Properties

Label 6930.2.gk
Level $6930$
Weight $2$
Character orbit 6930.gk
Rep. character $\chi_{6930}(499,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $4608$
Sturm bound $3456$

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Defining parameters

Level: \( N \) \(=\) \( 6930 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6930.gk (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3465 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(3456\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(6930, [\chi])\).

Total New Old
Modular forms 13952 4608 9344
Cusp forms 13696 4608 9088
Eisenstein series 256 0 256

Decomposition of \(S_{2}^{\mathrm{new}}(6930, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(6930, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(6930, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(3465, [\chi])\)\(^{\oplus 2}\)