Properties

Label 800.4.o
Level $800$
Weight $4$
Character orbit 800.o
Rep. character $\chi_{800}(143,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $104$
Sturm bound $480$

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Defining parameters

Level: \( N \) \(=\) \( 800 = 2^{5} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 800.o (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 40 \)
Character field: \(\Q(i)\)
Sturm bound: \(480\)

Dimensions

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

Total New Old
Modular forms 768 112 656
Cusp forms 672 104 568
Eisenstein series 96 8 88

Trace form

\( 104 q - 4 q^{3} + O(q^{10}) \) \( 104 q - 4 q^{3} + 8 q^{11} - 48 q^{17} + 104 q^{27} + 112 q^{33} - 8 q^{41} - 868 q^{43} + 2984 q^{51} - 104 q^{57} - 1852 q^{67} + 744 q^{73} - 3376 q^{81} + 2676 q^{83} - 3384 q^{91} + 584 q^{97} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(800, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(200, [\chi])\)\(^{\oplus 3}\)