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Properties

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

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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

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

Display 100 coefficients 10 coefficients

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 available 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

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