Properties

Label 825.4.bs
Level $825$
Weight $4$
Character orbit 825.bs
Rep. character $\chi_{825}(74,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $848$
Sturm bound $480$

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Defining parameters

Level: \( N \) \(=\) \( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 825.bs (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 165 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(480\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(825, [\chi])\).

Total New Old
Modular forms 1488 880 608
Cusp forms 1392 848 544
Eisenstein series 96 32 64

Trace form

\( 848 q + 844 q^{4} - 10 q^{6} - 122 q^{9} + O(q^{10}) \) \( 848 q + 844 q^{4} - 10 q^{6} - 122 q^{9} - 2932 q^{16} + 20 q^{19} - 70 q^{24} + 456 q^{31} - 320 q^{34} - 854 q^{36} - 1830 q^{39} - 580 q^{46} - 8504 q^{49} - 1050 q^{51} + 460 q^{61} + 13244 q^{64} + 6052 q^{66} + 1088 q^{69} - 4660 q^{79} - 1062 q^{81} - 6160 q^{84} + 892 q^{91} + 12500 q^{94} - 20100 q^{96} + 5864 q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(825, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(825, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(825, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(165, [\chi])\)\(^{\oplus 2}\)