Properties

Label 4008.2.t
Level 4008
Weight 2
Character orbit t
Rep. character \(\chi_{4008}(17,\cdot)\)
Character field \(\Q(\zeta_{166})\)
Dimension 13776
Sturm bound 1344

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Defining parameters

Level: \( N \) = \( 4008 = 2^{3} \cdot 3 \cdot 167 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4008.t (of order \(166\) and degree \(82\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 501 \)
Character field: \(\Q(\zeta_{166})\)
Sturm bound: \(1344\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(4008, [\chi])\).

Total New Old
Modular forms 55760 13776 41984
Cusp forms 54448 13776 40672
Eisenstein series 1312 0 1312

Decomposition of \(S_{2}^{\mathrm{new}}(4008, [\chi])\) into irreducible Hecke orbits

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

Decomposition of \(S_{2}^{\mathrm{old}}(4008, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(4008, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(501, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1002, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2004, [\chi])\)\(^{\oplus 2}\)