Properties

Label 588.6.y
Level $588$
Weight $6$
Character orbit 588.y
Rep. character $\chi_{588}(25,\cdot)$
Character field $\Q(\zeta_{21})$
Dimension $564$
Sturm bound $672$

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Defining parameters

Level: \( N \) \(=\) \( 588 = 2^{2} \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 588.y (of order \(21\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 49 \)
Character field: \(\Q(\zeta_{21})\)
Sturm bound: \(672\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(588, [\chi])\).

Total New Old
Modular forms 6792 564 6228
Cusp forms 6648 564 6084
Eisenstein series 144 0 144

Trace form

\( 564 q - 9 q^{3} - 22 q^{5} - 29 q^{7} + 3807 q^{9} + 1284 q^{11} + 314 q^{13} - 990 q^{15} - 2994 q^{17} + 6891 q^{19} - 180 q^{21} - 1276 q^{23} + 29085 q^{25} + 1458 q^{27} + 11088 q^{29} - 4705 q^{31}+ \cdots - 28836 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{6}^{\mathrm{new}}(588, [\chi])\) into newform subspaces

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

Decomposition of \(S_{6}^{\mathrm{old}}(588, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(588, [\chi]) \simeq \) \(S_{6}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(98, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(196, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(294, [\chi])\)\(^{\oplus 2}\)