Properties

Label 784.4.p
Level $784$
Weight $4$
Character orbit 784.p
Rep. character $\chi_{784}(31,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $120$
Sturm bound $448$

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Defining parameters

Level: \( N \) \(=\) \( 784 = 2^{4} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 784.p (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 28 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(448\)

Dimensions

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

Total New Old
Modular forms 720 120 600
Cusp forms 624 120 504
Eisenstein series 96 0 96

Trace form

\( 120q - 540q^{9} + O(q^{10}) \) \( 120q - 540q^{9} + 1248q^{25} + 168q^{29} + 108q^{33} + 252q^{37} - 1980q^{45} + 588q^{53} + 5256q^{57} + 900q^{61} - 1812q^{65} + 324q^{73} - 6696q^{81} - 8952q^{85} - 1908q^{89} + 1980q^{93} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(784, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(196, [\chi])\)\(^{\oplus 3}\)