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Properties

Label 800.6.u
Level $800$
Weight $6$
Character orbit 800.u
Rep. character $\chi_{800}(161,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $600$
Sturm bound $720$

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Defining parameters

Level: \( N \) \(=\) \( 800 = 2^{5} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 800.u (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 25 \)
Character field: \(\Q(\zeta_{5})\)
Sturm bound: \(720\)

Dimensions

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

Total New Old
Modular forms 2432 600 1832
Cusp forms 2368 600 1768
Eisenstein series 64 0 64

Trace form

\( 600 q - 38 q^{5} - 12150 q^{9} + O(q^{10}) \) \( 600 q - 38 q^{5} - 12150 q^{9} + 244 q^{13} - 1212 q^{17} + 7402 q^{25} + 8564 q^{29} - 18864 q^{33} - 28230 q^{37} + 7428 q^{41} - 51414 q^{45} + 1403816 q^{49} + 17346 q^{53} + 82592 q^{57} - 91580 q^{61} + 32554 q^{65} + 285072 q^{69} + 28244 q^{73} - 241008 q^{77} - 612678 q^{81} + 348074 q^{85} - 158022 q^{89} + 378384 q^{93} + 353580 q^{97} + O(q^{100}) \)

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

\( S_{6}^{\mathrm{old}}(800, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(200, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(400, [\chi])\)\(^{\oplus 2}\)