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Properties

Label 800.6.bj
Level $800$
Weight $6$
Character orbit 800.bj
Rep. character $\chi_{800}(81,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $592$
Sturm bound $720$

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Defining parameters

Level: \( N \) \(=\) \( 800 = 2^{5} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 800.bj (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 200 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(720\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(800, [\chi])\).

Total New Old
Modular forms 2432 608 1824
Cusp forms 2368 592 1776
Eisenstein series 64 16 48

Trace form

\( 592 q + 16 q^{7} + 11658 q^{9} + O(q^{10}) \) \( 592 q + 16 q^{7} + 11658 q^{9} + 494 q^{15} - 410 q^{17} + 6 q^{23} - 1566 q^{25} - 11526 q^{31} - 978 q^{33} + 25314 q^{39} - 2482 q^{41} - 65250 q^{47} + 1306128 q^{49} + 61282 q^{55} - 988 q^{57} + 101820 q^{63} - 153540 q^{65} + 141154 q^{71} + 25174 q^{73} - 124814 q^{79} - 867030 q^{81} + 283162 q^{87} - 263376 q^{89} + 396566 q^{95} - 278674 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(800, [\chi])\) into newform subspaces

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

Decomposition of \(S_{6}^{\mathrm{old}}(800, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(800, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(200, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(400, [\chi])\)\(^{\oplus 2}\)