# Properties

 Label 1205.2 Level 1205 Weight 2 Dimension 52519 Nonzero newspaces 40 Sturm bound 232320 Trace bound 5

# Learn more about

## Defining parameters

 Level: $$N$$ = $$1205 = 5 \cdot 241$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$40$$ Sturm bound: $$232320$$ Trace bound: $$5$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(1205))$$.

Total New Old
Modular forms 59040 53955 5085
Cusp forms 57121 52519 4602
Eisenstein series 1919 1436 483

## Trace form

 $$52519q - 243q^{2} - 244q^{3} - 247q^{4} - 361q^{5} - 732q^{6} - 248q^{7} - 255q^{8} - 253q^{9} + O(q^{10})$$ $$52519q - 243q^{2} - 244q^{3} - 247q^{4} - 361q^{5} - 732q^{6} - 248q^{7} - 255q^{8} - 253q^{9} - 363q^{10} - 732q^{11} - 268q^{12} - 254q^{13} - 264q^{14} - 364q^{15} - 751q^{16} - 258q^{17} - 279q^{18} - 260q^{19} - 367q^{20} - 752q^{21} - 276q^{22} - 264q^{23} - 300q^{24} - 361q^{25} - 762q^{26} - 280q^{27} - 296q^{28} - 270q^{29} - 372q^{30} - 752q^{31} - 303q^{32} - 288q^{33} - 294q^{34} - 368q^{35} - 811q^{36} - 278q^{37} - 300q^{38} - 296q^{39} - 375q^{40} - 762q^{41} - 336q^{42} - 284q^{43} - 324q^{44} - 373q^{45} - 792q^{46} - 288q^{47} - 364q^{48} - 297q^{49} - 363q^{50} - 792q^{51} - 338q^{52} - 294q^{53} - 360q^{54} - 372q^{55} - 840q^{56} - 320q^{57} - 330q^{58} - 300q^{59} - 388q^{60} - 782q^{61} - 336q^{62} - 344q^{63} - 367q^{64} - 374q^{65} - 864q^{66} - 308q^{67} - 366q^{68} - 336q^{69} - 384q^{70} - 792q^{71} - 435q^{72} - 314q^{73} - 354q^{74} - 364q^{75} - 860q^{76} - 336q^{77} - 408q^{78} - 320q^{79} - 391q^{80} - 841q^{81} - 366q^{82} - 324q^{83} - 464q^{84} - 378q^{85} - 852q^{86} - 360q^{87} - 420q^{88} - 330q^{89} - 399q^{90} - 832q^{91} - 408q^{92} - 368q^{93} - 384q^{94} - 380q^{95} - 972q^{96} - 338q^{97} - 411q^{98} - 396q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(1205))$$

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
1205.2.a $$\chi_{1205}(1, \cdot)$$ 1205.2.a.a 5 1
1205.2.a.b 11
1205.2.a.c 15
1205.2.a.d 25
1205.2.a.e 25
1205.2.b $$\chi_{1205}(724, \cdot)$$ 1205.2.b.a 4 1
1205.2.b.b 4
1205.2.b.c 46
1205.2.b.d 66
1205.2.c $$\chi_{1205}(1204, \cdot)$$ n/a 120 1
1205.2.d $$\chi_{1205}(481, \cdot)$$ 1205.2.d.a 6 1
1205.2.d.b 34
1205.2.d.c 42
1205.2.e $$\chi_{1205}(256, \cdot)$$ n/a 160 2
1205.2.f $$\chi_{1205}(546, \cdot)$$ n/a 164 2
1205.2.k $$\chi_{1205}(64, \cdot)$$ n/a 240 2
1205.2.l $$\chi_{1205}(91, \cdot)$$ n/a 328 4
1205.2.m $$\chi_{1205}(16, \cdot)$$ n/a 160 2
1205.2.n $$\chi_{1205}(739, \cdot)$$ n/a 240 2
1205.2.o $$\chi_{1205}(979, \cdot)$$ n/a 240 2
1205.2.q $$\chi_{1205}(249, \cdot)$$ n/a 472 4
1205.2.r $$\chi_{1205}(211, \cdot)$$ n/a 328 4
1205.2.t $$\chi_{1205}(154, \cdot)$$ n/a 480 4
1205.2.u $$\chi_{1205}(339, \cdot)$$ n/a 480 4
1205.2.v $$\chi_{1205}(36, \cdot)$$ n/a 328 4
1205.2.w $$\chi_{1205}(4, \cdot)$$ n/a 480 4
1205.2.bb $$\chi_{1205}(181, \cdot)$$ n/a 320 4
1205.2.bc $$\chi_{1205}(231, \cdot)$$ n/a 640 8
1205.2.bd $$\chi_{1205}(352, \cdot)$$ n/a 952 8
1205.2.be $$\chi_{1205}(197, \cdot)$$ n/a 952 8
1205.2.bh $$\chi_{1205}(6, \cdot)$$ n/a 656 8
1205.2.bm $$\chi_{1205}(729, \cdot)$$ n/a 960 8
1205.2.bo $$\chi_{1205}(121, \cdot)$$ n/a 640 8
1205.2.bp $$\chi_{1205}(209, \cdot)$$ n/a 944 8
1205.2.br $$\chi_{1205}(81, \cdot)$$ n/a 640 8
1205.2.bs $$\chi_{1205}(24, \cdot)$$ n/a 960 8
1205.2.bt $$\chi_{1205}(299, \cdot)$$ n/a 960 8
1205.2.bv $$\chi_{1205}(41, \cdot)$$ n/a 1312 16
1205.2.bw $$\chi_{1205}(79, \cdot)$$ n/a 1888 16
1205.2.ca $$\chi_{1205}(38, \cdot)$$ n/a 1904 16
1205.2.cb $$\chi_{1205}(22, \cdot)$$ n/a 1904 16
1205.2.cc $$\chi_{1205}(9, \cdot)$$ n/a 1920 16
1205.2.ch $$\chi_{1205}(96, \cdot)$$ n/a 1280 16
1205.2.ck $$\chi_{1205}(33, \cdot)$$ n/a 3808 32
1205.2.cl $$\chi_{1205}(17, \cdot)$$ n/a 3808 32
1205.2.cn $$\chi_{1205}(29, \cdot)$$ n/a 3776 32
1205.2.co $$\chi_{1205}(161, \cdot)$$ n/a 2560 32
1205.2.cq $$\chi_{1205}(52, \cdot)$$ n/a 7616 64
1205.2.cr $$\chi_{1205}(7, \cdot)$$ n/a 7616 64

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(1205))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(1205)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(241))$$$$^{\oplus 2}$$