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Properties

Label 144.3
Level 144
Weight 3
Dimension 493
Nonzero newspaces 8
Newform subspaces 19
Sturm bound 3456
Trace bound 2

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Defining parameters

Level: \( N \) = \( 144 = 2^{4} \cdot 3^{2} \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 8 \)
Newform subspaces: \( 19 \)
Sturm bound: \(3456\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(144))\).

Total New Old
Modular forms 1264 533 731
Cusp forms 1040 493 547
Eisenstein series 224 40 184

Trace form

\( 493 q - 6 q^{2} - 6 q^{3} - 12 q^{4} - 15 q^{5} - 8 q^{6} - 23 q^{7} - 10 q^{9} + O(q^{10}) \) \( 493 q - 6 q^{2} - 6 q^{3} - 12 q^{4} - 15 q^{5} - 8 q^{6} - 23 q^{7} - 10 q^{9} + 20 q^{10} - 19 q^{11} - 8 q^{12} + 19 q^{13} + 40 q^{14} + 27 q^{15} + 68 q^{16} + 102 q^{17} + 92 q^{18} + 82 q^{19} + 80 q^{20} + 31 q^{21} - 8 q^{22} + 67 q^{23} - 40 q^{24} - 79 q^{25} - 100 q^{26} + 66 q^{27} - 200 q^{28} - 127 q^{29} - 220 q^{30} - 107 q^{31} - 356 q^{32} - 75 q^{33} - 256 q^{34} + 96 q^{35} - 204 q^{36} + 52 q^{37} - 468 q^{38} + 129 q^{39} - 412 q^{40} + 15 q^{41} - 208 q^{42} + 283 q^{43} - 248 q^{44} - 171 q^{45} - 20 q^{46} - 225 q^{47} + 44 q^{48} - 117 q^{49} + 322 q^{50} - 320 q^{51} + 416 q^{52} - 124 q^{53} + 300 q^{54} - 446 q^{55} + 352 q^{56} - 316 q^{57} + 732 q^{58} - 587 q^{59} - 524 q^{60} + 83 q^{61} - 216 q^{62} - 339 q^{63} + 552 q^{64} - 59 q^{65} - 608 q^{66} - 69 q^{67} + 80 q^{68} - 103 q^{69} + 28 q^{70} - 268 q^{71} + 104 q^{72} - 146 q^{73} + 72 q^{74} - 62 q^{75} - 432 q^{76} + 173 q^{77} + 532 q^{78} - 563 q^{79} - 192 q^{80} + 646 q^{81} - 1544 q^{82} - 283 q^{83} + 520 q^{84} + 308 q^{85} - 72 q^{86} - 69 q^{87} - 844 q^{88} + 426 q^{89} + 280 q^{90} + 142 q^{91} - 500 q^{92} + 567 q^{93} - 84 q^{94} + 714 q^{95} + 60 q^{96} + 429 q^{97} + 838 q^{98} + 747 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(144))\)

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
144.3.b \(\chi_{144}(55, \cdot)\) None 0 1
144.3.e \(\chi_{144}(17, \cdot)\) 144.3.e.a 2 1
144.3.e.b 2
144.3.g \(\chi_{144}(127, \cdot)\) 144.3.g.a 1 1
144.3.g.b 2
144.3.g.c 2
144.3.h \(\chi_{144}(89, \cdot)\) None 0 1
144.3.j \(\chi_{144}(53, \cdot)\) 144.3.j.a 32 2
144.3.m \(\chi_{144}(19, \cdot)\) 144.3.m.a 6 2
144.3.m.b 16
144.3.m.c 16
144.3.n \(\chi_{144}(41, \cdot)\) None 0 2
144.3.o \(\chi_{144}(31, \cdot)\) 144.3.o.a 8 2
144.3.o.b 8
144.3.o.c 8
144.3.q \(\chi_{144}(65, \cdot)\) 144.3.q.a 2 2
144.3.q.b 4
144.3.q.c 4
144.3.q.d 4
144.3.q.e 8
144.3.t \(\chi_{144}(7, \cdot)\) None 0 2
144.3.v \(\chi_{144}(43, \cdot)\) 144.3.v.a 184 4
144.3.w \(\chi_{144}(5, \cdot)\) 144.3.w.a 184 4

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(144))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(144)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 15}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 10}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 9}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(144))\)\(^{\oplus 1}\)