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Properties

Label 2664.1
Level 2664
Weight 1
Dimension 58
Nonzero newspaces 7
Newform subspaces 13
Sturm bound 393984
Trace bound 7

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Defining parameters

Level: \( N \) = \( 2664 = 2^{3} \cdot 3^{2} \cdot 37 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 7 \)
Newform subspaces: \( 13 \)
Sturm bound: \(393984\)
Trace bound: \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(2664))\).

Total New Old
Modular forms 3936 688 3248
Cusp forms 480 58 422
Eisenstein series 3456 630 2826

The following table gives the dimensions of subspaces with specified projective image type.

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 32 8 18 0

Trace form

\( 58 q + 2 q^{2} - 2 q^{3} - 4 q^{4} + 2 q^{5} - 8 q^{6} - 10 q^{7} + 8 q^{8} + 2 q^{9} + O(q^{10}) \) \( 58 q + 2 q^{2} - 2 q^{3} - 4 q^{4} + 2 q^{5} - 8 q^{6} - 10 q^{7} + 8 q^{8} + 2 q^{9} - 10 q^{10} + 6 q^{11} - 2 q^{12} + 2 q^{13} - 8 q^{16} + 4 q^{17} + 2 q^{18} - 12 q^{19} - 6 q^{22} - 2 q^{23} - 2 q^{24} - 2 q^{25} + 2 q^{26} - 8 q^{27} + 4 q^{28} - 2 q^{29} + 2 q^{32} - 4 q^{33} + 2 q^{34} - 10 q^{35} + 8 q^{36} - 2 q^{37} - 4 q^{38} + 10 q^{40} + 2 q^{41} + 6 q^{43} + 6 q^{44} + 6 q^{46} + 2 q^{47} - 8 q^{48} - 14 q^{49} - 6 q^{50} - 4 q^{51} - 4 q^{52} + 2 q^{53} - 2 q^{54} - 10 q^{55} - 2 q^{57} + 2 q^{58} + 2 q^{59} + 2 q^{62} + 32 q^{64} + 4 q^{65} - 4 q^{66} + 2 q^{67} + 4 q^{68} - 8 q^{70} - 2 q^{71} + 2 q^{72} + 6 q^{73} - 14 q^{74} + 14 q^{75} + 2 q^{76} - 10 q^{78} + 2 q^{81} + 4 q^{83} + 2 q^{86} - 4 q^{88} - 4 q^{89} + 20 q^{90} + 2 q^{91} - 8 q^{94} - 2 q^{96} + 4 q^{97} + 18 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(2664))\)

We only show spaces with odd 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
2664.1.b \(\chi_{2664}(2071, \cdot)\) None 0 1
2664.1.d \(\chi_{2664}(667, \cdot)\) None 0 1
2664.1.g \(\chi_{2664}(593, \cdot)\) None 0 1
2664.1.i \(\chi_{2664}(1997, \cdot)\) None 0 1
2664.1.k \(\chi_{2664}(1999, \cdot)\) None 0 1
2664.1.m \(\chi_{2664}(739, \cdot)\) 2664.1.m.a 2 1
2664.1.m.b 2
2664.1.m.c 8
2664.1.n \(\chi_{2664}(665, \cdot)\) None 0 1
2664.1.p \(\chi_{2664}(1925, \cdot)\) None 0 1
2664.1.v \(\chi_{2664}(1079, \cdot)\) None 0 2
2664.1.x \(\chi_{2664}(179, \cdot)\) None 0 2
2664.1.y \(\chi_{2664}(1153, \cdot)\) 2664.1.y.a 2 2
2664.1.ba \(\chi_{2664}(253, \cdot)\) 2664.1.ba.a 4 2
2664.1.ba.b 4
2664.1.bd \(\chi_{2664}(677, \cdot)\) None 0 2
2664.1.bf \(\chi_{2664}(137, \cdot)\) None 0 2
2664.1.bg \(\chi_{2664}(787, \cdot)\) 2664.1.bg.a 4 2
2664.1.bi \(\chi_{2664}(175, \cdot)\) None 0 2
2664.1.bk \(\chi_{2664}(619, \cdot)\) None 0 2
2664.1.bm \(\chi_{2664}(1231, \cdot)\) None 0 2
2664.1.bp \(\chi_{2664}(233, \cdot)\) None 0 2
2664.1.bq \(\chi_{2664}(149, \cdot)\) None 0 2
2664.1.bs \(\chi_{2664}(1553, \cdot)\) None 0 2
2664.1.bt \(\chi_{2664}(269, \cdot)\) None 0 2
2664.1.bu \(\chi_{2664}(343, \cdot)\) None 0 2
2664.1.bw \(\chi_{2664}(1627, \cdot)\) 2664.1.bw.a 2 2
2664.1.bw.b 2
2664.1.bw.c 8
2664.1.bw.d 8
2664.1.by \(\chi_{2664}(223, \cdot)\) None 0 2
2664.1.ca \(\chi_{2664}(307, \cdot)\) None 0 2
2664.1.cc \(\chi_{2664}(581, \cdot)\) None 0 2
2664.1.ce \(\chi_{2664}(1121, \cdot)\) None 0 2
2664.1.cg \(\chi_{2664}(211, \cdot)\) 2664.1.cg.a 4 2
2664.1.ci \(\chi_{2664}(751, \cdot)\) None 0 2
2664.1.cj \(\chi_{2664}(1025, \cdot)\) None 0 2
2664.1.cl \(\chi_{2664}(221, \cdot)\) None 0 2
2664.1.cn \(\chi_{2664}(1481, \cdot)\) None 0 2
2664.1.cp \(\chi_{2664}(989, \cdot)\) None 0 2
2664.1.cs \(\chi_{2664}(1063, \cdot)\) None 0 2
2664.1.cu \(\chi_{2664}(1555, \cdot)\) None 0 2
2664.1.cw \(\chi_{2664}(295, \cdot)\) None 0 2
2664.1.cy \(\chi_{2664}(1099, \cdot)\) 2664.1.cy.a 8 2
2664.1.cz \(\chi_{2664}(101, \cdot)\) None 0 2
2664.1.db \(\chi_{2664}(713, \cdot)\) None 0 2
2664.1.dd \(\chi_{2664}(1157, \cdot)\) None 0 2
2664.1.de \(\chi_{2664}(545, \cdot)\) None 0 2
2664.1.dh \(\chi_{2664}(1195, \cdot)\) None 0 2
2664.1.dj \(\chi_{2664}(655, \cdot)\) None 0 2
2664.1.dn \(\chi_{2664}(563, \cdot)\) None 0 4
2664.1.dp \(\chi_{2664}(911, \cdot)\) None 0 4
2664.1.ds \(\chi_{2664}(865, \cdot)\) None 0 4
2664.1.dt \(\chi_{2664}(637, \cdot)\) None 0 4
2664.1.dw \(\chi_{2664}(709, \cdot)\) None 0 4
2664.1.dx \(\chi_{2664}(985, \cdot)\) None 0 4
2664.1.ea \(\chi_{2664}(265, \cdot)\) None 0 4
2664.1.ec \(\chi_{2664}(325, \cdot)\) None 0 4
2664.1.ed \(\chi_{2664}(791, \cdot)\) None 0 4
2664.1.eg \(\chi_{2664}(347, \cdot)\) None 0 4
2664.1.eh \(\chi_{2664}(635, \cdot)\) None 0 4
2664.1.ek \(\chi_{2664}(23, \cdot)\) None 0 4
2664.1.el \(\chi_{2664}(191, \cdot)\) None 0 4
2664.1.en \(\chi_{2664}(251, \cdot)\) None 0 4
2664.1.eq \(\chi_{2664}(421, \cdot)\) None 0 4
2664.1.es \(\chi_{2664}(97, \cdot)\) None 0 4
2664.1.et \(\chi_{2664}(329, \cdot)\) None 0 6
2664.1.ew \(\chi_{2664}(895, \cdot)\) None 0 6
2664.1.ex \(\chi_{2664}(583, \cdot)\) None 0 6
2664.1.fa \(\chi_{2664}(41, \cdot)\) None 0 6
2664.1.fb \(\chi_{2664}(115, \cdot)\) None 0 6
2664.1.fc \(\chi_{2664}(595, \cdot)\) None 0 6
2664.1.fe \(\chi_{2664}(485, \cdot)\) None 0 6
2664.1.ff \(\chi_{2664}(509, \cdot)\) None 0 6
2664.1.fi \(\chi_{2664}(821, \cdot)\) None 0 6
2664.1.fj \(\chi_{2664}(53, \cdot)\) None 0 6
2664.1.fm \(\chi_{2664}(379, \cdot)\) None 0 6
2664.1.fn \(\chi_{2664}(403, \cdot)\) None 0 6
2664.1.fp \(\chi_{2664}(521, \cdot)\) None 0 6
2664.1.fs \(\chi_{2664}(617, \cdot)\) None 0 6
2664.1.ft \(\chi_{2664}(151, \cdot)\) None 0 6
2664.1.fw \(\chi_{2664}(559, \cdot)\) None 0 6
2664.1.fx \(\chi_{2664}(127, \cdot)\) None 0 6
2664.1.ga \(\chi_{2664}(7, \cdot)\) None 0 6
2664.1.gb \(\chi_{2664}(1193, \cdot)\) None 0 6
2664.1.ge \(\chi_{2664}(305, \cdot)\) None 0 6
2664.1.gf \(\chi_{2664}(1267, \cdot)\) None 0 6
2664.1.gi \(\chi_{2664}(293, \cdot)\) None 0 6
2664.1.gj \(\chi_{2664}(77, \cdot)\) None 0 6
2664.1.gl \(\chi_{2664}(67, \cdot)\) None 0 6
2664.1.gm \(\chi_{2664}(167, \cdot)\) None 0 12
2664.1.gn \(\chi_{2664}(313, \cdot)\) None 0 12
2664.1.gs \(\chi_{2664}(109, \cdot)\) None 0 12
2664.1.gt \(\chi_{2664}(35, \cdot)\) None 0 12
2664.1.gw \(\chi_{2664}(59, \cdot)\) None 0 12
2664.1.gx \(\chi_{2664}(61, \cdot)\) None 0 12
2664.1.ha \(\chi_{2664}(143, \cdot)\) None 0 12
2664.1.hb \(\chi_{2664}(217, \cdot)\) None 0 12
2664.1.he \(\chi_{2664}(241, \cdot)\) None 0 12
2664.1.hf \(\chi_{2664}(239, \cdot)\) None 0 12
2664.1.hg \(\chi_{2664}(13, \cdot)\) None 0 12
2664.1.hh \(\chi_{2664}(203, \cdot)\) None 0 12

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(2664))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(2664)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 24}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 18}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 16}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(37))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(74))\)\(^{\oplus 9}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(111))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(148))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(222))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(296))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(333))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(444))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(666))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(888))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(1332))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(2664))\)\(^{\oplus 1}\)