Properties

Label 2011.1
Level 2011
Weight 1
Dimension 3
Nonzero newspaces 1
Newforms 1
Sturm bound 337010
Trace bound 0

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Defining parameters

Level: \( N \) = \( 2011 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 1 \)
Newforms: \( 1 \)
Sturm bound: \(337010\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(2011))\).

Total New Old
Modular forms 1008 1008 0
Cusp forms 3 3 0
Eisenstein series 1005 1005 0

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

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

Trace form

\( 3q + 3q^{4} - q^{5} + 3q^{9} + O(q^{10}) \) \( 3q + 3q^{4} - q^{5} + 3q^{9} - q^{13} + 3q^{16} - q^{20} - q^{23} + 2q^{25} - q^{31} + 3q^{36} - q^{41} - q^{43} - q^{45} + 3q^{49} - q^{52} + 3q^{64} - 2q^{65} - q^{71} - q^{80} + 3q^{81} - q^{83} - q^{89} - q^{92} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(2011))\)

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
2011.1.b \(\chi_{2011}(2010, \cdot)\) 2011.1.b.a 3 1
2011.1.e \(\chi_{2011}(206, \cdot)\) None 0 2
2011.1.f \(\chi_{2011}(53, \cdot)\) None 0 4
2011.1.h \(\chi_{2011}(72, \cdot)\) None 0 8
2011.1.j \(\chi_{2011}(8, \cdot)\) None 0 66
2011.1.m \(\chi_{2011}(2, \cdot)\) None 0 132
2011.1.n \(\chi_{2011}(10, \cdot)\) None 0 264
2011.1.p \(\chi_{2011}(3, \cdot)\) None 0 528