Properties

Label 4008.2.q
Level 4008
Weight 2
Character orbit q
Rep. character \(\chi_{4008}(25,\cdot)\)
Character field \(\Q(\zeta_{83})\)
Dimension 6888
Sturm bound 1344

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 4008 = 2^{3} \cdot 3 \cdot 167 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4008.q (of order \(83\) and degree \(82\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 167 \)
Character field: \(\Q(\zeta_{83})\)
Sturm bound: \(1344\)

Dimensions

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

Total New Old
Modular forms 55760 6888 48872
Cusp forms 54448 6888 47560
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

\( S_{2}^{\mathrm{old}}(4008, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(167, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(334, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(501, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(668, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1002, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1336, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2004, [\chi])\)\(^{\oplus 2}\)