Properties

Label 6044.2
Level 6044
Weight 2
Dimension 664400
Nonzero newspaces 8
Sturm bound 4566240

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Defining parameters

Level: \( N \) = \( 6044\( 6044 = 2^{2} \cdot 1511 \) \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 8 \)
Sturm bound: \(4566240\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(6044))\).

Total New Old
Modular forms 1145335 667420 477915
Cusp forms 1137786 664400 473386
Eisenstein series 7549 3020 4529

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(6044))\)

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
6044.2.a \(\chi_{6044}(1, \cdot)\) 6044.2.a.a 63 1
6044.2.a.b 63
6044.2.c \(\chi_{6044}(6043, \cdot)\) n/a 754 1
6044.2.e \(\chi_{6044}(2045, \cdot)\) n/a 504 4
6044.2.f \(\chi_{6044}(423, \cdot)\) n/a 3016 4
6044.2.i \(\chi_{6044}(9, \cdot)\) n/a 18900 150
6044.2.k \(\chi_{6044}(55, \cdot)\) n/a 113100 150
6044.2.m \(\chi_{6044}(5, \cdot)\) n/a 75600 600
6044.2.p \(\chi_{6044}(11, \cdot)\) n/a 452400 600

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(6044))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(6044)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1511))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3022))\)\(^{\oplus 2}\)

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database