Properties

Label 784.4.bl
Level $784$
Weight $4$
Character orbit 784.bl
Rep. character $\chi_{784}(9,\cdot)$
Character field $\Q(\zeta_{42})$
Dimension $0$
Newform subspaces $0$
Sturm bound $448$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 784 = 2^{4} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 784.bl (of order \(42\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 392 \)
Character field: \(\Q(\zeta_{42})\)
Newform subspaces: \( 0 \)
Sturm bound: \(448\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(784, [\chi])\).

Total New Old
Modular forms 4080 0 4080
Cusp forms 3984 0 3984
Eisenstein series 96 0 96

Decomposition of \(S_{4}^{\mathrm{old}}(784, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(784, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(392, [\chi])\)\(^{\oplus 2}\)