## Defining parameters

 Level: $$N$$ = $$605 = 5 \cdot 11^{2}$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$12$$ Newform subspaces: $$67$$ Sturm bound: $$58080$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(605))$$.

Total New Old
Modular forms 15160 13513 1647
Cusp forms 13881 12671 1210
Eisenstein series 1279 842 437

## Trace form

 $$12671q - 87q^{2} - 86q^{3} - 83q^{4} - 134q^{5} - 278q^{6} - 102q^{7} - 115q^{8} - 117q^{9} + O(q^{10})$$ $$12671q - 87q^{2} - 86q^{3} - 83q^{4} - 134q^{5} - 278q^{6} - 102q^{7} - 115q^{8} - 117q^{9} - 162q^{10} - 310q^{11} - 222q^{12} - 96q^{13} - 126q^{14} - 171q^{15} - 359q^{16} - 132q^{17} - 171q^{18} - 130q^{19} - 198q^{20} - 338q^{21} - 160q^{22} - 206q^{23} - 250q^{24} - 194q^{25} - 408q^{26} - 170q^{27} - 254q^{28} - 160q^{29} - 253q^{30} - 318q^{31} - 227q^{32} - 180q^{33} - 276q^{34} - 217q^{35} - 539q^{36} - 172q^{37} - 250q^{38} - 254q^{39} - 130q^{40} - 408q^{41} - 294q^{42} - 146q^{43} - 160q^{44} - 262q^{45} - 298q^{46} - 62q^{47} - 106q^{48} - 53q^{49} - 82q^{50} - 298q^{51} - 12q^{52} - 136q^{53} - 110q^{54} - 130q^{55} - 510q^{56} - 150q^{57} - 20q^{58} - 110q^{59} - 117q^{60} - 228q^{61} - 254q^{62} - 166q^{63} - 163q^{64} - 151q^{65} - 470q^{66} - 242q^{67} - 304q^{68} - 274q^{69} - 301q^{70} - 478q^{71} - 415q^{72} - 276q^{73} - 436q^{74} - 311q^{75} - 670q^{76} - 270q^{77} - 602q^{78} - 350q^{79} - 474q^{80} - 609q^{81} - 384q^{82} - 346q^{83} - 566q^{84} - 327q^{85} - 598q^{86} - 430q^{87} - 420q^{88} - 340q^{89} - 186q^{90} - 538q^{91} - 382q^{92} - 242q^{93} - 286q^{94} - 185q^{95} - 478q^{96} - 152q^{97} - 119q^{98} - 180q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(605))$$

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
605.2.a $$\chi_{605}(1, \cdot)$$ 605.2.a.a 1 1
605.2.a.b 1
605.2.a.c 1
605.2.a.d 2
605.2.a.e 2
605.2.a.f 2
605.2.a.g 3
605.2.a.h 3
605.2.a.i 4
605.2.a.j 4
605.2.a.k 4
605.2.a.l 4
605.2.a.m 6
605.2.b $$\chi_{605}(364, \cdot)$$ 605.2.b.a 2 1
605.2.b.b 4
605.2.b.c 4
605.2.b.d 4
605.2.b.e 4
605.2.b.f 8
605.2.b.g 8
605.2.b.h 12
605.2.e $$\chi_{605}(362, \cdot)$$ 605.2.e.a 20 2
605.2.e.b 32
605.2.e.c 40
605.2.g $$\chi_{605}(81, \cdot)$$ 605.2.g.a 4 4
605.2.g.b 4
605.2.g.c 4
605.2.g.d 4
605.2.g.e 8
605.2.g.f 8
605.2.g.g 8
605.2.g.h 8
605.2.g.i 8
605.2.g.j 8
605.2.g.k 8
605.2.g.l 8
605.2.g.m 8
605.2.g.n 8
605.2.g.o 12
605.2.g.p 12
605.2.g.q 24
605.2.j $$\chi_{605}(9, \cdot)$$ 605.2.j.a 8 4
605.2.j.b 8
605.2.j.c 8
605.2.j.d 16
605.2.j.e 16
605.2.j.f 16
605.2.j.g 16
605.2.j.h 16
605.2.j.i 16
605.2.j.j 16
605.2.j.k 48
605.2.k $$\chi_{605}(56, \cdot)$$ 605.2.k.a 220 10
605.2.k.b 220
605.2.m $$\chi_{605}(112, \cdot)$$ 605.2.m.a 16 8
605.2.m.b 16
605.2.m.c 32
605.2.m.d 32
605.2.m.e 32
605.2.m.f 80
605.2.m.g 160
605.2.o $$\chi_{605}(34, \cdot)$$ 605.2.o.a 640 10
605.2.r $$\chi_{605}(32, \cdot)$$ 605.2.r.a 1280 20
605.2.s $$\chi_{605}(16, \cdot)$$ 605.2.s.a 880 40
605.2.s.b 880
605.2.u $$\chi_{605}(4, \cdot)$$ 605.2.u.a 2560 40
605.2.w $$\chi_{605}(2, \cdot)$$ 605.2.w.a 5120 80

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(605))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(605)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(11))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(55))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(121))$$$$^{\oplus 2}$$