Properties

Label 1296.4.bd
Level $1296$
Weight $4$
Character orbit 1296.bd
Rep. character $\chi_{1296}(71,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $0$
Newform subspaces $0$
Sturm bound $864$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 1296 = 2^{4} \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1296.bd (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 216 \)
Character field: \(\Q(\zeta_{18})\)
Newform subspaces: \( 0 \)
Sturm bound: \(864\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1296, [\chi])\).

Total New Old
Modular forms 3960 0 3960
Cusp forms 3816 0 3816
Eisenstein series 144 0 144

Decomposition of \(S_{4}^{\mathrm{old}}(1296, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1296, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(216, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(432, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(648, [\chi])\)\(^{\oplus 2}\)