Properties

Label 324.1
Level 324
Weight 1
Dimension 8
Nonzero newspaces 3
Newform subspaces 5
Sturm bound 5832
Trace bound 4

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Defining parameters

Level: \( N \) = \( 324 = 2^{2} \cdot 3^{4} \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 3 \)
Newform subspaces: \( 5 \)
Sturm bound: \(5832\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(324))\).

Total New Old
Modular forms 280 64 216
Cusp forms 10 8 2
Eisenstein series 270 56 214

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 8 0 0 0

Trace form

\( 8q + q^{7} + O(q^{10}) \) \( 8q + q^{7} - 6q^{10} + q^{13} - 2q^{19} - q^{25} - 2q^{31} - 8q^{37} - 2q^{43} + q^{61} + 6q^{64} + q^{67} - 8q^{73} + q^{79} + 12q^{82} + 2q^{91} + q^{97} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(324))\)

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
324.1.c \(\chi_{324}(161, \cdot)\) None 0 1
324.1.d \(\chi_{324}(163, \cdot)\) 324.1.d.a 1 1
324.1.d.b 1
324.1.f \(\chi_{324}(55, \cdot)\) 324.1.f.a 2 2
324.1.f.b 2
324.1.g \(\chi_{324}(53, \cdot)\) 324.1.g.a 2 2
324.1.j \(\chi_{324}(19, \cdot)\) None 0 6
324.1.k \(\chi_{324}(17, \cdot)\) None 0 6
324.1.n \(\chi_{324}(7, \cdot)\) None 0 18
324.1.o \(\chi_{324}(5, \cdot)\) None 0 18

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(324))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(324)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(108))\)\(^{\oplus 2}\)