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Properties

Label 648.3
Level 648
Weight 3
Dimension 10256
Nonzero newspaces 12
Sturm bound 69984
Trace bound 7

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Defining parameters

Level: \( N \) = \( 648 = 2^{3} \cdot 3^{4} \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 12 \)
Sturm bound: \(69984\)
Trace bound: \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(648))\).

Total New Old
Modular forms 23976 10480 13496
Cusp forms 22680 10256 12424
Eisenstein series 1296 224 1072

Trace form

\( 10256 q - 24 q^{2} - 36 q^{3} - 40 q^{4} - 36 q^{6} - 40 q^{7} - 24 q^{8} - 72 q^{9} + O(q^{10}) \) \( 10256 q - 24 q^{2} - 36 q^{3} - 40 q^{4} - 36 q^{6} - 40 q^{7} - 24 q^{8} - 72 q^{9} - 58 q^{10} - 6 q^{11} - 36 q^{12} + 24 q^{13} - 24 q^{14} - 36 q^{15} - 40 q^{16} - 48 q^{17} - 36 q^{18} - 70 q^{19} - 24 q^{20} - 56 q^{22} - 96 q^{23} - 36 q^{24} - 128 q^{25} - 186 q^{26} - 36 q^{27} - 226 q^{28} - 108 q^{29} - 36 q^{30} - 112 q^{31} - 204 q^{32} - 72 q^{33} - 76 q^{34} - 30 q^{35} - 36 q^{36} + 36 q^{37} + 156 q^{38} - 36 q^{39} + 140 q^{40} - 354 q^{41} - 36 q^{42} - 106 q^{43} + 408 q^{44} - 432 q^{45} + 222 q^{46} - 348 q^{47} - 36 q^{48} - 248 q^{49} + 126 q^{50} - 162 q^{51} + 24 q^{52} - 36 q^{54} - 14 q^{55} + 270 q^{56} + 144 q^{57} + 272 q^{58} + 174 q^{59} - 36 q^{60} + 156 q^{61} + 570 q^{62} + 504 q^{63} + 194 q^{64} + 816 q^{65} - 36 q^{66} + 62 q^{67} + 210 q^{68} + 288 q^{69} + 88 q^{70} - 18 q^{71} - 36 q^{72} + 16 q^{73} - 252 q^{74} - 36 q^{75} - 400 q^{76} + 504 q^{77} + 126 q^{78} + 524 q^{79} - 834 q^{80} - 72 q^{81} - 508 q^{82} + 876 q^{83} - 36 q^{84} + 324 q^{85} - 924 q^{86} - 36 q^{87} + 448 q^{88} + 924 q^{89} + 2106 q^{90} + 1242 q^{91} + 4476 q^{92} + 756 q^{93} + 1614 q^{94} + 3186 q^{95} + 2538 q^{96} + 406 q^{97} + 5106 q^{98} + 1260 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(648))\)

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
648.3.b \(\chi_{648}(163, \cdot)\) 648.3.b.a 2 1
648.3.b.b 2
648.3.b.c 12
648.3.b.d 12
648.3.b.e 20
648.3.b.f 20
648.3.b.g 24
648.3.e \(\chi_{648}(161, \cdot)\) 648.3.e.a 4 1
648.3.e.b 4
648.3.e.c 8
648.3.e.d 8
648.3.g \(\chi_{648}(487, \cdot)\) None 0 1
648.3.h \(\chi_{648}(485, \cdot)\) 648.3.h.a 44 1
648.3.h.b 48
648.3.j \(\chi_{648}(53, \cdot)\) n/a 188 2
648.3.k \(\chi_{648}(55, \cdot)\) None 0 2
648.3.m \(\chi_{648}(377, \cdot)\) 648.3.m.a 4 2
648.3.m.b 4
648.3.m.c 4
648.3.m.d 4
648.3.m.e 8
648.3.m.f 8
648.3.m.g 16
648.3.p \(\chi_{648}(379, \cdot)\) n/a 188 2
648.3.r \(\chi_{648}(19, \cdot)\) n/a 420 6
648.3.s \(\chi_{648}(127, \cdot)\) None 0 6
648.3.u \(\chi_{648}(17, \cdot)\) n/a 108 6
648.3.x \(\chi_{648}(125, \cdot)\) n/a 420 6
648.3.z \(\chi_{648}(5, \cdot)\) n/a 3852 18
648.3.ba \(\chi_{648}(7, \cdot)\) None 0 18
648.3.bc \(\chi_{648}(41, \cdot)\) n/a 972 18
648.3.bf \(\chi_{648}(43, \cdot)\) n/a 3852 18

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

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(648))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(648)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 9}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(54))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(81))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(108))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(162))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(216))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(324))\)\(^{\oplus 2}\)