Properties

Label 2400.2.df
Level $2400$
Weight $2$
Character orbit 2400.df
Rep. character $\chi_{2400}(103,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $0$
Newform subspaces $0$
Sturm bound $960$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 2400 = 2^{5} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2400.df (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 400 \)
Character field: \(\Q(\zeta_{20})\)
Newform subspaces: \( 0 \)
Sturm bound: \(960\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2400, [\chi])\).

Total New Old
Modular forms 3904 0 3904
Cusp forms 3776 0 3776
Eisenstein series 128 0 128

Decomposition of \(S_{2}^{\mathrm{old}}(2400, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2400, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(400, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1200, [\chi])\)\(^{\oplus 2}\)