Properties

Label 8008.2.nn
Level $8008$
Weight $2$
Character orbit 8008.nn
Rep. character $\chi_{8008}(477,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $8064$
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.nn (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1144 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(2688\)

Dimensions

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

Total New Old
Modular forms 10816 8064 2752
Cusp forms 10688 8064 2624
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

\( S_{2}^{\mathrm{old}}(8008, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(1144, [\chi])\)\(^{\oplus 2}\)