Properties

Label 432.5
Level 432
Weight 5
Dimension 9144
Nonzero newspaces 12
Sturm bound 51840
Trace bound 10

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Defining parameters

Level: \( N \) = \( 432 = 2^{4} \cdot 3^{3} \)
Weight: \( k \) = \( 5 \)
Nonzero newspaces: \( 12 \)
Sturm bound: \(51840\)
Trace bound: \(10\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(432))\).

Total New Old
Modular forms 21156 9288 11868
Cusp forms 20316 9144 11172
Eisenstein series 840 144 696

Trace form

\( 9144 q - 16 q^{2} - 18 q^{3} - 28 q^{4} - 19 q^{5} - 24 q^{6} - 5 q^{7} - 16 q^{8} - 6 q^{9} + O(q^{10}) \) \( 9144 q - 16 q^{2} - 18 q^{3} - 28 q^{4} - 19 q^{5} - 24 q^{6} - 5 q^{7} - 16 q^{8} - 6 q^{9} - 28 q^{10} - 13 q^{11} - 24 q^{12} + 141 q^{13} - 80 q^{14} - 18 q^{15} - 980 q^{16} - 185 q^{17} - 24 q^{18} - 85 q^{19} + 2588 q^{20} - 30 q^{21} + 1004 q^{22} - 17 q^{23} - 24 q^{24} - 2104 q^{25} - 4144 q^{26} - 1458 q^{27} - 3784 q^{28} + 3149 q^{29} - 24 q^{30} + 4091 q^{31} + 3044 q^{32} + 2922 q^{33} + 4636 q^{34} - 2507 q^{35} - 24 q^{36} - 5555 q^{37} + 1244 q^{38} - 8946 q^{39} - 6972 q^{40} - 9939 q^{41} - 24 q^{42} + 7307 q^{43} - 10444 q^{44} + 2370 q^{45} - 2812 q^{46} + 21591 q^{47} - 24 q^{48} + 2498 q^{49} + 14244 q^{50} + 225 q^{51} + 12612 q^{52} - 10096 q^{53} - 24 q^{54} - 18030 q^{55} + 59164 q^{56} + 27789 q^{57} + 42308 q^{58} + 18707 q^{59} + 1296 q^{60} - 8083 q^{61} - 103272 q^{62} - 14898 q^{63} - 39844 q^{64} - 81251 q^{65} - 96324 q^{66} - 4501 q^{67} - 100100 q^{68} - 25758 q^{69} - 26716 q^{70} + 13 q^{71} + 24000 q^{72} + 4345 q^{73} + 116744 q^{74} + 22494 q^{75} + 121892 q^{76} + 92329 q^{77} + 116820 q^{78} + 34907 q^{79} + 244484 q^{80} + 59466 q^{81} + 36592 q^{82} + 5267 q^{83} - 1740 q^{84} - 2469 q^{85} - 201604 q^{86} - 23634 q^{87} - 158532 q^{88} - 42633 q^{89} - 78756 q^{90} - 20247 q^{91} - 40940 q^{92} + 10050 q^{93} - 9132 q^{94} - 33567 q^{95} - 24 q^{96} + 19233 q^{97} + 28464 q^{98} - 115794 q^{99} + O(q^{100}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(432))\)

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
432.5.b \(\chi_{432}(55, \cdot)\) None 0 1
432.5.e \(\chi_{432}(161, \cdot)\) 432.5.e.a 1 1
432.5.e.b 1
432.5.e.c 2
432.5.e.d 2
432.5.e.e 2
432.5.e.f 2
432.5.e.g 2
432.5.e.h 4
432.5.e.i 4
432.5.e.j 4
432.5.e.k 8
432.5.g \(\chi_{432}(271, \cdot)\) 432.5.g.a 2 1
432.5.g.b 2
432.5.g.c 4
432.5.g.d 4
432.5.g.e 4
432.5.g.f 4
432.5.g.g 6
432.5.g.h 6
432.5.h \(\chi_{432}(377, \cdot)\) None 0 1
432.5.j \(\chi_{432}(53, \cdot)\) n/a 256 2
432.5.m \(\chi_{432}(163, \cdot)\) n/a 256 2
432.5.n \(\chi_{432}(89, \cdot)\) None 0 2
432.5.o \(\chi_{432}(127, \cdot)\) 432.5.o.a 16 2
432.5.o.b 16
432.5.o.c 16
432.5.q \(\chi_{432}(17, \cdot)\) 432.5.q.a 6 2
432.5.q.b 8
432.5.q.c 8
432.5.q.d 24
432.5.t \(\chi_{432}(199, \cdot)\) None 0 2
432.5.w \(\chi_{432}(19, \cdot)\) n/a 376 4
432.5.x \(\chi_{432}(125, \cdot)\) n/a 376 4
432.5.z \(\chi_{432}(7, \cdot)\) None 0 6
432.5.ba \(\chi_{432}(31, \cdot)\) n/a 432 6
432.5.bc \(\chi_{432}(65, \cdot)\) n/a 426 6
432.5.bf \(\chi_{432}(41, \cdot)\) None 0 6
432.5.bh \(\chi_{432}(43, \cdot)\) n/a 3432 12
432.5.bi \(\chi_{432}(5, \cdot)\) n/a 3432 12

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

Decomposition of \(S_{5}^{\mathrm{old}}(\Gamma_1(432))\) into lower level spaces

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