Properties

Label 3600.3.fc
Level $3600$
Weight $3$
Character orbit 3600.fc
Rep. character $\chi_{3600}(391,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $0$
Newform subspaces $0$
Sturm bound $2160$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 3600 = 2^{4} \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 3600.fc (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1800 \)
Character field: \(\Q(\zeta_{30})\)
Newform subspaces: \( 0 \)
Sturm bound: \(2160\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(3600, [\chi])\).

Total New Old
Modular forms 11584 0 11584
Cusp forms 11456 0 11456
Eisenstein series 128 0 128

Decomposition of \(S_{3}^{\mathrm{old}}(3600, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(3600, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(1800, [\chi])\)\(^{\oplus 2}\)