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Properties

Label 1664.2
Level 1664
Weight 2
Dimension 47280
Nonzero newspaces 36
Sturm bound 344064
Trace bound 26

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Defining parameters

Level: \( N \) = \( 1664 = 2^{7} \cdot 13 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 36 \)
Sturm bound: \(344064\)
Trace bound: \(26\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1664))\).

Total New Old
Modular forms 87936 48336 39600
Cusp forms 84097 47280 36817
Eisenstein series 3839 1056 2783

Trace form

\( 47280 q - 160 q^{2} - 120 q^{3} - 160 q^{4} - 160 q^{5} - 160 q^{6} - 120 q^{7} - 160 q^{8} - 200 q^{9} + O(q^{10}) \) \( 47280 q - 160 q^{2} - 120 q^{3} - 160 q^{4} - 160 q^{5} - 160 q^{6} - 120 q^{7} - 160 q^{8} - 200 q^{9} - 160 q^{10} - 120 q^{11} - 160 q^{12} - 176 q^{13} - 352 q^{14} - 112 q^{15} - 160 q^{16} - 240 q^{17} - 160 q^{18} - 120 q^{19} - 160 q^{20} - 136 q^{21} - 160 q^{22} - 104 q^{23} - 160 q^{24} - 168 q^{25} - 176 q^{26} - 216 q^{27} - 160 q^{28} - 128 q^{29} - 160 q^{30} - 80 q^{31} - 160 q^{32} - 256 q^{33} - 160 q^{34} - 72 q^{35} - 160 q^{36} - 128 q^{37} - 160 q^{38} - 108 q^{39} - 352 q^{40} - 168 q^{41} - 160 q^{42} - 104 q^{43} - 160 q^{44} - 168 q^{45} - 160 q^{46} - 112 q^{47} - 160 q^{48} - 296 q^{49} - 256 q^{50} - 128 q^{51} - 272 q^{52} - 416 q^{53} - 416 q^{54} - 184 q^{55} - 384 q^{56} - 328 q^{57} - 448 q^{58} - 184 q^{59} - 544 q^{60} - 288 q^{61} - 352 q^{62} - 240 q^{63} - 544 q^{64} - 240 q^{65} - 736 q^{66} - 200 q^{67} - 352 q^{68} - 264 q^{69} - 544 q^{70} - 184 q^{71} - 448 q^{72} - 328 q^{73} - 384 q^{74} - 144 q^{75} - 416 q^{76} - 168 q^{77} - 272 q^{78} - 256 q^{79} - 256 q^{80} - 248 q^{81} - 160 q^{82} - 40 q^{83} - 160 q^{84} - 176 q^{85} - 160 q^{86} - 8 q^{87} - 160 q^{88} - 72 q^{89} - 160 q^{90} - 84 q^{91} - 352 q^{92} - 64 q^{93} - 160 q^{94} - 160 q^{96} - 192 q^{97} - 160 q^{98} - 16 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1664))\)

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
1664.2.a \(\chi_{1664}(1, \cdot)\) 1664.2.a.a 1 1
1664.2.a.b 1
1664.2.a.c 1
1664.2.a.d 1
1664.2.a.e 1
1664.2.a.f 1
1664.2.a.g 1
1664.2.a.h 1
1664.2.a.i 1
1664.2.a.j 1
1664.2.a.k 1
1664.2.a.l 1
1664.2.a.m 1
1664.2.a.n 1
1664.2.a.o 1
1664.2.a.p 1
1664.2.a.q 1
1664.2.a.r 1
1664.2.a.s 1
1664.2.a.t 1
1664.2.a.u 2
1664.2.a.v 2
1664.2.a.w 2
1664.2.a.x 2
1664.2.a.y 5
1664.2.a.z 5
1664.2.a.ba 5
1664.2.a.bb 5
1664.2.b \(\chi_{1664}(833, \cdot)\) 1664.2.b.a 2 1
1664.2.b.b 2
1664.2.b.c 2
1664.2.b.d 2
1664.2.b.e 4
1664.2.b.f 4
1664.2.b.g 4
1664.2.b.h 4
1664.2.b.i 4
1664.2.b.j 8
1664.2.b.k 12
1664.2.e \(\chi_{1664}(961, \cdot)\) 1664.2.e.a 2 1
1664.2.e.b 2
1664.2.e.c 4
1664.2.e.d 4
1664.2.e.e 8
1664.2.e.f 12
1664.2.e.g 12
1664.2.e.h 12
1664.2.f \(\chi_{1664}(129, \cdot)\) 1664.2.f.a 14 1
1664.2.f.b 14
1664.2.f.c 14
1664.2.f.d 14
1664.2.i \(\chi_{1664}(1153, \cdot)\) n/a 112 2
1664.2.k \(\chi_{1664}(255, \cdot)\) n/a 112 2
1664.2.l \(\chi_{1664}(671, \cdot)\) n/a 104 2
1664.2.n \(\chi_{1664}(417, \cdot)\) 1664.2.n.a 48 2
1664.2.n.b 48
1664.2.p \(\chi_{1664}(545, \cdot)\) n/a 104 2
1664.2.s \(\chi_{1664}(31, \cdot)\) n/a 104 2
1664.2.u \(\chi_{1664}(447, \cdot)\) n/a 112 2
1664.2.w \(\chi_{1664}(257, \cdot)\) n/a 112 2
1664.2.z \(\chi_{1664}(321, \cdot)\) n/a 112 2
1664.2.ba \(\chi_{1664}(1089, \cdot)\) n/a 112 2
1664.2.bd \(\chi_{1664}(239, \cdot)\) n/a 216 4
1664.2.bf \(\chi_{1664}(209, \cdot)\) n/a 192 4
1664.2.bg \(\chi_{1664}(337, \cdot)\) n/a 216 4
1664.2.bi \(\chi_{1664}(47, \cdot)\) n/a 216 4
1664.2.bk \(\chi_{1664}(63, \cdot)\) n/a 224 4
1664.2.bn \(\chi_{1664}(223, \cdot)\) n/a 208 4
1664.2.bp \(\chi_{1664}(225, \cdot)\) n/a 208 4
1664.2.br \(\chi_{1664}(289, \cdot)\) n/a 208 4
1664.2.bs \(\chi_{1664}(479, \cdot)\) n/a 208 4
1664.2.bu \(\chi_{1664}(383, \cdot)\) n/a 224 4
1664.2.bw \(\chi_{1664}(135, \cdot)\) None 0 8
1664.2.by \(\chi_{1664}(105, \cdot)\) None 0 8
1664.2.cb \(\chi_{1664}(25, \cdot)\) None 0 8
1664.2.cc \(\chi_{1664}(343, \cdot)\) None 0 8
1664.2.cf \(\chi_{1664}(15, \cdot)\) n/a 432 8
1664.2.ch \(\chi_{1664}(17, \cdot)\) n/a 432 8
1664.2.ci \(\chi_{1664}(81, \cdot)\) n/a 432 8
1664.2.ck \(\chi_{1664}(175, \cdot)\) n/a 432 8
1664.2.cn \(\chi_{1664}(99, \cdot)\) n/a 3552 16
1664.2.cp \(\chi_{1664}(53, \cdot)\) n/a 3072 16
1664.2.cr \(\chi_{1664}(77, \cdot)\) n/a 3552 16
1664.2.cs \(\chi_{1664}(83, \cdot)\) n/a 3552 16
1664.2.cv \(\chi_{1664}(7, \cdot)\) None 0 16
1664.2.cx \(\chi_{1664}(9, \cdot)\) None 0 16
1664.2.cy \(\chi_{1664}(121, \cdot)\) None 0 16
1664.2.db \(\chi_{1664}(71, \cdot)\) None 0 16
1664.2.dc \(\chi_{1664}(115, \cdot)\) n/a 7104 32
1664.2.de \(\chi_{1664}(69, \cdot)\) n/a 7104 32
1664.2.dg \(\chi_{1664}(29, \cdot)\) n/a 7104 32
1664.2.dj \(\chi_{1664}(11, \cdot)\) n/a 7104 32

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1664))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1664)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(52))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(104))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(128))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(208))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(416))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(832))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1664))\)\(^{\oplus 1}\)