$ 241.2.m.a 160 8
241.2.n $$\chi_{241}(10, \cdot)$$ 241.2.n.a 152 8
241.2.o $$\chi_{241}(5, \cdot)$$ 241.2.o.a 304 16
241.2.q $$\chi_{241}(9, \cdot)$$ 241.2.q.a 304 16
241.2.s $$\chi_{241}(3, \cdot)$$ 241.2.s.a 640 32