Properties

Label 6048.2.do
Level 6048
Weight 2
Character orbit do
Rep. character \(\chi_{6048}(323,\cdot)\)
Character field \(\Q(\zeta_{8})\)
Dimension 1536
Sturm bound 2304

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Defining parameters

Level: \( N \) = \( 6048 = 2^{5} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6048.do (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 96 \)
Character field: \(\Q(\zeta_{8})\)
Sturm bound: \(2304\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(6048, [\chi])\).

Total New Old
Modular forms 4656 1536 3120
Cusp forms 4560 1536 3024
Eisenstein series 96 0 96

Decomposition of \(S_{2}^{\mathrm{new}}(6048, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(6048, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(6048, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(672, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(864, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2016, [\chi])\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database