# Properties

 Label 2205.2 Level 2205 Weight 2 Dimension 116619 Nonzero newspaces 60 Sturm bound 677376 Trace bound 9

## Defining parameters

 Level: $$N$$ = $$2205 = 3^{2} \cdot 5 \cdot 7^{2}$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$60$$ Sturm bound: $$677376$$ Trace bound: $$9$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(2205))$$.

Total New Old
Modular forms 173184 119237 53947
Cusp forms 165505 116619 48886
Eisenstein series 7679 2618 5061

## Trace form

 $$116619 q - 97 q^{2} - 128 q^{3} - 117 q^{4} - 150 q^{5} - 376 q^{6} - 116 q^{7} - 201 q^{8} - 124 q^{9} + O(q^{10})$$ $$116619 q - 97 q^{2} - 128 q^{3} - 117 q^{4} - 150 q^{5} - 376 q^{6} - 116 q^{7} - 201 q^{8} - 124 q^{9} - 450 q^{10} - 310 q^{11} - 64 q^{12} - 120 q^{13} - 96 q^{14} - 296 q^{15} - 229 q^{16} - 4 q^{17} - 8 q^{18} - 246 q^{19} - 20 q^{20} - 396 q^{21} - 82 q^{22} - 18 q^{23} + 60 q^{24} - 138 q^{25} - 76 q^{26} - 32 q^{27} - 288 q^{28} - 92 q^{29} - 64 q^{30} - 234 q^{31} + 259 q^{32} - 16 q^{33} + 128 q^{34} - 93 q^{35} - 440 q^{36} - 88 q^{37} + 326 q^{38} - 8 q^{39} + 226 q^{40} + 88 q^{41} - 12 q^{42} - 22 q^{43} + 490 q^{44} - 112 q^{45} - 346 q^{46} + 86 q^{47} - 208 q^{48} + 84 q^{49} - 331 q^{50} - 376 q^{51} + 384 q^{52} - 136 q^{53} - 244 q^{54} - 282 q^{55} - 180 q^{56} - 392 q^{57} + 188 q^{58} - 214 q^{59} - 364 q^{60} - 54 q^{61} - 294 q^{62} - 312 q^{63} - 297 q^{64} - 55 q^{65} - 440 q^{66} + 114 q^{67} - 344 q^{68} - 156 q^{69} + 51 q^{70} - 302 q^{71} - 312 q^{72} + 84 q^{73} + 256 q^{74} - 164 q^{75} + 242 q^{76} + 54 q^{77} - 112 q^{78} + 270 q^{79} - 89 q^{80} - 64 q^{81} + 330 q^{82} + 402 q^{83} + 15 q^{85} + 416 q^{86} + 52 q^{87} + 480 q^{88} + 216 q^{89} - 344 q^{90} - 818 q^{91} - 228 q^{92} - 60 q^{93} + 104 q^{94} - 337 q^{95} - 536 q^{96} - 50 q^{97} + 312 q^{98} - 404 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(2205))$$

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 available newforms together with their dimension.

Label $$\chi$$ Newforms Dimension $$\chi$$ degree
2205.2.a $$\chi_{2205}(1, \cdot)$$ 2205.2.a.a 1 1
2205.2.a.b 1
2205.2.a.c 1
2205.2.a.d 1
2205.2.a.e 1
2205.2.a.f 1
2205.2.a.g 1
2205.2.a.h 1
2205.2.a.i 1
2205.2.a.j 1
2205.2.a.k 1
2205.2.a.l 1
2205.2.a.m 1
2205.2.a.n 2
2205.2.a.o 2
2205.2.a.p 2
2205.2.a.q 2
2205.2.a.r 2
2205.2.a.s 2
2205.2.a.t 2
2205.2.a.u 2
2205.2.a.v 2
2205.2.a.w 2
2205.2.a.x 2
2205.2.a.y 2
2205.2.a.z 2
2205.2.a.ba 2
2205.2.a.bb 3
2205.2.a.bc 3
2205.2.a.bd 3
2205.2.a.be 3
2205.2.a.bf 4
2205.2.a.bg 4
2205.2.a.bh 4
2205.2.a.bi 4
2205.2.b $$\chi_{2205}(881, \cdot)$$ 2205.2.b.a 12 1
2205.2.b.b 12
2205.2.b.c 16
2205.2.b.d 16
2205.2.d $$\chi_{2205}(1324, \cdot)$$ 2205.2.d.a 2 1
2205.2.d.b 2
2205.2.d.c 2
2205.2.d.d 2
2205.2.d.e 2
2205.2.d.f 2
2205.2.d.g 2
2205.2.d.h 2
2205.2.d.i 4
2205.2.d.j 4
2205.2.d.k 4
2205.2.d.l 6
2205.2.d.m 8
2205.2.d.n 8
2205.2.d.o 8
2205.2.d.p 8
2205.2.d.q 8
2205.2.d.r 8
2205.2.d.s 8
2205.2.d.t 8
2205.2.g $$\chi_{2205}(2204, \cdot)$$ 2205.2.g.a 8 1
2205.2.g.b 24
2205.2.g.c 48
2205.2.i $$\chi_{2205}(736, \cdot)$$ n/a 328 2
2205.2.j $$\chi_{2205}(226, \cdot)$$ n/a 132 2
2205.2.k $$\chi_{2205}(961, \cdot)$$ n/a 320 2
2205.2.l $$\chi_{2205}(1096, \cdot)$$ n/a 320 2
2205.2.m $$\chi_{2205}(197, \cdot)$$ n/a 164 2
2205.2.p $$\chi_{2205}(1567, \cdot)$$ n/a 192 2
2205.2.r $$\chi_{2205}(214, \cdot)$$ n/a 464 2
2205.2.t $$\chi_{2205}(1391, \cdot)$$ n/a 320 2
2205.2.u $$\chi_{2205}(374, \cdot)$$ n/a 464 2
2205.2.z $$\chi_{2205}(734, \cdot)$$ n/a 464 2
2205.2.bb $$\chi_{2205}(1844, \cdot)$$ n/a 160 2
2205.2.be $$\chi_{2205}(1256, \cdot)$$ n/a 320 2
2205.2.bf $$\chi_{2205}(1549, \cdot)$$ n/a 192 2
2205.2.bh $$\chi_{2205}(589, \cdot)$$ n/a 472 2
2205.2.bj $$\chi_{2205}(521, \cdot)$$ n/a 104 2
2205.2.bl $$\chi_{2205}(146, \cdot)$$ n/a 320 2
2205.2.bo $$\chi_{2205}(79, \cdot)$$ n/a 464 2
2205.2.bq $$\chi_{2205}(509, \cdot)$$ n/a 464 2
2205.2.bs $$\chi_{2205}(316, \cdot)$$ n/a 552 6
2205.2.bt $$\chi_{2205}(178, \cdot)$$ n/a 928 4
2205.2.bw $$\chi_{2205}(263, \cdot)$$ n/a 928 4
2205.2.by $$\chi_{2205}(128, \cdot)$$ n/a 928 4
2205.2.ca $$\chi_{2205}(1207, \cdot)$$ n/a 384 4
2205.2.cc $$\chi_{2205}(97, \cdot)$$ n/a 928 4
2205.2.cd $$\chi_{2205}(932, \cdot)$$ n/a 944 4
2205.2.cf $$\chi_{2205}(422, \cdot)$$ n/a 320 4
2205.2.ch $$\chi_{2205}(313, \cdot)$$ n/a 928 4
2205.2.ck $$\chi_{2205}(314, \cdot)$$ n/a 672 6
2205.2.cn $$\chi_{2205}(64, \cdot)$$ n/a 828 6
2205.2.cp $$\chi_{2205}(251, \cdot)$$ n/a 432 6
2205.2.cq $$\chi_{2205}(121, \cdot)$$ n/a 2688 12
2205.2.cr $$\chi_{2205}(16, \cdot)$$ n/a 2688 12
2205.2.cs $$\chi_{2205}(46, \cdot)$$ n/a 1128 12
2205.2.ct $$\chi_{2205}(106, \cdot)$$ n/a 2688 12
2205.2.cv $$\chi_{2205}(118, \cdot)$$ n/a 1656 12
2205.2.cw $$\chi_{2205}(8, \cdot)$$ n/a 1344 12
2205.2.cz $$\chi_{2205}(164, \cdot)$$ n/a 3984 12
2205.2.db $$\chi_{2205}(4, \cdot)$$ n/a 3984 12
2205.2.de $$\chi_{2205}(41, \cdot)$$ n/a 2688 12
2205.2.dg $$\chi_{2205}(26, \cdot)$$ n/a 912 12
2205.2.di $$\chi_{2205}(169, \cdot)$$ n/a 3984 12
2205.2.dk $$\chi_{2205}(109, \cdot)$$ n/a 1656 12
2205.2.dl $$\chi_{2205}(236, \cdot)$$ n/a 2688 12
2205.2.do $$\chi_{2205}(89, \cdot)$$ n/a 1344 12
2205.2.dq $$\chi_{2205}(104, \cdot)$$ n/a 3984 12
2205.2.dv $$\chi_{2205}(59, \cdot)$$ n/a 3984 12
2205.2.dw $$\chi_{2205}(101, \cdot)$$ n/a 2688 12
2205.2.dy $$\chi_{2205}(184, \cdot)$$ n/a 3984 12
2205.2.ea $$\chi_{2205}(157, \cdot)$$ n/a 7968 24
2205.2.ec $$\chi_{2205}(92, \cdot)$$ n/a 7968 24
2205.2.ee $$\chi_{2205}(53, \cdot)$$ n/a 2688 24
2205.2.eh $$\chi_{2205}(73, \cdot)$$ n/a 3312 24
2205.2.ej $$\chi_{2205}(13, \cdot)$$ n/a 7968 24
2205.2.el $$\chi_{2205}(2, \cdot)$$ n/a 7968 24
2205.2.en $$\chi_{2205}(23, \cdot)$$ n/a 7968 24
2205.2.eo $$\chi_{2205}(52, \cdot)$$ n/a 7968 24

"n/a" means that newforms for that character have not been added to the database yet

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(2205))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(2205)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 18}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(3))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(5))$$$$^{\oplus 9}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(7))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(9))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(15))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(21))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(35))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(45))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(49))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(63))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(105))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(147))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(245))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(315))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(441))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(735))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2205))$$$$^{\oplus 1}$$