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Properties

Label 432.6
Level 432
Weight 6
Dimension 11448
Nonzero newspaces 12
Sturm bound 62208
Trace bound 10

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Defining parameters

Level: \( N \) = \( 432 = 2^{4} \cdot 3^{3} \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 12 \)
Sturm bound: \(62208\)
Trace bound: \(10\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(432))\).

Total New Old
Modular forms 26340 11592 14748
Cusp forms 25500 11448 14052
Eisenstein series 840 144 696

Trace form

\( 11448 q - 16 q^{2} - 18 q^{3} - 28 q^{4} - 21 q^{5} - 24 q^{6} + 41 q^{7} - 16 q^{8} - 6 q^{9} + O(q^{10}) \) \( 11448 q - 16 q^{2} - 18 q^{3} - 28 q^{4} - 21 q^{5} - 24 q^{6} + 41 q^{7} - 16 q^{8} - 6 q^{9} - 28 q^{10} - 737 q^{11} - 24 q^{12} - 151 q^{13} + 112 q^{14} - 18 q^{15} + 2412 q^{16} - 1035 q^{17} - 24 q^{18} - 2819 q^{19} - 1668 q^{20} - 30 q^{21} + 10028 q^{22} + 3167 q^{23} - 24 q^{24} + 8574 q^{25} + 1744 q^{26} - 6480 q^{27} - 16648 q^{28} - 55741 q^{29} - 24 q^{30} - 9563 q^{31} - 3836 q^{32} + 16962 q^{33} + 27612 q^{34} + 92233 q^{35} - 24 q^{36} + 31153 q^{37} + 34396 q^{38} - 3438 q^{39} + 60100 q^{40} - 63849 q^{41} - 24 q^{42} - 49223 q^{43} - 36492 q^{44} - 35430 q^{45} - 63612 q^{46} + 173819 q^{47} - 24 q^{48} + 35136 q^{49} - 63900 q^{50} - 747 q^{51} + 18244 q^{52} - 24 q^{53} - 24 q^{54} - 151550 q^{55} - 179716 q^{56} - 194853 q^{57} - 63676 q^{58} - 62669 q^{59} + 424656 q^{60} + 294057 q^{61} + 873848 q^{62} + 120912 q^{63} + 209564 q^{64} + 257537 q^{65} - 5604 q^{66} - 34739 q^{67} - 750052 q^{68} - 379134 q^{69} - 900700 q^{70} - 235427 q^{71} - 834816 q^{72} - 168519 q^{73} - 996536 q^{74} - 95820 q^{75} - 134620 q^{76} + 225609 q^{77} + 465012 q^{78} - 16559 q^{79} + 1846884 q^{80} + 742890 q^{81} + 856368 q^{82} + 534467 q^{83} + 920148 q^{84} - 14225 q^{85} + 366716 q^{86} - 113220 q^{87} - 846404 q^{88} - 1474623 q^{89} - 708612 q^{90} - 96673 q^{91} - 456556 q^{92} + 548538 q^{93} - 410412 q^{94} + 569395 q^{95} - 24 q^{96} - 92871 q^{97} - 411568 q^{98} + 551970 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(432))\)

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
432.6.a \(\chi_{432}(1, \cdot)\) 432.6.a.a 1 1
432.6.a.b 1
432.6.a.c 1
432.6.a.d 1
432.6.a.e 1
432.6.a.f 1
432.6.a.g 1
432.6.a.h 1
432.6.a.i 1
432.6.a.j 1
432.6.a.k 2
432.6.a.l 2
432.6.a.m 2
432.6.a.n 2
432.6.a.o 2
432.6.a.p 2
432.6.a.q 2
432.6.a.r 2
432.6.a.s 2
432.6.a.t 2
432.6.a.u 2
432.6.a.v 2
432.6.a.w 3
432.6.a.x 3
432.6.c \(\chi_{432}(431, \cdot)\) 432.6.c.a 2 1
432.6.c.b 2
432.6.c.c 4
432.6.c.d 4
432.6.c.e 8
432.6.c.f 8
432.6.c.g 12
432.6.d \(\chi_{432}(217, \cdot)\) None 0 1
432.6.f \(\chi_{432}(215, \cdot)\) None 0 1
432.6.i \(\chi_{432}(145, \cdot)\) 432.6.i.a 4 2
432.6.i.b 6
432.6.i.c 8
432.6.i.d 10
432.6.i.e 14
432.6.i.f 16
432.6.k \(\chi_{432}(109, \cdot)\) n/a 320 2
432.6.l \(\chi_{432}(107, \cdot)\) n/a 320 2
432.6.p \(\chi_{432}(71, \cdot)\) None 0 2
432.6.r \(\chi_{432}(73, \cdot)\) None 0 2
432.6.s \(\chi_{432}(143, \cdot)\) 432.6.s.a 20 2
432.6.s.b 20
432.6.s.c 20
432.6.u \(\chi_{432}(49, \cdot)\) n/a 534 6
432.6.v \(\chi_{432}(35, \cdot)\) n/a 472 4
432.6.y \(\chi_{432}(37, \cdot)\) n/a 472 4
432.6.bb \(\chi_{432}(25, \cdot)\) None 0 6
432.6.bd \(\chi_{432}(23, \cdot)\) None 0 6
432.6.be \(\chi_{432}(47, \cdot)\) n/a 540 6
432.6.bg \(\chi_{432}(13, \cdot)\) n/a 4296 12
432.6.bj \(\chi_{432}(11, \cdot)\) n/a 4296 12

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

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(432))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(432)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 15}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 12}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 12}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 10}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 9}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 5}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(54))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(108))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(144))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(216))\)\(^{\oplus 2}\)