Properties

Label 4200.2.gu
Level $4200$
Weight $2$
Character orbit 4200.gu
Rep. character $\chi_{4200}(397,\cdot)$
Character field $\Q(\zeta_{60})$
Dimension $7680$
Sturm bound $1920$

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Defining parameters

Level: \( N \) \(=\) \( 4200 = 2^{3} \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4200.gu (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1400 \)
Character field: \(\Q(\zeta_{60})\)
Sturm bound: \(1920\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(4200, [\chi])\).

Total New Old
Modular forms 15488 7680 7808
Cusp forms 15232 7680 7552
Eisenstein series 256 0 256

Decomposition of \(S_{2}^{\mathrm{new}}(4200, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(4200, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(4200, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(1400, [\chi])\)\(^{\oplus 2}\)