Properties

Label 1331.1
Level 1331
Weight 1
Dimension 25
Nonzero newspaces 2
Newform subspaces 2
Sturm bound 146410
Trace bound 1

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Defining parameters

Level: \( N \) = \( 1331 = 11^{3} \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 2 \)
Sturm bound: \(146410\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(1331))\).

Total New Old
Modular forms 1180 1025 155
Cusp forms 25 25 0
Eisenstein series 1155 1000 155

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 25 0 0 0

Trace form

\( 25 q + O(q^{10}) \) \( 25 q - 5 q^{12} - 5 q^{23} - 15 q^{45} - 5 q^{67} - 5 q^{89} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(1331))\)

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
1331.1.b \(\chi_{1331}(1330, \cdot)\) 1331.1.b.a 5 1
1331.1.d \(\chi_{1331}(161, \cdot)\) 1331.1.d.a 20 4
1331.1.f \(\chi_{1331}(120, \cdot)\) None 0 10
1331.1.h \(\chi_{1331}(40, \cdot)\) None 0 40
1331.1.j \(\chi_{1331}(10, \cdot)\) None 0 110
1331.1.l \(\chi_{1331}(2, \cdot)\) None 0 440