Properties

Label 8008.2.ka
Level $8008$
Weight $2$
Character orbit 8008.ka
Rep. character $\chi_{8008}(89,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $1120$
Sturm bound $2688$

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Defining parameters

Level: \( N \) \(=\) \( 8008 = 2^{3} \cdot 7 \cdot 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8008.ka (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 91 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(2688\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(8008, [\chi])\).

Total New Old
Modular forms 5440 1120 4320
Cusp forms 5312 1120 4192
Eisenstein series 128 0 128

Decomposition of \(S_{2}^{\mathrm{new}}(8008, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(8008, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(8008, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(182, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(364, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(728, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1001, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2002, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(4004, [\chi])\)\(^{\oplus 2}\)