Properties

Label 432.1
Level 432
Weight 1
Dimension 7
Nonzero newspaces 3
Newform subspaces 3
Sturm bound 10368
Trace bound 1

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Defining parameters

Level: \( N \) = \( 432 = 2^{4} \cdot 3^{3} \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 3 \)
Newform subspaces: \( 3 \)
Sturm bound: \(10368\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(432))\).

Total New Old
Modular forms 460 79 381
Cusp forms 40 7 33
Eisenstein series 420 72 348

The following table gives the dimensions of subspaces with specified projective image type.

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 3 0 4 0

Trace form

\( 7q + q^{7} + O(q^{10}) \) \( 7q + q^{7} - 3q^{13} - 4q^{16} + q^{19} - q^{25} + 4q^{28} + 2q^{31} - 4q^{34} - 3q^{37} - 4q^{40} - 6q^{43} - 4q^{49} + 4q^{52} - 3q^{61} + 5q^{67} + 4q^{70} + q^{73} + q^{79} - 4q^{85} + 4q^{88} - 5q^{91} + 4q^{94} + 5q^{97} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(432))\)

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
432.1.b \(\chi_{432}(55, \cdot)\) None 0 1
432.1.e \(\chi_{432}(161, \cdot)\) 432.1.e.a 1 1
432.1.g \(\chi_{432}(271, \cdot)\) 432.1.g.a 2 1
432.1.h \(\chi_{432}(377, \cdot)\) None 0 1
432.1.j \(\chi_{432}(53, \cdot)\) 432.1.j.a 4 2
432.1.m \(\chi_{432}(163, \cdot)\) None 0 2
432.1.n \(\chi_{432}(89, \cdot)\) None 0 2
432.1.o \(\chi_{432}(127, \cdot)\) None 0 2
432.1.q \(\chi_{432}(17, \cdot)\) None 0 2
432.1.t \(\chi_{432}(199, \cdot)\) None 0 2
432.1.w \(\chi_{432}(19, \cdot)\) None 0 4
432.1.x \(\chi_{432}(125, \cdot)\) None 0 4
432.1.z \(\chi_{432}(7, \cdot)\) None 0 6
432.1.ba \(\chi_{432}(31, \cdot)\) None 0 6
432.1.bc \(\chi_{432}(65, \cdot)\) None 0 6
432.1.bf \(\chi_{432}(41, \cdot)\) None 0 6
432.1.bh \(\chi_{432}(43, \cdot)\) None 0 12
432.1.bi \(\chi_{432}(5, \cdot)\) None 0 12

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(432))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(432)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(108))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(144))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(216))\)\(^{\oplus 2}\)