Properties

Label 4008.2.n
Level $4008$
Weight $2$
Character orbit 4008.n
Rep. character $\chi_{4008}(1001,\cdot)$
Character field $\Q$
Dimension $168$
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.n (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 501 \)
Character field: \(\Q\)
Sturm bound: \(1344\)

Dimensions

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

Total New Old
Modular forms 680 168 512
Cusp forms 664 168 496
Eisenstein series 16 0 16

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

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