Properties

Label 800.4.bj
Level $800$
Weight $4$
Character orbit 800.bj
Rep. character $\chi_{800}(81,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $352$
Sturm bound $480$

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Defining parameters

Level: \( N \) \(=\) \( 800 = 2^{5} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 800.bj (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 200 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(480\)

Dimensions

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

Total New Old
Modular forms 1472 368 1104
Cusp forms 1408 352 1056
Eisenstein series 64 16 48

Trace form

\( 352 q + 16 q^{7} + 750 q^{9} + O(q^{10}) \) \( 352 q + 16 q^{7} + 750 q^{9} + 62 q^{15} + 46 q^{17} + 6 q^{23} + 14 q^{25} + 378 q^{31} - 114 q^{33} - 510 q^{39} + 230 q^{41} + 414 q^{47} + 14880 q^{49} + 114 q^{55} - 124 q^{57} + 2172 q^{63} + 1920 q^{65} - 1982 q^{71} + 734 q^{73} + 1586 q^{79} - 5946 q^{81} + 1402 q^{87} + 324 q^{89} + 806 q^{95} + 1318 q^{97} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(800, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(200, [\chi])\)\(^{\oplus 3}\)