↑

Properties

Label 3307.1
Level 3307
Weight 1
Dimension 4
Nonzero newspaces 1
Newform subspaces 2
Sturm bound 911354
Trace bound 0

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 3307 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 2 \)
Sturm bound: \(911354\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(3307))\).

Total New Old
Modular forms 1657 1657 0
Cusp forms 4 4 0
Eisenstein series 1653 1653 0

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

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

Trace form

\( 4 q + 4 q^{4} - q^{7} + 4 q^{9} + O(q^{10}) \) \( 4 q + 4 q^{4} - q^{7} + 4 q^{9} - q^{11} + 4 q^{16} - q^{17} + 4 q^{25} - q^{28} - q^{29} - q^{31} + 4 q^{36} - q^{43} - q^{44} + 3 q^{49} - q^{61} - q^{63} + 4 q^{64} - q^{68} - q^{71} - 2 q^{77} - q^{79} + 4 q^{81} - q^{97} - q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(3307))\)

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 available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
3307.1.b \(\chi_{3307}(3306, \cdot)\) 3307.1.b.a 1 1
3307.1.b.b 3
3307.1.d \(\chi_{3307}(58, \cdot)\) None 0 2
3307.1.g \(\chi_{3307}(12, \cdot)\) None 0 18
3307.1.i \(\chi_{3307}(470, \cdot)\) None 0 28
3307.1.k \(\chi_{3307}(88, \cdot)\) None 0 36
3307.1.l \(\chi_{3307}(72, \cdot)\) None 0 56
3307.1.n \(\chi_{3307}(8, \cdot)\) None 0 504
3307.1.p \(\chi_{3307}(2, \cdot)\) None 0 1008