## Defining parameters

 Level: $$N$$ = $$1045 = 5 \cdot 11 \cdot 19$$ Weight: $$k$$ = $$6$$ Nonzero newspaces: $$36$$ Sturm bound: $$518400$$ Trace bound: $$6$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{6}(\Gamma_1(1045))$$.

Total New Old
Modular forms 217440 194532 22908
Cusp forms 214560 192700 21860
Eisenstein series 2880 1832 1048

## Trace form

 $$192700 q - 116 q^{2} - 140 q^{3} - 332 q^{4} - 446 q^{5} + 572 q^{6} + 1824 q^{7} + 36 q^{8} - 4456 q^{9} + O(q^{10})$$ $$192700 q - 116 q^{2} - 140 q^{3} - 332 q^{4} - 446 q^{5} + 572 q^{6} + 1824 q^{7} + 36 q^{8} - 4456 q^{9} - 3756 q^{10} - 1494 q^{11} - 8028 q^{12} + 11728 q^{13} + 18440 q^{14} + 15738 q^{15} + 13180 q^{16} - 8420 q^{17} - 48148 q^{18} - 28984 q^{19} - 28924 q^{20} - 44468 q^{21} - 33950 q^{22} - 8604 q^{23} + 121036 q^{24} + 58818 q^{25} + 155872 q^{26} - 28520 q^{27} - 64908 q^{28} - 6872 q^{29} + 48598 q^{30} + 21204 q^{31} - 149676 q^{32} - 143586 q^{33} - 52040 q^{34} + 13652 q^{35} - 114472 q^{36} + 39720 q^{37} - 210416 q^{38} - 130896 q^{39} - 15998 q^{40} - 78656 q^{41} + 147592 q^{42} - 40492 q^{43} - 583676 q^{44} - 153088 q^{45} + 242988 q^{46} + 219324 q^{47} + 693420 q^{48} + 372464 q^{49} + 299946 q^{50} + 6448 q^{51} + 125728 q^{52} + 239584 q^{53} + 728844 q^{54} + 326311 q^{55} - 469840 q^{56} - 447744 q^{57} - 135304 q^{58} - 427744 q^{59} - 1212306 q^{60} - 1210992 q^{61} - 1082972 q^{62} - 310784 q^{63} + 699892 q^{64} + 458854 q^{65} + 1172458 q^{66} + 1473940 q^{67} + 1966756 q^{68} + 1293840 q^{69} + 562352 q^{70} - 1268472 q^{71} - 3455272 q^{72} - 1847464 q^{73} - 610192 q^{74} - 566864 q^{75} - 1477092 q^{76} + 1021942 q^{77} + 1883396 q^{78} + 486328 q^{79} - 891944 q^{80} - 2562456 q^{81} - 1902504 q^{82} - 1319668 q^{83} - 45608 q^{84} - 383360 q^{85} + 2730984 q^{86} + 1972536 q^{87} + 1630242 q^{88} + 2058124 q^{89} + 4510194 q^{90} + 724384 q^{91} + 217172 q^{92} - 904748 q^{93} - 4124596 q^{94} - 744286 q^{95} - 3611760 q^{96} - 377464 q^{97} + 2261236 q^{98} + 549940 q^{99} + O(q^{100})$$

## Decomposition of $$S_{6}^{\mathrm{new}}(\Gamma_1(1045))$$

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 the newforms together with their dimension.

Label $$\chi$$ Newforms Dimension $$\chi$$ degree
1045.6.a $$\chi_{1045}(1, \cdot)$$ 1045.6.a.a 35 1
1045.6.a.b 36
1045.6.a.c 37
1045.6.a.d 37
1045.6.a.e 38
1045.6.a.f 38
1045.6.a.g 39
1045.6.a.h 40
1045.6.b $$\chi_{1045}(419, \cdot)$$ n/a 452 1
1045.6.e $$\chi_{1045}(1044, \cdot)$$ n/a 596 1
1045.6.f $$\chi_{1045}(626, \cdot)$$ n/a 400 1
1045.6.i $$\chi_{1045}(771, \cdot)$$ n/a 672 2
1045.6.j $$\chi_{1045}(153, \cdot)$$ n/a 1080 2
1045.6.m $$\chi_{1045}(683, \cdot)$$ n/a 1000 2
1045.6.n $$\chi_{1045}(191, \cdot)$$ n/a 1440 4
1045.6.p $$\chi_{1045}(791, \cdot)$$ n/a 800 2
1045.6.s $$\chi_{1045}(164, \cdot)$$ n/a 1192 2
1045.6.t $$\chi_{1045}(144, \cdot)$$ n/a 1000 2
1045.6.v $$\chi_{1045}(111, \cdot)$$ n/a 1992 6
1045.6.y $$\chi_{1045}(151, \cdot)$$ n/a 1600 4
1045.6.z $$\chi_{1045}(94, \cdot)$$ n/a 2384 4
1045.6.bc $$\chi_{1045}(229, \cdot)$$ n/a 2160 4
1045.6.bd $$\chi_{1045}(12, \cdot)$$ n/a 2000 4
1045.6.bg $$\chi_{1045}(87, \cdot)$$ n/a 2384 4
1045.6.bh $$\chi_{1045}(26, \cdot)$$ n/a 3200 8
1045.6.bj $$\chi_{1045}(109, \cdot)$$ n/a 3576 6
1045.6.bm $$\chi_{1045}(21, \cdot)$$ n/a 2400 6
1045.6.bo $$\chi_{1045}(199, \cdot)$$ n/a 3000 6
1045.6.bp $$\chi_{1045}(37, \cdot)$$ n/a 4768 8
1045.6.bs $$\chi_{1045}(172, \cdot)$$ n/a 4320 8
1045.6.bu $$\chi_{1045}(49, \cdot)$$ n/a 4768 8
1045.6.bv $$\chi_{1045}(84, \cdot)$$ n/a 4768 8
1045.6.by $$\chi_{1045}(46, \cdot)$$ n/a 3200 8
1045.6.cb $$\chi_{1045}(43, \cdot)$$ n/a 7152 12
1045.6.cc $$\chi_{1045}(67, \cdot)$$ n/a 6000 12
1045.6.ce $$\chi_{1045}(16, \cdot)$$ n/a 9600 24
1045.6.cf $$\chi_{1045}(7, \cdot)$$ n/a 9536 16
1045.6.ci $$\chi_{1045}(27, \cdot)$$ n/a 9536 16
1045.6.ck $$\chi_{1045}(4, \cdot)$$ n/a 14304 24
1045.6.cm $$\chi_{1045}(41, \cdot)$$ n/a 9600 24
1045.6.cn $$\chi_{1045}(29, \cdot)$$ n/a 14304 24
1045.6.cr $$\chi_{1045}(3, \cdot)$$ n/a 28608 48
1045.6.cs $$\chi_{1045}(17, \cdot)$$ n/a 28608 48

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

## Decomposition of $$S_{6}^{\mathrm{old}}(\Gamma_1(1045))$$ into lower level spaces

$$S_{6}^{\mathrm{old}}(\Gamma_1(1045)) \cong$$ $$S_{6}^{\mathrm{new}}(\Gamma_1(5))$$$$^{\oplus 4}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(11))$$$$^{\oplus 4}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(19))$$$$^{\oplus 4}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(55))$$$$^{\oplus 2}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(95))$$$$^{\oplus 2}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(209))$$$$^{\oplus 2}$$