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

\( 11448 q - 16 q^{2} - 18 q^{3} - 28 q^{4} - 21 q^{5} - 24 q^{6} + 41 q^{7} - 16 q^{8} - 6 q^{9} - 28 q^{10} - 737 q^{11} - 24 q^{12} - 151 q^{13} + 112 q^{14} - 18 q^{15} + 2412 q^{16} - 1035 q^{17} - 24 q^{18}+ \cdots + 551970 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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

\( S_{6}^{\mathrm{old}}(\Gamma_1(432)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 20}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 16}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 15}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 12}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 12}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 10}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 9}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 5}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(54))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(108))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(144))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(216))\)\(^{\oplus 2}\)