Properties

Label 432.8
Level 432
Weight 8
Dimension 16056
Nonzero newspaces 12
Sturm bound 82944
Trace bound 10

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Defining parameters

Level: \( N \) = \( 432 = 2^{4} \cdot 3^{3} \)
Weight: \( k \) = \( 8 \)
Nonzero newspaces: \( 12 \)
Sturm bound: \(82944\)
Trace bound: \(10\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(432))\).

Total New Old
Modular forms 36708 16200 20508
Cusp forms 35868 16056 19812
Eisenstein series 840 144 696

Trace form

\( 16056 q - 16 q^{2} - 18 q^{3} - 28 q^{4} - 21 q^{5} - 24 q^{6} + 985 q^{7} - 16 q^{8} - 6 q^{9} - 28 q^{10} + 7975 q^{11} - 24 q^{12} - 3567 q^{13} + 496 q^{14} - 18 q^{15} - 26132 q^{16} - 24003 q^{17}+ \cdots - 111014190 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(432))\)

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
432.8.a \(\chi_{432}(1, \cdot)\) 432.8.a.a 1 1
432.8.a.b 1
432.8.a.c 1
432.8.a.d 1
432.8.a.e 1
432.8.a.f 1
432.8.a.g 1
432.8.a.h 1
432.8.a.i 2
432.8.a.j 2
432.8.a.k 2
432.8.a.l 2
432.8.a.m 2
432.8.a.n 2
432.8.a.o 2
432.8.a.p 2
432.8.a.q 2
432.8.a.r 2
432.8.a.s 3
432.8.a.t 3
432.8.a.u 3
432.8.a.v 3
432.8.a.w 4
432.8.a.x 4
432.8.a.y 4
432.8.a.z 4
432.8.c \(\chi_{432}(431, \cdot)\) 432.8.c.a 2 1
432.8.c.b 2
432.8.c.c 8
432.8.c.d 8
432.8.c.e 8
432.8.c.f 8
432.8.c.g 20
432.8.d \(\chi_{432}(217, \cdot)\) None 0 1
432.8.f \(\chi_{432}(215, \cdot)\) None 0 1
432.8.i \(\chi_{432}(145, \cdot)\) 432.8.i.a 6 2
432.8.i.b 8
432.8.i.c 12
432.8.i.d 14
432.8.i.e 20
432.8.i.f 22
432.8.k \(\chi_{432}(109, \cdot)\) n/a 448 2
432.8.l \(\chi_{432}(107, \cdot)\) n/a 448 2
432.8.p \(\chi_{432}(71, \cdot)\) None 0 2
432.8.r \(\chi_{432}(73, \cdot)\) None 0 2
432.8.s \(\chi_{432}(143, \cdot)\) 432.8.s.a 28 2
432.8.s.b 28
432.8.s.c 28
432.8.u \(\chi_{432}(49, \cdot)\) n/a 750 6
432.8.v \(\chi_{432}(35, \cdot)\) n/a 664 4
432.8.y \(\chi_{432}(37, \cdot)\) n/a 664 4
432.8.bb \(\chi_{432}(25, \cdot)\) None 0 6
432.8.bd \(\chi_{432}(23, \cdot)\) None 0 6
432.8.be \(\chi_{432}(47, \cdot)\) n/a 756 6
432.8.bg \(\chi_{432}(13, \cdot)\) n/a 6024 12
432.8.bj \(\chi_{432}(11, \cdot)\) n/a 6024 12

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

Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_1(432))\) into lower level spaces

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