# Properties

 Label 1045.2 Level 1045 Weight 2 Dimension 37811 Nonzero newspaces 36 Sturm bound 172800 Trace bound 6

## Defining parameters

 Level: $$N$$ = $$1045 = 5 \cdot 11 \cdot 19$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$36$$ Sturm bound: $$172800$$ Trace bound: $$6$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(1045))$$.

Total New Old
Modular forms 44640 39643 4997
Cusp forms 41761 37811 3950
Eisenstein series 2879 1832 1047

## Trace form

 $$37811 q - 115 q^{2} - 112 q^{3} - 103 q^{4} - 183 q^{5} - 356 q^{6} - 120 q^{7} - 119 q^{8} - 125 q^{9} + O(q^{10})$$ $$37811 q - 115 q^{2} - 112 q^{3} - 103 q^{4} - 183 q^{5} - 356 q^{6} - 120 q^{7} - 119 q^{8} - 125 q^{9} - 207 q^{10} - 423 q^{11} - 328 q^{12} - 150 q^{13} - 184 q^{14} - 250 q^{15} - 543 q^{16} - 166 q^{17} - 271 q^{18} - 209 q^{19} - 523 q^{20} - 460 q^{21} - 247 q^{22} - 308 q^{23} - 308 q^{24} - 279 q^{25} - 498 q^{26} - 208 q^{27} - 332 q^{28} - 206 q^{29} - 406 q^{30} - 428 q^{31} - 315 q^{32} - 318 q^{33} - 462 q^{34} - 324 q^{35} - 891 q^{36} - 238 q^{37} - 379 q^{38} - 536 q^{39} - 313 q^{40} - 498 q^{41} - 496 q^{42} - 248 q^{43} - 245 q^{44} - 569 q^{45} - 580 q^{46} - 180 q^{47} - 396 q^{48} - 129 q^{49} - 325 q^{50} - 472 q^{51} - 114 q^{52} - 206 q^{53} - 228 q^{54} - 186 q^{55} - 1080 q^{56} - 228 q^{57} - 162 q^{58} - 204 q^{59} - 418 q^{60} - 470 q^{61} - 492 q^{62} - 328 q^{63} - 495 q^{64} - 372 q^{65} - 778 q^{66} - 592 q^{67} - 590 q^{68} - 512 q^{69} - 592 q^{70} - 688 q^{71} - 563 q^{72} - 498 q^{73} - 602 q^{74} - 420 q^{75} - 759 q^{76} - 622 q^{77} - 668 q^{78} - 488 q^{79} - 355 q^{80} - 649 q^{81} - 562 q^{82} - 248 q^{83} - 152 q^{84} - 270 q^{85} - 544 q^{86} - 224 q^{87} - 401 q^{88} - 382 q^{89} + 147 q^{90} - 464 q^{91} + 28 q^{92} + 148 q^{93} + 148 q^{94} - 107 q^{95} - 220 q^{96} - 26 q^{97} + 81 q^{98} + 15 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(1045))$$

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
1045.2.a $$\chi_{1045}(1, \cdot)$$ 1045.2.a.a 1 1
1045.2.a.b 1
1045.2.a.c 2
1045.2.a.d 5
1045.2.a.e 5
1045.2.a.f 6
1045.2.a.g 6
1045.2.a.h 7
1045.2.a.i 8
1045.2.a.j 9
1045.2.a.k 9
1045.2.b $$\chi_{1045}(419, \cdot)$$ 1045.2.b.a 4 1
1045.2.b.b 16
1045.2.b.c 20
1045.2.b.d 22
1045.2.b.e 30
1045.2.e $$\chi_{1045}(1044, \cdot)$$ n/a 116 1
1045.2.f $$\chi_{1045}(626, \cdot)$$ 1045.2.f.a 40 1
1045.2.f.b 40
1045.2.i $$\chi_{1045}(771, \cdot)$$ n/a 128 2
1045.2.j $$\chi_{1045}(153, \cdot)$$ n/a 216 2
1045.2.m $$\chi_{1045}(683, \cdot)$$ n/a 200 2
1045.2.n $$\chi_{1045}(191, \cdot)$$ n/a 288 4
1045.2.p $$\chi_{1045}(791, \cdot)$$ n/a 160 2
1045.2.s $$\chi_{1045}(164, \cdot)$$ n/a 232 2
1045.2.t $$\chi_{1045}(144, \cdot)$$ n/a 200 2
1045.2.v $$\chi_{1045}(111, \cdot)$$ n/a 408 6
1045.2.y $$\chi_{1045}(151, \cdot)$$ n/a 320 4
1045.2.z $$\chi_{1045}(94, \cdot)$$ n/a 464 4
1045.2.bc $$\chi_{1045}(229, \cdot)$$ n/a 432 4
1045.2.bd $$\chi_{1045}(12, \cdot)$$ n/a 400 4
1045.2.bg $$\chi_{1045}(87, \cdot)$$ n/a 464 4
1045.2.bh $$\chi_{1045}(26, \cdot)$$ n/a 640 8
1045.2.bj $$\chi_{1045}(109, \cdot)$$ n/a 696 6
1045.2.bm $$\chi_{1045}(21, \cdot)$$ n/a 480 6
1045.2.bo $$\chi_{1045}(199, \cdot)$$ n/a 600 6
1045.2.bp $$\chi_{1045}(37, \cdot)$$ n/a 928 8
1045.2.bs $$\chi_{1045}(172, \cdot)$$ n/a 864 8
1045.2.bu $$\chi_{1045}(49, \cdot)$$ n/a 928 8
1045.2.bv $$\chi_{1045}(84, \cdot)$$ n/a 928 8
1045.2.by $$\chi_{1045}(46, \cdot)$$ n/a 640 8
1045.2.cb $$\chi_{1045}(43, \cdot)$$ n/a 1392 12
1045.2.cc $$\chi_{1045}(67, \cdot)$$ n/a 1200 12
1045.2.ce $$\chi_{1045}(16, \cdot)$$ n/a 1920 24
1045.2.cf $$\chi_{1045}(7, \cdot)$$ n/a 1856 16
1045.2.ci $$\chi_{1045}(27, \cdot)$$ n/a 1856 16
1045.2.ck $$\chi_{1045}(4, \cdot)$$ n/a 2784 24
1045.2.cm $$\chi_{1045}(41, \cdot)$$ n/a 1920 24
1045.2.cn $$\chi_{1045}(29, \cdot)$$ n/a 2784 24
1045.2.cr $$\chi_{1045}(3, \cdot)$$ n/a 5568 48
1045.2.cs $$\chi_{1045}(17, \cdot)$$ n/a 5568 48

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(1045))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(1045)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(5))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(11))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(19))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(55))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(95))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(209))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1045))$$$$^{\oplus 1}$$