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Properties

Label 656.6.l
Level $656$
Weight $6$
Character orbit 656.l
Rep. character $\chi_{656}(337,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $208$
Sturm bound $504$

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Defining parameters

Level: \( N \) \(=\) \( 656 = 2^{4} \cdot 41 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 656.l (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 41 \)
Character field: \(\Q(i)\)
Sturm bound: \(504\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(656, [\chi])\).

Total New Old
Modular forms 852 212 640
Cusp forms 828 208 620
Eisenstein series 24 4 20

Trace form

\( 208 q + 2 q^{3} + 2 q^{7} + O(q^{10}) \) \( 208 q + 2 q^{3} + 2 q^{7} + 2 q^{11} - 124 q^{13} - 484 q^{15} - 1208 q^{17} + 2 q^{19} + 6352 q^{23} - 128120 q^{25} + 3248 q^{27} + 12240 q^{29} + 11536 q^{31} - 8636 q^{35} - 4 q^{37} - 8404 q^{41} - 18284 q^{45} + 35138 q^{47} + 62428 q^{51} + 20120 q^{53} + 33392 q^{55} - 30812 q^{57} + 94816 q^{59} - 77334 q^{63} + 7500 q^{65} + 58070 q^{67} - 21328 q^{69} + 2 q^{71} + 66058 q^{75} - 85810 q^{79} - 1328188 q^{81} + 248008 q^{83} + 90012 q^{85} + 62564 q^{89} + 182272 q^{93} - 544808 q^{95} + 76088 q^{97} - 302578 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(656, [\chi])\) into newform subspaces

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

Decomposition of \(S_{6}^{\mathrm{old}}(656, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(656, [\chi]) \simeq \) \(S_{6}^{\mathrm{new}}(41, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(82, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(164, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(328, [\chi])\)\(^{\oplus 2}\)