# Properties

 Label 2415.2 Level 2415 Weight 2 Dimension 131809 Nonzero newspaces 48 Sturm bound 811008 Trace bound 6

## Defining parameters

 Level: $$N$$ = $$2415 = 3 \cdot 5 \cdot 7 \cdot 23$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$48$$ Sturm bound: $$811008$$ Trace bound: $$6$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(2415))$$.

Total New Old
Modular forms 206976 134337 72639
Cusp forms 198529 131809 66720
Eisenstein series 8447 2528 5919

## Trace form

 $$131809q - 13q^{2} - 79q^{3} - 145q^{4} + 13q^{5} - 197q^{6} - 179q^{7} + 39q^{8} - 47q^{9} + O(q^{10})$$ $$131809q - 13q^{2} - 79q^{3} - 145q^{4} + 13q^{5} - 197q^{6} - 179q^{7} + 39q^{8} - 47q^{9} - 181q^{10} + 20q^{11} - 41q^{12} - 122q^{13} + 51q^{14} - 267q^{15} - 233q^{16} + 90q^{17} + 99q^{18} - 28q^{19} + 223q^{20} - 215q^{21} - 76q^{22} + 177q^{23} + 31q^{24} - 103q^{25} + 130q^{26} + 5q^{27} - 29q^{28} + 38q^{29} - 121q^{30} - 384q^{31} - 57q^{32} - 88q^{33} - 122q^{34} - 31q^{35} - 701q^{36} + 86q^{37} + 268q^{38} + 14q^{39} - 17q^{40} + 90q^{41} - 7q^{42} - 44q^{43} + 524q^{44} - 145q^{45} + 179q^{46} + 408q^{47} + 231q^{48} + 157q^{49} + 195q^{50} - 54q^{51} + 642q^{52} + 166q^{53} - 69q^{54} - 44q^{55} + 211q^{56} - 124q^{57} + 2q^{58} + 124q^{59} - 445q^{60} - 666q^{61} - 192q^{62} - 171q^{63} - 737q^{64} - 158q^{65} - 704q^{66} - 404q^{67} - 386q^{68} - 403q^{69} - 1161q^{70} - 200q^{71} - 745q^{72} - 518q^{73} - 334q^{74} - 381q^{75} - 444q^{76} - 4q^{77} - 226q^{78} - 88q^{79} + 227q^{80} + 105q^{81} + 78q^{82} + 292q^{83} + 121q^{84} - 122q^{85} + 780q^{86} + 502q^{87} + 20q^{88} + 474q^{89} + 469q^{90} + 38q^{91} + 799q^{92} + 480q^{93} + 1000q^{94} + 404q^{95} + 699q^{96} + 266q^{97} + 199q^{98} + 456q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(2415))$$

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
2415.2.a $$\chi_{2415}(1, \cdot)$$ 2415.2.a.a 1 1
2415.2.a.b 1
2415.2.a.c 1
2415.2.a.d 1
2415.2.a.e 1
2415.2.a.f 1
2415.2.a.g 1
2415.2.a.h 1
2415.2.a.i 1
2415.2.a.j 2
2415.2.a.k 2
2415.2.a.l 3
2415.2.a.m 3
2415.2.a.n 3
2415.2.a.o 5
2415.2.a.p 6
2415.2.a.q 6
2415.2.a.r 7
2415.2.a.s 7
2415.2.a.t 7
2415.2.a.u 9
2415.2.a.v 10
2415.2.a.w 10
2415.2.b $$\chi_{2415}(461, \cdot)$$ n/a 232 1
2415.2.e $$\chi_{2415}(1609, \cdot)$$ n/a 192 1
2415.2.g $$\chi_{2415}(484, \cdot)$$ n/a 128 1
2415.2.h $$\chi_{2415}(2276, \cdot)$$ n/a 192 1
2415.2.k $$\chi_{2415}(1126, \cdot)$$ n/a 128 1
2415.2.l $$\chi_{2415}(944, \cdot)$$ n/a 352 1
2415.2.n $$\chi_{2415}(344, \cdot)$$ n/a 288 1
2415.2.q $$\chi_{2415}(1381, \cdot)$$ n/a 232 2
2415.2.s $$\chi_{2415}(323, \cdot)$$ n/a 528 2
2415.2.t $$\chi_{2415}(22, \cdot)$$ n/a 288 2
2415.2.w $$\chi_{2415}(482, \cdot)$$ n/a 752 2
2415.2.x $$\chi_{2415}(622, \cdot)$$ n/a 352 2
2415.2.z $$\chi_{2415}(1724, \cdot)$$ n/a 752 2
2415.2.bd $$\chi_{2415}(1816, \cdot)$$ n/a 256 2
2415.2.be $$\chi_{2415}(1634, \cdot)$$ n/a 704 2
2415.2.bh $$\chi_{2415}(1864, \cdot)$$ n/a 352 2
2415.2.bi $$\chi_{2415}(1241, \cdot)$$ n/a 512 2
2415.2.bk $$\chi_{2415}(1151, \cdot)$$ n/a 472 2
2415.2.bn $$\chi_{2415}(229, \cdot)$$ n/a 384 2
2415.2.bo $$\chi_{2415}(211, \cdot)$$ n/a 960 10
2415.2.bp $$\chi_{2415}(208, \cdot)$$ n/a 704 4
2415.2.bs $$\chi_{2415}(68, \cdot)$$ n/a 1504 4
2415.2.bt $$\chi_{2415}(298, \cdot)$$ n/a 768 4
2415.2.bw $$\chi_{2415}(737, \cdot)$$ n/a 1408 4
2415.2.bz $$\chi_{2415}(134, \cdot)$$ n/a 2880 10
2415.2.cb $$\chi_{2415}(104, \cdot)$$ n/a 3760 10
2415.2.cc $$\chi_{2415}(76, \cdot)$$ n/a 1280 10
2415.2.cf $$\chi_{2415}(176, \cdot)$$ n/a 1920 10
2415.2.cg $$\chi_{2415}(64, \cdot)$$ n/a 1440 10
2415.2.ci $$\chi_{2415}(34, \cdot)$$ n/a 1920 10
2415.2.cl $$\chi_{2415}(41, \cdot)$$ n/a 2560 10
2415.2.cm $$\chi_{2415}(16, \cdot)$$ n/a 2560 20
2415.2.co $$\chi_{2415}(13, \cdot)$$ n/a 3840 20
2415.2.cp $$\chi_{2415}(83, \cdot)$$ n/a 7520 20
2415.2.cs $$\chi_{2415}(43, \cdot)$$ n/a 2880 20
2415.2.ct $$\chi_{2415}(8, \cdot)$$ n/a 5760 20
2415.2.cv $$\chi_{2415}(19, \cdot)$$ n/a 3840 20
2415.2.cy $$\chi_{2415}(26, \cdot)$$ n/a 5120 20
2415.2.da $$\chi_{2415}(11, \cdot)$$ n/a 5120 20
2415.2.db $$\chi_{2415}(4, \cdot)$$ n/a 3840 20
2415.2.de $$\chi_{2415}(59, \cdot)$$ n/a 7520 20
2415.2.df $$\chi_{2415}(61, \cdot)$$ n/a 2560 20
2415.2.dj $$\chi_{2415}(44, \cdot)$$ n/a 7520 20
2415.2.dk $$\chi_{2415}(2, \cdot)$$ n/a 15040 40
2415.2.dn $$\chi_{2415}(37, \cdot)$$ n/a 7680 40
2415.2.do $$\chi_{2415}(17, \cdot)$$ n/a 15040 40
2415.2.dr $$\chi_{2415}(52, \cdot)$$ n/a 7680 40

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(2415))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(2415)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(15))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(21))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(23))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(35))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(69))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(105))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(115))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(161))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(345))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(483))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(805))$$$$^{\oplus 2}$$