Properties

Label 784.4.b
Level $784$
Weight $4$
Character orbit 784.b
Rep. character $\chi_{784}(393,\cdot)$
Character field $\Q$
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.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 8 \)
Character field: \(\Q\)
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 352 0 352
Cusp forms 320 0 320
Eisenstein series 32 0 32

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

\( S_{4}^{\mathrm{old}}(784, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(8, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(392, [\chi])\)\(^{\oplus 2}\)