Properties

Label 784.4.bp
Level $784$
Weight $4$
Character orbit 784.bp
Rep. character $\chi_{784}(47,\cdot)$
Character field $\Q(\zeta_{42})$
Dimension $1008$
Sturm bound $448$

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Defining parameters

Level: \( N \) \(=\) \( 784 = 2^{4} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 784.bp (of order \(42\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 196 \)
Character field: \(\Q(\zeta_{42})\)
Sturm bound: \(448\)

Dimensions

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

Total New Old
Modular forms 4104 1008 3096
Cusp forms 3960 1008 2952
Eisenstein series 144 0 144

Trace form

\( 1008q + 756q^{9} + O(q^{10}) \) \( 1008q + 756q^{9} + 324q^{21} - 2352q^{25} - 420q^{29} + 108q^{33} + 2016q^{37} - 1980q^{45} - 480q^{49} + 588q^{53} + 168q^{57} + 4680q^{61} - 420q^{65} + 10920q^{69} + 324q^{73} - 816q^{77} - 588q^{81} - 1176q^{85} - 1908q^{89} - 756q^{93} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(784, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

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

\( S_{4}^{\mathrm{old}}(784, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(196, [\chi])\)\(^{\oplus 3}\)