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Properties

Label 768.4.o
Level $768$
Weight $4$
Character orbit 768.o
Rep. character $\chi_{768}(95,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $368$
Sturm bound $512$

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Defining parameters

Level: \( N \) \(=\) \( 768 = 2^{8} \cdot 3 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 768.o (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 96 \)
Character field: \(\Q(\zeta_{8})\)
Sturm bound: \(512\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(768, [\chi])\).

Total New Old
Modular forms 1600 400 1200
Cusp forms 1472 368 1104
Eisenstein series 128 32 96

Trace form

\( 368 q - 8 q^{9} + O(q^{10}) \) \( 368 q - 8 q^{9} + 16 q^{13} + 8 q^{21} - 16 q^{25} - 16 q^{33} + 16 q^{37} + 8 q^{45} - 8 q^{57} - 3632 q^{61} + 8 q^{69} - 16 q^{73} + 2016 q^{85} - 208 q^{93} - 32 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(768, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(768, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(768, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(384, [\chi])\)\(^{\oplus 2}\)