# Properties

 Label 605.2 Level 605 Weight 2 Dimension 12671 Nonzero newspaces 12 Newform subspaces 67 Sturm bound 58080 Trace bound 1

## 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

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

## 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

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