Properties

Label 4013.2
Level 4013
Weight 2
Dimension 669002
Nonzero newspaces 8
Sturm bound 2684028

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Defining parameters

Level: \( N \) = \( 4013 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 8 \)
Sturm bound: \(2684028\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(4013))\).

Total New Old
Modular forms 673013 673013 0
Cusp forms 669002 669002 0
Eisenstein series 4011 4011 0

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(4013))\)

We only show spaces with even 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
4013.2.a \(\chi_{4013}(1, \cdot)\) 4013.2.a.a 1 1
4013.2.a.b 157
4013.2.a.c 176
4013.2.b \(\chi_{4013}(4012, \cdot)\) n/a 334 1
4013.2.d \(\chi_{4013}(53, \cdot)\) n/a 5328 16
4013.2.e \(\chi_{4013}(10, \cdot)\) n/a 5344 16
4013.2.f \(\chi_{4013}(40, \cdot)\) n/a 19314 58
4013.2.h \(\chi_{4013}(114, \cdot)\) n/a 19372 58
4013.2.j \(\chi_{4013}(7, \cdot)\) n/a 309024 928
4013.2.k \(\chi_{4013}(4, \cdot)\) n/a 309952 928

"n/a" means that newforms for that character have not been added to the database yet