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Properties

Label 1648.2
Level 1648
Weight 2
Dimension 47273
Nonzero newspaces 16
Sturm bound 339456
Trace bound 3

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Defining parameters

Level: \( N \) = \( 1648 = 2^{4} \cdot 103 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 16 \)
Sturm bound: \(339456\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1648))\).

Total New Old
Modular forms 86292 48181 38111
Cusp forms 83437 47273 36164
Eisenstein series 2855 908 1947

Trace form

\( 47273 q - 200 q^{2} - 149 q^{3} - 204 q^{4} - 251 q^{5} - 212 q^{6} - 153 q^{7} - 212 q^{8} - 51 q^{9} + O(q^{10}) \) \( 47273 q - 200 q^{2} - 149 q^{3} - 204 q^{4} - 251 q^{5} - 212 q^{6} - 153 q^{7} - 212 q^{8} - 51 q^{9} - 204 q^{10} - 157 q^{11} - 196 q^{12} - 251 q^{13} - 196 q^{14} - 161 q^{15} - 188 q^{16} - 451 q^{17} - 208 q^{18} - 165 q^{19} - 212 q^{20} - 263 q^{21} - 204 q^{22} - 153 q^{23} - 204 q^{24} - 51 q^{25} - 212 q^{26} - 137 q^{27} - 220 q^{28} - 267 q^{29} - 196 q^{30} - 121 q^{31} - 220 q^{32} - 451 q^{33} - 212 q^{34} - 145 q^{35} - 196 q^{36} - 267 q^{37} - 180 q^{38} - 153 q^{39} - 188 q^{40} - 51 q^{41} - 204 q^{42} - 173 q^{43} - 196 q^{44} - 259 q^{45} - 228 q^{46} - 185 q^{47} - 220 q^{48} - 471 q^{49} - 192 q^{50} - 161 q^{51} - 196 q^{52} - 235 q^{53} - 204 q^{54} - 153 q^{55} - 188 q^{56} - 51 q^{57} - 180 q^{58} - 141 q^{59} - 204 q^{60} - 219 q^{61} - 236 q^{62} - 161 q^{63} - 204 q^{64} - 467 q^{65} - 212 q^{66} - 133 q^{67} - 204 q^{68} - 231 q^{69} - 220 q^{70} - 153 q^{71} - 212 q^{72} - 51 q^{73} - 204 q^{74} - 165 q^{75} - 228 q^{76} - 263 q^{77} - 196 q^{78} - 153 q^{79} - 220 q^{80} - 479 q^{81} - 204 q^{82} - 149 q^{83} - 188 q^{84} - 263 q^{85} - 204 q^{86} - 153 q^{87} - 220 q^{88} - 51 q^{89} - 196 q^{90} - 161 q^{91} - 156 q^{92} - 287 q^{93} - 172 q^{94} - 129 q^{95} - 172 q^{96} - 451 q^{97} - 192 q^{98} - 149 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1648))\)

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
1648.2.a \(\chi_{1648}(1, \cdot)\) 1648.2.a.a 1 1
1648.2.a.b 2
1648.2.a.c 2
1648.2.a.d 2
1648.2.a.e 2
1648.2.a.f 2
1648.2.a.g 2
1648.2.a.h 2
1648.2.a.i 2
1648.2.a.j 2
1648.2.a.k 4
1648.2.a.l 4
1648.2.a.m 6
1648.2.a.n 9
1648.2.a.o 9
1648.2.b \(\chi_{1648}(825, \cdot)\) None 0 1
1648.2.d \(\chi_{1648}(823, \cdot)\) None 0 1
1648.2.g \(\chi_{1648}(1647, \cdot)\) 1648.2.g.a 16 1
1648.2.g.b 36
1648.2.i \(\chi_{1648}(561, \cdot)\) n/a 102 2
1648.2.k \(\chi_{1648}(413, \cdot)\) n/a 408 2
1648.2.m \(\chi_{1648}(411, \cdot)\) n/a 412 2
1648.2.n \(\chi_{1648}(263, \cdot)\) None 0 2
1648.2.p \(\chi_{1648}(777, \cdot)\) None 0 2
1648.2.t \(\chi_{1648}(47, \cdot)\) n/a 104 2
1648.2.v \(\chi_{1648}(459, \cdot)\) n/a 824 4
1648.2.x \(\chi_{1648}(149, \cdot)\) n/a 824 4
1648.2.y \(\chi_{1648}(81, \cdot)\) n/a 816 16
1648.2.ba \(\chi_{1648}(31, \cdot)\) n/a 832 16
1648.2.bd \(\chi_{1648}(39, \cdot)\) None 0 16
1648.2.bf \(\chi_{1648}(9, \cdot)\) None 0 16
1648.2.bg \(\chi_{1648}(17, \cdot)\) n/a 1632 32
1648.2.bh \(\chi_{1648}(3, \cdot)\) n/a 6592 32
1648.2.bj \(\chi_{1648}(13, \cdot)\) n/a 6592 32
1648.2.bl \(\chi_{1648}(143, \cdot)\) n/a 1664 32
1648.2.bp \(\chi_{1648}(25, \cdot)\) None 0 32
1648.2.br \(\chi_{1648}(71, \cdot)\) None 0 32
1648.2.bs \(\chi_{1648}(29, \cdot)\) n/a 13184 64
1648.2.bu \(\chi_{1648}(11, \cdot)\) n/a 13184 64

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1648))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1648)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(103))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(206))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(412))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(824))\)\(^{\oplus 2}\)