# Properties

 Label 1305.4 Level 1305 Weight 4 Dimension 130628 Nonzero newspaces 40 Sturm bound 483840 Trace bound 11

## Defining parameters

 Level: $$N$$ = $$1305 = 3^{2} \cdot 5 \cdot 29$$ Weight: $$k$$ = $$4$$ Nonzero newspaces: $$40$$ Sturm bound: $$483840$$ Trace bound: $$11$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(\Gamma_1(1305))$$.

Total New Old
Modular forms 183232 132088 51144
Cusp forms 179648 130628 49020
Eisenstein series 3584 1460 2124

## Trace form

 $$130628 q - 80 q^{2} - 108 q^{3} - 144 q^{4} - 138 q^{5} - 268 q^{6} - 36 q^{7} + 60 q^{8} - 44 q^{9} + O(q^{10})$$ $$130628 q - 80 q^{2} - 108 q^{3} - 144 q^{4} - 138 q^{5} - 268 q^{6} - 36 q^{7} + 60 q^{8} - 44 q^{9} - 554 q^{10} - 500 q^{11} - 464 q^{12} + 148 q^{13} + 612 q^{14} + 238 q^{15} + 944 q^{16} + 1048 q^{17} + 768 q^{18} - 1004 q^{19} - 1138 q^{20} - 1356 q^{21} - 1976 q^{22} - 1756 q^{23} - 1060 q^{24} + 202 q^{25} - 2016 q^{26} - 720 q^{27} + 592 q^{28} - 112 q^{29} + 2576 q^{30} + 1536 q^{31} + 3376 q^{32} + 2920 q^{33} - 820 q^{34} + 1354 q^{35} + 652 q^{36} - 1784 q^{37} + 1400 q^{38} - 132 q^{39} - 2494 q^{40} - 5128 q^{41} - 8848 q^{42} - 2048 q^{43} - 4496 q^{44} - 6022 q^{45} + 7168 q^{46} - 5404 q^{47} - 9668 q^{48} + 370 q^{49} - 4264 q^{50} - 76 q^{51} - 292 q^{52} - 470 q^{53} + 12196 q^{54} - 1406 q^{55} + 752 q^{56} + 5484 q^{57} - 15008 q^{58} + 2552 q^{59} + 5960 q^{60} - 4884 q^{61} - 2560 q^{62} + 4508 q^{63} - 8984 q^{64} + 3397 q^{65} - 2168 q^{66} - 2568 q^{67} + 10948 q^{68} + 3452 q^{69} - 8778 q^{70} - 21348 q^{71} - 30148 q^{72} - 10790 q^{73} - 27104 q^{74} + 1742 q^{75} - 9464 q^{76} + 6024 q^{77} + 14328 q^{78} + 12288 q^{79} + 32450 q^{80} + 22900 q^{81} + 42124 q^{82} + 17436 q^{83} + 34520 q^{84} + 25546 q^{85} + 45484 q^{86} + 12858 q^{87} + 63660 q^{88} + 360 q^{89} - 22752 q^{90} + 9084 q^{91} + 22644 q^{92} - 9804 q^{93} + 7764 q^{94} + 922 q^{95} - 12528 q^{96} + 17406 q^{97} - 6384 q^{98} - 19444 q^{99} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(\Gamma_1(1305))$$

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
1305.4.a $$\chi_{1305}(1, \cdot)$$ 1305.4.a.a 1 1
1305.4.a.b 1
1305.4.a.c 1
1305.4.a.d 1
1305.4.a.e 2
1305.4.a.f 2
1305.4.a.g 5
1305.4.a.h 6
1305.4.a.i 6
1305.4.a.j 6
1305.4.a.k 6
1305.4.a.l 7
1305.4.a.m 7
1305.4.a.n 7
1305.4.a.o 8
1305.4.a.p 8
1305.4.a.q 10
1305.4.a.r 12
1305.4.a.s 12
1305.4.a.t 16
1305.4.a.u 16
1305.4.c $$\chi_{1305}(784, \cdot)$$ n/a 210 1
1305.4.d $$\chi_{1305}(811, \cdot)$$ n/a 150 1
1305.4.f $$\chi_{1305}(289, \cdot)$$ n/a 224 1
1305.4.i $$\chi_{1305}(436, \cdot)$$ n/a 672 2
1305.4.k $$\chi_{1305}(568, \cdot)$$ n/a 446 2
1305.4.m $$\chi_{1305}(539, \cdot)$$ n/a 360 2
1305.4.n $$\chi_{1305}(233, \cdot)$$ n/a 336 2
1305.4.q $$\chi_{1305}(782, \cdot)$$ n/a 360 2
1305.4.r $$\chi_{1305}(476, \cdot)$$ n/a 240 2
1305.4.t $$\chi_{1305}(307, \cdot)$$ n/a 446 2
1305.4.w $$\chi_{1305}(724, \cdot)$$ n/a 1072 2
1305.4.y $$\chi_{1305}(376, \cdot)$$ n/a 720 2
1305.4.bb $$\chi_{1305}(349, \cdot)$$ n/a 1008 2
1305.4.bc $$\chi_{1305}(136, \cdot)$$ n/a 900 6
1305.4.bd $$\chi_{1305}(418, \cdot)$$ n/a 2144 4
1305.4.bg $$\chi_{1305}(41, \cdot)$$ n/a 1440 4
1305.4.bi $$\chi_{1305}(173, \cdot)$$ n/a 2144 4
1305.4.bj $$\chi_{1305}(407, \cdot)$$ n/a 2016 4
1305.4.bl $$\chi_{1305}(104, \cdot)$$ n/a 2144 4
1305.4.bo $$\chi_{1305}(133, \cdot)$$ n/a 2144 4
1305.4.br $$\chi_{1305}(64, \cdot)$$ n/a 1344 6
1305.4.bt $$\chi_{1305}(91, \cdot)$$ n/a 900 6
1305.4.bu $$\chi_{1305}(199, \cdot)$$ n/a 1332 6
1305.4.bw $$\chi_{1305}(16, \cdot)$$ n/a 4320 12
1305.4.by $$\chi_{1305}(73, \cdot)$$ n/a 2676 12
1305.4.ca $$\chi_{1305}(26, \cdot)$$ n/a 1440 12
1305.4.cb $$\chi_{1305}(62, \cdot)$$ n/a 2160 12
1305.4.ce $$\chi_{1305}(53, \cdot)$$ n/a 2160 12
1305.4.cf $$\chi_{1305}(44, \cdot)$$ n/a 2160 12
1305.4.ch $$\chi_{1305}(37, \cdot)$$ n/a 2676 12
1305.4.cj $$\chi_{1305}(49, \cdot)$$ n/a 6432 12
1305.4.cm $$\chi_{1305}(121, \cdot)$$ n/a 4320 12
1305.4.co $$\chi_{1305}(4, \cdot)$$ n/a 6432 12
1305.4.cq $$\chi_{1305}(43, \cdot)$$ n/a 12864 24
1305.4.ct $$\chi_{1305}(14, \cdot)$$ n/a 12864 24
1305.4.cv $$\chi_{1305}(23, \cdot)$$ n/a 12864 24
1305.4.cw $$\chi_{1305}(38, \cdot)$$ n/a 12864 24
1305.4.cy $$\chi_{1305}(11, \cdot)$$ n/a 8640 24
1305.4.db $$\chi_{1305}(292, \cdot)$$ n/a 12864 24

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

## Decomposition of $$S_{4}^{\mathrm{old}}(\Gamma_1(1305))$$ into lower level spaces

$$S_{4}^{\mathrm{old}}(\Gamma_1(1305)) \cong$$ $$S_{4}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 12}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(3))$$$$^{\oplus 8}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(5))$$$$^{\oplus 6}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(9))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(15))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(29))$$$$^{\oplus 6}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(45))$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(87))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(145))$$$$^{\oplus 3}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(261))$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(435))$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(1305))$$$$^{\oplus 1}$$