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Properties

Label 256.8.g
Level $256$
Weight $8$
Character orbit 256.g
Rep. character $\chi_{256}(33,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $216$
Sturm bound $256$

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Defining parameters

Level: \( N \) \(=\) \( 256 = 2^{8} \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 256.g (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 32 \)
Character field: \(\Q(\zeta_{8})\)
Sturm bound: \(256\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(256, [\chi])\).

Total New Old
Modular forms 928 232 696
Cusp forms 864 216 648
Eisenstein series 64 16 48

Trace form

\( 216 q + 8 q^{5} - 8 q^{9} + 8 q^{13} + 8 q^{21} - 8 q^{25} + 8 q^{29} - 16 q^{33} + 8 q^{37} - 8 q^{41} - 17488 q^{45} + 3631272 q^{53} - 8 q^{57} + 9119560 q^{61} - 16 q^{65} - 19161784 q^{69} - 8 q^{73}+ \cdots - 16 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{8}^{\mathrm{new}}(256, [\chi])\) into newform subspaces

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

Decomposition of \(S_{8}^{\mathrm{old}}(256, [\chi])\) into lower level spaces

\( S_{8}^{\mathrm{old}}(256, [\chi]) \simeq \) \(S_{8}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(128, [\chi])\)\(^{\oplus 2}\)