# Properties

 Label 1045.4 Level 1045 Weight 4 Dimension 115252 Nonzero newspaces 36 Sturm bound 345600 Trace bound 6

## Defining parameters

 Level: $$N$$ = $$1045 = 5 \cdot 11 \cdot 19$$ Weight: $$k$$ = $$4$$ Nonzero newspaces: $$36$$ Sturm bound: $$345600$$ Trace bound: $$6$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(\Gamma_1(1045))$$.

Total New Old
Modular forms 131040 117084 13956
Cusp forms 128160 115252 12908
Eisenstein series 2880 1832 1048

## Trace form

 $$115252 q - 140 q^{2} - 116 q^{3} - 92 q^{4} - 206 q^{5} - 604 q^{6} - 140 q^{7} + 36 q^{8} + 104 q^{9} + O(q^{10})$$ $$115252 q - 140 q^{2} - 116 q^{3} - 92 q^{4} - 206 q^{5} - 604 q^{6} - 140 q^{7} + 36 q^{8} + 104 q^{9} + 84 q^{10} - 162 q^{11} - 732 q^{12} - 772 q^{13} - 1144 q^{14} - 630 q^{15} - 420 q^{16} - 44 q^{17} + 2132 q^{18} + 2028 q^{19} + 1460 q^{20} + 2344 q^{21} + 2446 q^{22} - 1068 q^{23} - 2612 q^{24} - 1070 q^{25} - 3200 q^{26} - 6164 q^{27} - 9772 q^{28} - 3044 q^{29} - 3170 q^{30} - 2724 q^{31} + 3060 q^{32} + 1002 q^{33} + 2440 q^{34} + 2066 q^{35} + 11384 q^{36} + 4128 q^{37} + 9160 q^{38} + 10068 q^{39} + 6226 q^{40} + 3556 q^{41} + 14104 q^{42} + 4560 q^{43} - 980 q^{44} - 22 q^{45} - 6740 q^{46} - 7068 q^{47} - 21204 q^{48} - 9032 q^{49} - 9006 q^{50} - 9044 q^{51} - 11776 q^{52} - 7940 q^{53} - 18756 q^{54} - 10429 q^{55} + 944 q^{56} + 3696 q^{57} - 312 q^{58} + 12056 q^{59} - 1698 q^{60} - 14100 q^{61} - 1340 q^{62} - 9872 q^{63} - 4268 q^{64} + 3904 q^{65} + 9706 q^{66} + 12188 q^{67} + 12244 q^{68} + 14136 q^{69} + 16112 q^{70} - 5556 q^{71} + 25688 q^{72} + 5928 q^{73} + 10496 q^{74} + 3496 q^{75} + 28588 q^{76} + 8116 q^{77} + 44036 q^{78} + 31796 q^{79} + 38536 q^{80} + 23304 q^{81} + 14352 q^{82} + 9944 q^{83} + 7768 q^{84} + 1950 q^{85} - 15792 q^{86} - 13824 q^{87} - 2446 q^{88} - 23108 q^{89} - 34806 q^{90} - 20452 q^{91} - 33964 q^{92} - 26924 q^{93} - 21844 q^{94} - 23197 q^{95} - 65232 q^{96} - 16280 q^{97} - 51500 q^{98} - 17612 q^{99} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(\Gamma_1(1045))$$

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
1045.4.a $$\chi_{1045}(1, \cdot)$$ 1045.4.a.a 1 1
1045.4.a.b 20
1045.4.a.c 20
1045.4.a.d 22
1045.4.a.e 22
1045.4.a.f 23
1045.4.a.g 23
1045.4.a.h 24
1045.4.a.i 25
1045.4.b $$\chi_{1045}(419, \cdot)$$ n/a 268 1
1045.4.e $$\chi_{1045}(1044, \cdot)$$ n/a 356 1
1045.4.f $$\chi_{1045}(626, \cdot)$$ n/a 240 1
1045.4.i $$\chi_{1045}(771, \cdot)$$ n/a 400 2
1045.4.j $$\chi_{1045}(153, \cdot)$$ n/a 648 2
1045.4.m $$\chi_{1045}(683, \cdot)$$ n/a 600 2
1045.4.n $$\chi_{1045}(191, \cdot)$$ n/a 864 4
1045.4.p $$\chi_{1045}(791, \cdot)$$ n/a 480 2
1045.4.s $$\chi_{1045}(164, \cdot)$$ n/a 712 2
1045.4.t $$\chi_{1045}(144, \cdot)$$ n/a 600 2
1045.4.v $$\chi_{1045}(111, \cdot)$$ n/a 1200 6
1045.4.y $$\chi_{1045}(151, \cdot)$$ n/a 960 4
1045.4.z $$\chi_{1045}(94, \cdot)$$ n/a 1424 4
1045.4.bc $$\chi_{1045}(229, \cdot)$$ n/a 1296 4
1045.4.bd $$\chi_{1045}(12, \cdot)$$ n/a 1200 4
1045.4.bg $$\chi_{1045}(87, \cdot)$$ n/a 1424 4
1045.4.bh $$\chi_{1045}(26, \cdot)$$ n/a 1920 8
1045.4.bj $$\chi_{1045}(109, \cdot)$$ n/a 2136 6
1045.4.bm $$\chi_{1045}(21, \cdot)$$ n/a 1440 6
1045.4.bo $$\chi_{1045}(199, \cdot)$$ n/a 1800 6
1045.4.bp $$\chi_{1045}(37, \cdot)$$ n/a 2848 8
1045.4.bs $$\chi_{1045}(172, \cdot)$$ n/a 2592 8
1045.4.bu $$\chi_{1045}(49, \cdot)$$ n/a 2848 8
1045.4.bv $$\chi_{1045}(84, \cdot)$$ n/a 2848 8
1045.4.by $$\chi_{1045}(46, \cdot)$$ n/a 1920 8
1045.4.cb $$\chi_{1045}(43, \cdot)$$ n/a 4272 12
1045.4.cc $$\chi_{1045}(67, \cdot)$$ n/a 3600 12
1045.4.ce $$\chi_{1045}(16, \cdot)$$ n/a 5760 24
1045.4.cf $$\chi_{1045}(7, \cdot)$$ n/a 5696 16
1045.4.ci $$\chi_{1045}(27, \cdot)$$ n/a 5696 16
1045.4.ck $$\chi_{1045}(4, \cdot)$$ n/a 8544 24
1045.4.cm $$\chi_{1045}(41, \cdot)$$ n/a 5760 24
1045.4.cn $$\chi_{1045}(29, \cdot)$$ n/a 8544 24
1045.4.cr $$\chi_{1045}(3, \cdot)$$ n/a 17088 48
1045.4.cs $$\chi_{1045}(17, \cdot)$$ n/a 17088 48

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

## Decomposition of $$S_{4}^{\mathrm{old}}(\Gamma_1(1045))$$ into lower level spaces

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