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Properties

Label 2418.2
Level 2418
Weight 2
Dimension 39753
Nonzero newspaces 60
Sturm bound 645120
Trace bound 11

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Defining parameters

Level: \( N \) = \( 2418 = 2 \cdot 3 \cdot 13 \cdot 31 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 60 \)
Sturm bound: \(645120\)
Trace bound: \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2418))\).

Total New Old
Modular forms 164160 39753 124407
Cusp forms 158401 39753 118648
Eisenstein series 5759 0 5759

Trace form

\( 39753 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 18 q^{5} - 3 q^{6} - 8 q^{7} + 9 q^{8} + 5 q^{9} + O(q^{10}) \) \( 39753 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 18 q^{5} - 3 q^{6} - 8 q^{7} + 9 q^{8} + 5 q^{9} + 42 q^{10} + 12 q^{11} + 5 q^{12} + 69 q^{13} + 24 q^{14} + 30 q^{15} + 13 q^{16} + 6 q^{17} + 9 q^{18} + 52 q^{19} - 6 q^{20} + 52 q^{21} + 84 q^{22} + 96 q^{23} - 3 q^{24} + 247 q^{25} + 33 q^{26} + 69 q^{27} + 136 q^{28} + 210 q^{29} + 54 q^{30} + 201 q^{31} - 3 q^{32} + 60 q^{33} + 186 q^{34} + 144 q^{35} - 31 q^{36} + 258 q^{37} + 60 q^{38} - 45 q^{39} - 18 q^{40} + 6 q^{41} - 36 q^{42} - 28 q^{43} - 36 q^{44} - 126 q^{45} - 72 q^{46} - 96 q^{47} - 3 q^{48} - 35 q^{49} - 81 q^{50} + 174 q^{51} - 15 q^{52} + 102 q^{53} + 69 q^{54} + 264 q^{55} + 24 q^{56} + 248 q^{57} + 18 q^{58} + 132 q^{59} + 30 q^{60} + 330 q^{61} + 9 q^{62} + 344 q^{63} + 9 q^{64} + 222 q^{65} + 60 q^{66} + 124 q^{67} - 42 q^{68} + 204 q^{69} + 120 q^{71} + 45 q^{72} + 58 q^{73} + 42 q^{74} + 83 q^{75} + 52 q^{76} + 120 q^{77} + 3 q^{78} + 48 q^{79} - 6 q^{80} - 283 q^{81} + 78 q^{82} - 108 q^{83} - 88 q^{84} - 24 q^{85} - 36 q^{86} - 282 q^{87} - 36 q^{88} - 30 q^{89} - 330 q^{90} - 8 q^{91} + 24 q^{92} - 503 q^{93} + 96 q^{94} - 168 q^{95} - 3 q^{96} - 6 q^{97} - 75 q^{98} - 408 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2418))\)

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
2418.2.a \(\chi_{2418}(1, \cdot)\) 2418.2.a.a 1 1
2418.2.a.b 1
2418.2.a.c 1
2418.2.a.d 2
2418.2.a.e 2
2418.2.a.f 2
2418.2.a.g 2
2418.2.a.h 2
2418.2.a.i 2
2418.2.a.j 3
2418.2.a.k 4
2418.2.a.l 4
2418.2.a.m 4
2418.2.a.n 4
2418.2.a.o 5
2418.2.a.p 5
2418.2.a.q 5
2418.2.a.r 6
2418.2.a.s 6
2418.2.b \(\chi_{2418}(1117, \cdot)\) 2418.2.b.a 2 1
2418.2.b.b 2
2418.2.b.c 2
2418.2.b.d 14
2418.2.b.e 14
2418.2.b.f 16
2418.2.b.g 18
2418.2.e \(\chi_{2418}(1301, \cdot)\) n/a 128 1
2418.2.f \(\chi_{2418}(2417, \cdot)\) n/a 152 1
2418.2.i \(\chi_{2418}(1699, \cdot)\) n/a 148 2
2418.2.j \(\chi_{2418}(625, \cdot)\) n/a 128 2
2418.2.k \(\chi_{2418}(211, \cdot)\) n/a 148 2
2418.2.l \(\chi_{2418}(373, \cdot)\) n/a 144 2
2418.2.o \(\chi_{2418}(125, \cdot)\) n/a 280 2
2418.2.p \(\chi_{2418}(619, \cdot)\) n/a 144 2
2418.2.q \(\chi_{2418}(157, \cdot)\) n/a 256 4
2418.2.r \(\chi_{2418}(185, \cdot)\) n/a 296 2
2418.2.u \(\chi_{2418}(745, \cdot)\) n/a 136 2
2418.2.v \(\chi_{2418}(1421, \cdot)\) n/a 300 2
2418.2.bb \(\chi_{2418}(491, \cdot)\) n/a 300 2
2418.2.bc \(\chi_{2418}(1091, \cdot)\) n/a 296 2
2418.2.be \(\chi_{2418}(1141, \cdot)\) n/a 148 2
2418.2.bg \(\chi_{2418}(347, \cdot)\) n/a 300 2
2418.2.bh \(\chi_{2418}(677, \cdot)\) n/a 256 2
2418.2.bm \(\chi_{2418}(439, \cdot)\) n/a 148 2
2418.2.bn \(\chi_{2418}(25, \cdot)\) n/a 152 2
2418.2.bp \(\chi_{2418}(1049, \cdot)\) n/a 300 2
2418.2.bs \(\chi_{2418}(1115, \cdot)\) n/a 296 2
2418.2.bt \(\chi_{2418}(209, \cdot)\) n/a 512 4
2418.2.bw \(\chi_{2418}(1039, \cdot)\) n/a 288 4
2418.2.bz \(\chi_{2418}(77, \cdot)\) n/a 608 4
2418.2.cc \(\chi_{2418}(1177, \cdot)\) n/a 304 4
2418.2.cd \(\chi_{2418}(683, \cdot)\) n/a 560 4
2418.2.ce \(\chi_{2418}(409, \cdot)\) n/a 296 4
2418.2.cf \(\chi_{2418}(149, \cdot)\) n/a 600 4
2418.2.cg \(\chi_{2418}(5, \cdot)\) n/a 592 4
2418.2.ch \(\chi_{2418}(967, \cdot)\) n/a 304 4
2418.2.co \(\chi_{2418}(37, \cdot)\) n/a 296 4
2418.2.cp \(\chi_{2418}(1307, \cdot)\) n/a 600 4
2418.2.cq \(\chi_{2418}(607, \cdot)\) n/a 592 8
2418.2.cr \(\chi_{2418}(235, \cdot)\) n/a 512 8
2418.2.cs \(\chi_{2418}(133, \cdot)\) n/a 592 8
2418.2.ct \(\chi_{2418}(295, \cdot)\) n/a 608 8
2418.2.cu \(\chi_{2418}(151, \cdot)\) n/a 576 8
2418.2.cv \(\chi_{2418}(47, \cdot)\) n/a 1216 8
2418.2.cy \(\chi_{2418}(283, \cdot)\) n/a 608 8
2418.2.db \(\chi_{2418}(29, \cdot)\) n/a 1184 8
2418.2.dd \(\chi_{2418}(389, \cdot)\) n/a 1184 8
2418.2.de \(\chi_{2418}(17, \cdot)\) n/a 1200 8
2418.2.dk \(\chi_{2418}(179, \cdot)\) n/a 1200 8
2418.2.dl \(\chi_{2418}(269, \cdot)\) n/a 1200 8
2418.2.dn \(\chi_{2418}(103, \cdot)\) n/a 608 8
2418.2.do \(\chi_{2418}(49, \cdot)\) n/a 592 8
2418.2.dt \(\chi_{2418}(53, \cdot)\) n/a 1024 8
2418.2.du \(\chi_{2418}(737, \cdot)\) n/a 1200 8
2418.2.dw \(\chi_{2418}(205, \cdot)\) n/a 592 8
2418.2.dx \(\chi_{2418}(23, \cdot)\) n/a 1184 8
2418.2.ea \(\chi_{2418}(71, \cdot)\) n/a 2400 16
2418.2.eb \(\chi_{2418}(331, \cdot)\) n/a 1184 16
2418.2.ei \(\chi_{2418}(73, \cdot)\) n/a 1216 16
2418.2.ej \(\chi_{2418}(317, \cdot)\) n/a 2368 16
2418.2.ek \(\chi_{2418}(605, \cdot)\) n/a 2368 16
2418.2.el \(\chi_{2418}(85, \cdot)\) n/a 1216 16
2418.2.em \(\chi_{2418}(41, \cdot)\) n/a 2400 16
2418.2.en \(\chi_{2418}(115, \cdot)\) n/a 1184 16

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2418))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(2418)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(31))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(62))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(78))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(93))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(186))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(403))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(806))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1209))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2418))\)\(^{\oplus 1}\)