# Properties

 Label 1053.2 Level 1053 Weight 2 Dimension 31256 Nonzero newspaces 33 Sturm bound 163296 Trace bound 24

## Defining parameters

 Level: $$N$$ = $$1053 = 3^{4} \cdot 13$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$33$$ Sturm bound: $$163296$$ Trace bound: $$24$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(1053))$$.

Total New Old
Modular forms 42120 32488 9632
Cusp forms 39529 31256 8273
Eisenstein series 2591 1232 1359

## Trace form

 $$31256 q - 120 q^{2} - 180 q^{3} - 196 q^{4} - 114 q^{5} - 180 q^{6} - 194 q^{7} - 96 q^{8} - 180 q^{9} + O(q^{10})$$ $$31256 q - 120 q^{2} - 180 q^{3} - 196 q^{4} - 114 q^{5} - 180 q^{6} - 194 q^{7} - 96 q^{8} - 180 q^{9} - 270 q^{10} - 102 q^{11} - 180 q^{12} - 211 q^{13} - 222 q^{14} - 180 q^{15} - 196 q^{16} - 90 q^{17} - 198 q^{18} - 302 q^{19} - 186 q^{20} - 234 q^{21} - 210 q^{22} - 186 q^{23} - 288 q^{24} - 220 q^{25} - 219 q^{26} - 450 q^{27} - 338 q^{28} - 174 q^{29} - 288 q^{30} - 218 q^{31} - 216 q^{32} - 234 q^{33} - 222 q^{34} - 138 q^{35} - 252 q^{36} - 266 q^{37} - 42 q^{38} - 198 q^{39} - 486 q^{40} - 114 q^{41} - 270 q^{42} - 194 q^{43} - 246 q^{44} - 288 q^{45} - 378 q^{46} - 246 q^{47} - 378 q^{48} - 240 q^{49} - 408 q^{50} - 306 q^{51} - 259 q^{52} - 414 q^{53} - 432 q^{54} - 378 q^{55} - 462 q^{56} - 288 q^{57} - 246 q^{58} - 258 q^{59} - 414 q^{60} - 230 q^{61} - 330 q^{62} - 288 q^{63} - 316 q^{64} - 141 q^{65} - 396 q^{66} - 218 q^{67} + 72 q^{68} - 72 q^{69} - 282 q^{70} + 90 q^{71} + 252 q^{72} - 212 q^{73} + 246 q^{74} - 290 q^{76} + 210 q^{77} - 81 q^{78} - 434 q^{79} + 516 q^{80} - 36 q^{81} - 432 q^{82} + 114 q^{83} + 270 q^{84} - 258 q^{85} + 282 q^{86} + 108 q^{87} - 306 q^{88} + 36 q^{89} - 18 q^{90} - 314 q^{91} - 78 q^{92} - 216 q^{93} - 282 q^{94} - 246 q^{95} - 162 q^{96} - 338 q^{97} - 540 q^{98} - 324 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(1053))$$

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
1053.2.a $$\chi_{1053}(1, \cdot)$$ 1053.2.a.a 1 1
1053.2.a.b 1
1053.2.a.c 1
1053.2.a.d 1
1053.2.a.e 2
1053.2.a.f 2
1053.2.a.g 3
1053.2.a.h 3
1053.2.a.i 4
1053.2.a.j 5
1053.2.a.k 5
1053.2.a.l 6
1053.2.a.m 6
1053.2.a.n 8
1053.2.b $$\chi_{1053}(649, \cdot)$$ 1053.2.b.a 2 1
1053.2.b.b 2
1053.2.b.c 2
1053.2.b.d 2
1053.2.b.e 2
1053.2.b.f 2
1053.2.b.g 4
1053.2.b.h 4
1053.2.b.i 10
1053.2.b.j 10
1053.2.b.k 12
1053.2.e $$\chi_{1053}(352, \cdot)$$ 1053.2.e.a 2 2
1053.2.e.b 2
1053.2.e.c 2
1053.2.e.d 2
1053.2.e.e 4
1053.2.e.f 4
1053.2.e.g 4
1053.2.e.h 4
1053.2.e.i 4
1053.2.e.j 4
1053.2.e.k 4
1053.2.e.l 4
1053.2.e.m 4
1053.2.e.n 6
1053.2.e.o 6
1053.2.e.p 8
1053.2.e.q 8
1053.2.e.r 8
1053.2.e.s 16
1053.2.f $$\chi_{1053}(217, \cdot)$$ n/a 108 2
1053.2.g $$\chi_{1053}(406, \cdot)$$ n/a 104 2
1053.2.h $$\chi_{1053}(55, \cdot)$$ n/a 108 2
1053.2.i $$\chi_{1053}(161, \cdot)$$ n/a 104 2
1053.2.l $$\chi_{1053}(433, \cdot)$$ n/a 108 2
1053.2.q $$\chi_{1053}(82, \cdot)$$ n/a 104 2
1053.2.r $$\chi_{1053}(595, \cdot)$$ n/a 108 2
1053.2.t $$\chi_{1053}(298, \cdot)$$ n/a 108 2
1053.2.w $$\chi_{1053}(118, \cdot)$$ n/a 216 6
1053.2.x $$\chi_{1053}(289, \cdot)$$ n/a 240 6
1053.2.y $$\chi_{1053}(100, \cdot)$$ n/a 240 6
1053.2.ba $$\chi_{1053}(215, \cdot)$$ n/a 216 4
1053.2.bc $$\chi_{1053}(512, \cdot)$$ n/a 216 4
1053.2.bd $$\chi_{1053}(80, \cdot)$$ n/a 208 4
1053.2.bf $$\chi_{1053}(188, \cdot)$$ n/a 216 4
1053.2.bl $$\chi_{1053}(64, \cdot)$$ n/a 240 6
1053.2.bn $$\chi_{1053}(127, \cdot)$$ n/a 240 6
1053.2.bo $$\chi_{1053}(10, \cdot)$$ n/a 240 6
1053.2.bq $$\chi_{1053}(40, \cdot)$$ n/a 1944 18
1053.2.br $$\chi_{1053}(16, \cdot)$$ n/a 2232 18
1053.2.bs $$\chi_{1053}(61, \cdot)$$ n/a 2232 18
1053.2.bt $$\chi_{1053}(206, \cdot)$$ n/a 480 12
1053.2.bw $$\chi_{1053}(8, \cdot)$$ n/a 480 12
1053.2.by $$\chi_{1053}(71, \cdot)$$ n/a 480 12
1053.2.bz $$\chi_{1053}(43, \cdot)$$ n/a 2232 18
1053.2.cd $$\chi_{1053}(25, \cdot)$$ n/a 2232 18
1053.2.ce $$\chi_{1053}(4, \cdot)$$ n/a 2232 18
1053.2.cl $$\chi_{1053}(5, \cdot)$$ n/a 4464 36
1053.2.cm $$\chi_{1053}(20, \cdot)$$ n/a 4464 36
1053.2.cn $$\chi_{1053}(2, \cdot)$$ n/a 4464 36

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(1053))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(1053)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(13))$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(27))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(39))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(81))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(117))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(351))$$$$^{\oplus 2}$$