# Properties

 Label 1815.4 Level 1815 Weight 4 Dimension 234794 Nonzero newspaces 24 Sturm bound 929280 Trace bound 1

## Defining parameters

 Level: $$N$$ = $$1815 = 3 \cdot 5 \cdot 11^{2}$$ Weight: $$k$$ = $$4$$ Nonzero newspaces: $$24$$ Sturm bound: $$929280$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(\Gamma_1(1815))$$.

Total New Old
Modular forms 351040 236482 114558
Cusp forms 345920 234794 111126
Eisenstein series 5120 1688 3432

## Trace form

 $$234794 q + 4 q^{2} - 96 q^{3} - 204 q^{4} + 6 q^{5} - 70 q^{6} - 120 q^{7} - 356 q^{8} - 428 q^{9} + O(q^{10})$$ $$234794 q + 4 q^{2} - 96 q^{3} - 204 q^{4} + 6 q^{5} - 70 q^{6} - 120 q^{7} - 356 q^{8} - 428 q^{9} - 746 q^{10} - 200 q^{11} - 702 q^{12} - 176 q^{13} + 1824 q^{14} + 659 q^{15} + 2804 q^{16} + 1240 q^{17} + 266 q^{18} - 2236 q^{19} - 2336 q^{20} - 2518 q^{21} - 2720 q^{22} - 1808 q^{23} - 4418 q^{24} - 904 q^{25} + 32 q^{26} + 732 q^{27} + 4716 q^{28} + 3588 q^{29} + 4851 q^{30} + 5612 q^{31} + 7236 q^{32} + 3510 q^{33} + 6612 q^{34} + 1800 q^{35} + 3914 q^{36} - 1600 q^{37} - 2992 q^{38} - 4994 q^{39} - 8602 q^{40} - 9244 q^{41} - 17702 q^{42} - 12808 q^{43} - 10500 q^{44} - 5469 q^{45} - 13068 q^{46} - 4968 q^{47} - 5290 q^{48} + 1650 q^{49} + 7424 q^{50} + 1826 q^{51} + 21124 q^{52} + 13872 q^{53} + 1834 q^{54} + 9740 q^{55} + 34720 q^{56} + 11966 q^{57} + 19996 q^{58} + 4576 q^{59} + 14511 q^{60} + 9056 q^{61} + 10712 q^{62} + 16382 q^{63} + 2004 q^{64} - 6032 q^{65} + 7750 q^{66} - 11336 q^{67} - 21288 q^{68} + 834 q^{69} - 21370 q^{70} + 6752 q^{71} - 2634 q^{72} + 18680 q^{73} + 4424 q^{74} - 4521 q^{75} - 20420 q^{76} - 1800 q^{77} - 30450 q^{78} - 16100 q^{79} - 18616 q^{80} - 30776 q^{81} - 47308 q^{82} - 29512 q^{83} - 46454 q^{84} - 20978 q^{85} - 19456 q^{86} - 21706 q^{87} - 22760 q^{88} - 14876 q^{89} - 13701 q^{90} - 27428 q^{91} - 33544 q^{92} - 12826 q^{93} - 17924 q^{94} - 21816 q^{95} + 18358 q^{96} + 3624 q^{97} + 404 q^{98} + 9440 q^{99} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(\Gamma_1(1815))$$

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
1815.4.a $$\chi_{1815}(1, \cdot)$$ 1815.4.a.a 1 1
1815.4.a.b 1
1815.4.a.c 1
1815.4.a.d 1
1815.4.a.e 1
1815.4.a.f 1
1815.4.a.g 1
1815.4.a.h 1
1815.4.a.i 2
1815.4.a.j 2
1815.4.a.k 2
1815.4.a.l 2
1815.4.a.m 2
1815.4.a.n 2
1815.4.a.o 2
1815.4.a.p 3
1815.4.a.q 3
1815.4.a.r 3
1815.4.a.s 3
1815.4.a.t 4
1815.4.a.u 4
1815.4.a.v 4
1815.4.a.w 4
1815.4.a.x 5
1815.4.a.y 5
1815.4.a.z 6
1815.4.a.ba 6
1815.4.a.bb 6
1815.4.a.bc 7
1815.4.a.bd 7
1815.4.a.be 8
1815.4.a.bf 10
1815.4.a.bg 12
1815.4.a.bh 12
1815.4.a.bi 12
1815.4.a.bj 12
1815.4.a.bk 12
1815.4.a.bl 12
1815.4.a.bm 12
1815.4.a.bn 12
1815.4.a.bo 12
1815.4.c $$\chi_{1815}(364, \cdot)$$ n/a 328 1
1815.4.d $$\chi_{1815}(1814, \cdot)$$ n/a 632 1
1815.4.f $$\chi_{1815}(1451, \cdot)$$ n/a 432 1
1815.4.j $$\chi_{1815}(967, \cdot)$$ n/a 648 2
1815.4.k $$\chi_{1815}(122, \cdot)$$ n/a 1272 2
1815.4.m $$\chi_{1815}(511, \cdot)$$ n/a 864 4
1815.4.p $$\chi_{1815}(161, \cdot)$$ n/a 1728 4
1815.4.r $$\chi_{1815}(239, \cdot)$$ n/a 2528 4
1815.4.s $$\chi_{1815}(124, \cdot)$$ n/a 1296 4
1815.4.u $$\chi_{1815}(166, \cdot)$$ n/a 2640 10
1815.4.w $$\chi_{1815}(323, \cdot)$$ n/a 5056 8
1815.4.x $$\chi_{1815}(112, \cdot)$$ n/a 2592 8
1815.4.bb $$\chi_{1815}(131, \cdot)$$ n/a 5280 10
1815.4.bd $$\chi_{1815}(164, \cdot)$$ n/a 7880 10
1815.4.be $$\chi_{1815}(34, \cdot)$$ n/a 3960 10
1815.4.bh $$\chi_{1815}(23, \cdot)$$ n/a 15760 20
1815.4.bi $$\chi_{1815}(43, \cdot)$$ n/a 7920 20
1815.4.bk $$\chi_{1815}(16, \cdot)$$ n/a 10560 40
1815.4.bm $$\chi_{1815}(4, \cdot)$$ n/a 15840 40
1815.4.bn $$\chi_{1815}(29, \cdot)$$ n/a 31520 40
1815.4.bp $$\chi_{1815}(41, \cdot)$$ n/a 21120 40
1815.4.bt $$\chi_{1815}(7, \cdot)$$ n/a 31680 80
1815.4.bu $$\chi_{1815}(38, \cdot)$$ n/a 63040 80

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

## Decomposition of $$S_{4}^{\mathrm{old}}(\Gamma_1(1815))$$ into lower level spaces

$$S_{4}^{\mathrm{old}}(\Gamma_1(1815)) \cong$$ $$S_{4}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 12}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(3))$$$$^{\oplus 6}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(5))$$$$^{\oplus 6}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(11))$$$$^{\oplus 8}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(15))$$$$^{\oplus 3}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(33))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(55))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(121))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(165))$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(363))$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(605))$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(1815))$$$$^{\oplus 1}$$