Properties

Label 432.3
Level 432
Weight 3
Dimension 4536
Nonzero newspaces 12
Newform subspaces 38
Sturm bound 31104
Trace bound 10

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Defining parameters

Level: \( N \) = \( 432 = 2^{4} \cdot 3^{3} \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 12 \)
Newform subspaces: \( 38 \)
Sturm bound: \(31104\)
Trace bound: \(10\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(432))\).

Total New Old
Modular forms 10788 4680 6108
Cusp forms 9948 4536 5412
Eisenstein series 840 144 696

Trace form

\( 4536 q - 16 q^{2} - 18 q^{3} - 28 q^{4} - 19 q^{5} - 24 q^{6} - 13 q^{7} - 16 q^{8} - 6 q^{9} + O(q^{10}) \) \( 4536 q - 16 q^{2} - 18 q^{3} - 28 q^{4} - 19 q^{5} - 24 q^{6} - 13 q^{7} - 16 q^{8} - 6 q^{9} - 28 q^{10} - 13 q^{11} - 24 q^{12} - 43 q^{13} - 32 q^{14} - 18 q^{15} - 84 q^{16} - 113 q^{17} - 24 q^{18} - 53 q^{19} - 100 q^{20} - 30 q^{21} - 52 q^{22} - 17 q^{23} - 24 q^{24} + 80 q^{26} - 162 q^{27} + 56 q^{28} - 163 q^{29} - 24 q^{30} - 77 q^{31} + 164 q^{32} - 102 q^{33} + 60 q^{34} - 107 q^{35} - 24 q^{36} - 11 q^{37} + 236 q^{38} + 126 q^{39} + 196 q^{40} + 213 q^{41} - 24 q^{42} - 5 q^{43} + 116 q^{44} + 210 q^{45} + 36 q^{46} + 423 q^{47} - 24 q^{48} + 66 q^{49} - 156 q^{50} + 9 q^{51} - 188 q^{52} + 128 q^{53} - 24 q^{54} + 370 q^{55} + 604 q^{56} + 357 q^{57} + 452 q^{58} + 707 q^{59} + 1296 q^{60} + 645 q^{61} + 1800 q^{62} + 222 q^{63} + 476 q^{64} + 829 q^{65} + 876 q^{66} + 43 q^{67} + 700 q^{68} + 162 q^{69} + 164 q^{70} + 13 q^{71} - 192 q^{72} - 135 q^{73} - 856 q^{74} - 186 q^{75} - 988 q^{76} - 1079 q^{77} - 1116 q^{78} - 29 q^{79} - 2236 q^{80} - 1014 q^{81} - 336 q^{82} - 253 q^{83} - 1740 q^{84} - 1253 q^{85} - 2548 q^{86} - 306 q^{87} - 836 q^{88} - 585 q^{89} - 996 q^{90} - 151 q^{91} + 148 q^{92} + 978 q^{93} - 12 q^{94} + 489 q^{95} - 24 q^{96} - 399 q^{97} - 432 q^{98} + 846 q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(432))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
432.3.b \(\chi_{432}(55, \cdot)\) None 0 1
432.3.e \(\chi_{432}(161, \cdot)\) 432.3.e.a 1 1
432.3.e.b 1
432.3.e.c 2
432.3.e.d 2
432.3.e.e 2
432.3.e.f 2
432.3.e.g 2
432.3.e.h 4
432.3.g \(\chi_{432}(271, \cdot)\) 432.3.g.a 2 1
432.3.g.b 2
432.3.g.c 2
432.3.g.d 2
432.3.g.e 4
432.3.g.f 4
432.3.h \(\chi_{432}(377, \cdot)\) None 0 1
432.3.j \(\chi_{432}(53, \cdot)\) 432.3.j.a 4 2
432.3.j.b 60
432.3.j.c 64
432.3.m \(\chi_{432}(163, \cdot)\) 432.3.m.a 64 2
432.3.m.b 64
432.3.n \(\chi_{432}(89, \cdot)\) None 0 2
432.3.o \(\chi_{432}(127, \cdot)\) 432.3.o.a 8 2
432.3.o.b 8
432.3.o.c 8
432.3.q \(\chi_{432}(17, \cdot)\) 432.3.q.a 2 2
432.3.q.b 4
432.3.q.c 4
432.3.q.d 4
432.3.q.e 8
432.3.t \(\chi_{432}(199, \cdot)\) None 0 2
432.3.w \(\chi_{432}(19, \cdot)\) 432.3.w.a 184 4
432.3.x \(\chi_{432}(125, \cdot)\) 432.3.x.a 184 4
432.3.z \(\chi_{432}(7, \cdot)\) None 0 6
432.3.ba \(\chi_{432}(31, \cdot)\) 432.3.ba.a 72 6
432.3.ba.b 72
432.3.ba.c 72
432.3.bc \(\chi_{432}(65, \cdot)\) 432.3.bc.a 30 6
432.3.bc.b 36
432.3.bc.c 36
432.3.bc.d 108
432.3.bf \(\chi_{432}(41, \cdot)\) None 0 6
432.3.bh \(\chi_{432}(43, \cdot)\) 432.3.bh.a 1704 12
432.3.bi \(\chi_{432}(5, \cdot)\) 432.3.bi.a 1704 12

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(432))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(432)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 10}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 9}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(54))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(108))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(144))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(216))\)\(^{\oplus 2}\)