Properties

Label 784.4.bb
Level $784$
Weight $4$
Character orbit 784.bb
Rep. character $\chi_{784}(111,\cdot)$
Character field $\Q(\zeta_{14})$
Dimension $504$
Sturm bound $448$

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Defining parameters

Level: \( N \) \(=\) \( 784 = 2^{4} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 784.bb (of order \(14\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 196 \)
Character field: \(\Q(\zeta_{14})\)
Sturm bound: \(448\)

Dimensions

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

Total New Old
Modular forms 2052 504 1548
Cusp forms 1980 504 1476
Eisenstein series 72 0 72

Trace form

\( 504q - 756q^{9} + O(q^{10}) \) \( 504q - 756q^{9} - 144q^{21} + 1596q^{25} + 420q^{29} - 1260q^{37} + 948q^{49} + 1176q^{53} - 168q^{57} - 3780q^{61} - 840q^{65} - 10920q^{69} - 2136q^{77} - 2184q^{81} + 1176q^{85} - 1512q^{93} + O(q^{100}) \)

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

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