Properties

Label 688.6.g
Level $688$
Weight $6$
Character orbit 688.g
Rep. character $\chi_{688}(687,\cdot)$
Character field $\Q$
Dimension $110$
Sturm bound $528$

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Defining parameters

Level: \( N \) \(=\) \( 688 = 2^{4} \cdot 43 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 688.g (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 172 \)
Character field: \(\Q\)
Sturm bound: \(528\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(688, [\chi])\).

Total New Old
Modular forms 446 110 336
Cusp forms 434 110 324
Eisenstein series 12 0 12

Trace form

\( 110 q + 9042 q^{9} + O(q^{10}) \) \( 110 q + 9042 q^{9} + 232 q^{13} + 3012 q^{17} + 9168 q^{21} - 68750 q^{25} + 17412 q^{41} + 278742 q^{49} + 131112 q^{57} + 587454 q^{81} - 269692 q^{97} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(688, [\chi])\) into newform subspaces

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

Decomposition of \(S_{6}^{\mathrm{old}}(688, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(688, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(172, [\chi])\)\(^{\oplus 3}\)