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Properties

Label 800.4.u
Level $800$
Weight $4$
Character orbit 800.u
Rep. character $\chi_{800}(161,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $360$
Sturm bound $480$

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Defining parameters

Level: \( N \) \(=\) \( 800 = 2^{5} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 800.u (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 25 \)
Character field: \(\Q(\zeta_{5})\)
Sturm bound: \(480\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(800, [\chi])\).

Total New Old
Modular forms 1472 360 1112
Cusp forms 1408 360 1048
Eisenstein series 64 0 64

Trace form

\( 360 q - 2 q^{5} - 810 q^{9} + O(q^{10}) \) \( 360 q - 2 q^{5} - 810 q^{9} + 92 q^{13} + 156 q^{17} - 234 q^{25} + 284 q^{29} + 48 q^{33} + 990 q^{37} - 708 q^{41} + 894 q^{45} + 18456 q^{49} - 42 q^{53} - 1696 q^{57} + 780 q^{61} - 2714 q^{65} - 1488 q^{69} + 2412 q^{73} + 3504 q^{77} - 8202 q^{81} - 4082 q^{85} + 198 q^{89} + 2352 q^{93} - 9420 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(800, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(800, [\chi])\) into lower level spaces

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