Properties

Label 768.3.i
Level $768$
Weight $3$
Character orbit 768.i
Rep. character $\chi_{768}(65,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $128$
Sturm bound $384$

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Defining parameters

Level: \( N \) \(=\) \( 768 = 2^{8} \cdot 3 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 768.i (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 48 \)
Character field: \(\Q(i)\)
Sturm bound: \(384\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(768, [\chi])\).

Total New Old
Modular forms 560 128 432
Cusp forms 464 128 336
Eisenstein series 96 0 96

Trace form

\( 128 q + O(q^{10}) \) \( 128 q - 896 q^{49} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(768, [\chi])\) into newform subspaces

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

Decomposition of \(S_{3}^{\mathrm{old}}(768, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(768, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(384, [\chi])\)\(^{\oplus 2}\)