Properties

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

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

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