Properties

Label 4730.2.by
Level 4730
Weight 2
Character orbit by
Rep. character \(\chi_{4730}(49,\cdot)\)
Character field \(\Q(\zeta_{30})\)
Dimension 2112
Sturm bound 1584

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Defining parameters

Level: \( N \) = \( 4730 = 2 \cdot 5 \cdot 11 \cdot 43 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4730.by (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 2365 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(1584\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(4730, [\chi])\).

Total New Old
Modular forms 6400 2112 4288
Cusp forms 6272 2112 4160
Eisenstein series 128 0 128

Decomposition of \(S_{2}^{\mathrm{new}}(4730, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(4730, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(4730, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(2365, [\chi])\)\(^{\oplus 2}\)