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Properties

Label 432.4
Level 432
Weight 4
Dimension 6840
Nonzero newspaces 12
Sturm bound 41472
Trace bound 10

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Defining parameters

Level: \( N \) = \( 432 = 2^{4} \cdot 3^{3} \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 12 \)
Sturm bound: \(41472\)
Trace bound: \(10\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(432))\).

Total New Old
Modular forms 15972 6984 8988
Cusp forms 15132 6840 8292
Eisenstein series 840 144 696

Trace form

\( 6840 q - 16 q^{2} - 18 q^{3} - 28 q^{4} - 21 q^{5} - 24 q^{6} - 39 q^{7} - 16 q^{8} - 6 q^{9} + O(q^{10}) \) \( 6840 q - 16 q^{2} - 18 q^{3} - 28 q^{4} - 21 q^{5} - 24 q^{6} - 39 q^{7} - 16 q^{8} - 6 q^{9} - 28 q^{10} + 55 q^{11} - 24 q^{12} + q^{13} + 16 q^{14} - 18 q^{15} + 236 q^{16} + 45 q^{17} - 24 q^{18} - 123 q^{19} - 324 q^{20} - 30 q^{21} - 532 q^{22} - 145 q^{23} - 24 q^{24} - 218 q^{25} - 560 q^{26} + 648 q^{27} - 136 q^{28} + 371 q^{29} - 24 q^{30} - 219 q^{31} + 964 q^{32} - 750 q^{33} + 668 q^{34} - 1367 q^{35} - 24 q^{36} - 839 q^{37} - 1220 q^{38} - 846 q^{39} - 316 q^{40} - 225 q^{41} - 24 q^{42} - 639 q^{43} + 1524 q^{44} + 1290 q^{45} + 1348 q^{46} - 37 q^{47} - 24 q^{48} - 128 q^{49} + 2148 q^{50} - 99 q^{51} + 836 q^{52} - 24 q^{53} - 24 q^{54} + 530 q^{55} - 7876 q^{56} - 3261 q^{57} - 9148 q^{58} + 1051 q^{59} - 7344 q^{60} - 1535 q^{61} - 6184 q^{62} - 48 q^{63} + 1052 q^{64} + 4817 q^{65} + 7356 q^{66} + 1269 q^{67} + 15068 q^{68} + 6210 q^{69} + 13220 q^{70} + 3181 q^{71} + 11904 q^{72} + 2105 q^{73} + 18184 q^{74} + 2460 q^{75} + 9764 q^{76} + 7881 q^{77} + 4500 q^{78} - 783 q^{79} - 4956 q^{80} - 1878 q^{81} - 6352 q^{82} - 3397 q^{83} - 11244 q^{84} - 5233 q^{85} - 27556 q^{86} - 3060 q^{87} - 11332 q^{88} - 12735 q^{89} - 8772 q^{90} + 3031 q^{91} + 6548 q^{92} - 7446 q^{93} + 4500 q^{94} - 365 q^{95} - 24 q^{96} - 1527 q^{97} + 7376 q^{98} + 3762 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(432))\)

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
432.4.a \(\chi_{432}(1, \cdot)\) 432.4.a.a 1 1
432.4.a.b 1
432.4.a.c 1
432.4.a.d 1
432.4.a.e 1
432.4.a.f 1
432.4.a.g 1
432.4.a.h 1
432.4.a.i 1
432.4.a.j 1
432.4.a.k 1
432.4.a.l 1
432.4.a.m 1
432.4.a.n 1
432.4.a.o 2
432.4.a.p 2
432.4.a.q 2
432.4.a.r 2
432.4.a.s 2
432.4.c \(\chi_{432}(431, \cdot)\) 432.4.c.a 2 1
432.4.c.b 2
432.4.c.c 2
432.4.c.d 2
432.4.c.e 4
432.4.c.f 4
432.4.c.g 4
432.4.c.h 4
432.4.d \(\chi_{432}(217, \cdot)\) None 0 1
432.4.f \(\chi_{432}(215, \cdot)\) None 0 1
432.4.i \(\chi_{432}(145, \cdot)\) 432.4.i.a 2 2
432.4.i.b 4
432.4.i.c 4
432.4.i.d 6
432.4.i.e 8
432.4.i.f 10
432.4.k \(\chi_{432}(109, \cdot)\) n/a 192 2
432.4.l \(\chi_{432}(107, \cdot)\) n/a 192 2
432.4.p \(\chi_{432}(71, \cdot)\) None 0 2
432.4.r \(\chi_{432}(73, \cdot)\) None 0 2
432.4.s \(\chi_{432}(143, \cdot)\) 432.4.s.a 2 2
432.4.s.b 2
432.4.s.c 10
432.4.s.d 10
432.4.s.e 12
432.4.u \(\chi_{432}(49, \cdot)\) n/a 318 6
432.4.v \(\chi_{432}(35, \cdot)\) n/a 280 4
432.4.y \(\chi_{432}(37, \cdot)\) n/a 280 4
432.4.bb \(\chi_{432}(25, \cdot)\) None 0 6
432.4.bd \(\chi_{432}(23, \cdot)\) None 0 6
432.4.be \(\chi_{432}(47, \cdot)\) n/a 324 6
432.4.bg \(\chi_{432}(13, \cdot)\) n/a 2568 12
432.4.bj \(\chi_{432}(11, \cdot)\) n/a 2568 12

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(432))\) into lower level spaces

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