Defining parameters

 Level: $$N$$ = $$275 = 5^{2} \cdot 11$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$21$$ Newform subspaces: $$52$$ Sturm bound: $$12000$$ Trace bound: $$6$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(275))$$.

Total New Old
Modular forms 3280 2904 376
Cusp forms 2721 2536 185
Eisenstein series 559 368 191

Trace form

 $$2536 q - 51 q^{2} - 53 q^{3} - 59 q^{4} - 70 q^{5} - 98 q^{6} - 66 q^{7} - 85 q^{8} - 81 q^{9} + O(q^{10})$$ $$2536 q - 51 q^{2} - 53 q^{3} - 59 q^{4} - 70 q^{5} - 98 q^{6} - 66 q^{7} - 85 q^{8} - 81 q^{9} - 90 q^{10} - 104 q^{11} - 186 q^{12} - 78 q^{13} - 108 q^{14} - 100 q^{15} - 129 q^{16} - 76 q^{17} - 103 q^{18} - 60 q^{19} - 60 q^{20} - 118 q^{21} - 81 q^{22} - 133 q^{23} - 80 q^{24} - 50 q^{25} - 238 q^{26} - 95 q^{27} - 92 q^{28} - 90 q^{29} - 100 q^{30} - 113 q^{31} - 151 q^{32} - 123 q^{33} - 208 q^{34} - 120 q^{35} - 229 q^{36} - 141 q^{37} - 160 q^{38} - 132 q^{39} - 30 q^{40} - 158 q^{41} - 52 q^{42} - 18 q^{43} + 21 q^{44} - 50 q^{45} + 2 q^{46} + 24 q^{47} + 212 q^{48} + 96 q^{49} + 50 q^{50} - 78 q^{51} + 214 q^{52} + 2 q^{53} + 210 q^{54} - 10 q^{55} - 20 q^{56} + 40 q^{57} + 150 q^{58} + 5 q^{59} + 100 q^{60} + 2 q^{61} + 38 q^{62} + 32 q^{63} + 111 q^{64} - 30 q^{65} - 88 q^{66} - 111 q^{67} - 22 q^{68} - 107 q^{69} - 100 q^{70} - 203 q^{71} - 45 q^{72} - 178 q^{73} - 168 q^{74} - 100 q^{75} - 340 q^{76} - 156 q^{77} - 336 q^{78} - 210 q^{79} - 90 q^{80} - 274 q^{81} - 162 q^{82} - 78 q^{83} - 148 q^{84} - 10 q^{85} - 208 q^{86} - 140 q^{87} - 195 q^{88} - 105 q^{89} + 150 q^{90} - 128 q^{91} - 66 q^{92} + 69 q^{93} + 112 q^{94} - 20 q^{95} + 172 q^{96} + 179 q^{97} + 213 q^{98} + 179 q^{99} + O(q^{100})$$

Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(275))$$

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
275.2.a $$\chi_{275}(1, \cdot)$$ 275.2.a.a 1 1
275.2.a.b 1
275.2.a.c 2
275.2.a.d 2
275.2.a.e 2
275.2.a.f 2
275.2.a.g 2
275.2.a.h 4
275.2.b $$\chi_{275}(199, \cdot)$$ 275.2.b.a 2 1
275.2.b.b 2
275.2.b.c 4
275.2.b.d 4
275.2.b.e 4
275.2.e $$\chi_{275}(32, \cdot)$$ 275.2.e.a 4 2
275.2.e.b 4
275.2.e.c 8
275.2.e.d 16
275.2.g $$\chi_{275}(16, \cdot)$$ 275.2.g.a 112 4
275.2.h $$\chi_{275}(26, \cdot)$$ 275.2.h.a 8 4
275.2.h.b 8
275.2.h.c 16
275.2.h.d 16
275.2.h.e 16
275.2.i $$\chi_{275}(56, \cdot)$$ 275.2.i.a 44 4
275.2.i.b 60
275.2.j $$\chi_{275}(81, \cdot)$$ 275.2.j.a 112 4
275.2.k $$\chi_{275}(36, \cdot)$$ 275.2.k.a 4 4
275.2.k.b 4
275.2.k.c 4
275.2.k.d 100
275.2.l $$\chi_{275}(31, \cdot)$$ 275.2.l.a 4 4
275.2.l.b 4
275.2.l.c 4
275.2.l.d 100
275.2.n $$\chi_{275}(104, \cdot)$$ 275.2.n.a 112 4
275.2.t $$\chi_{275}(14, \cdot)$$ 275.2.t.a 112 4
275.2.y $$\chi_{275}(34, \cdot)$$ 275.2.y.a 40 4
275.2.y.b 56
275.2.z $$\chi_{275}(49, \cdot)$$ 275.2.z.a 16 4
275.2.z.b 16
275.2.z.c 32
275.2.ba $$\chi_{275}(4, \cdot)$$ 275.2.ba.a 112 4
275.2.bb $$\chi_{275}(9, \cdot)$$ 275.2.bb.a 112 4
275.2.bf $$\chi_{275}(28, \cdot)$$ 275.2.bf.a 224 8
275.2.bg $$\chi_{275}(13, \cdot)$$ 275.2.bg.a 224 8
275.2.bl $$\chi_{275}(17, \cdot)$$ 275.2.bl.a 224 8
275.2.bm $$\chi_{275}(7, \cdot)$$ 275.2.bm.a 32 8
275.2.bm.b 32
275.2.bm.c 64
275.2.bn $$\chi_{275}(2, \cdot)$$ 275.2.bn.a 224 8
275.2.bo $$\chi_{275}(87, \cdot)$$ 275.2.bo.a 16 8
275.2.bo.b 208

Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(275))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(275)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(11))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(25))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(55))$$$$^{\oplus 2}$$