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Properties

Label 825.4.bx
Level $825$
Weight $4$
Character orbit 825.bx
Rep. character $\chi_{825}(49,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $432$
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.bx (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 55 \)
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 432 1056
Cusp forms 1392 432 960
Eisenstein series 96 0 96

Trace form

\( 432 q + 432 q^{4} + 24 q^{6} + 972 q^{9} + O(q^{10}) \) \( 432 q + 432 q^{4} + 24 q^{6} + 972 q^{9} - 112 q^{11} + 256 q^{14} - 1624 q^{16} - 528 q^{19} - 672 q^{21} - 288 q^{24} + 916 q^{26} + 396 q^{31} + 3296 q^{34} - 3888 q^{36} - 576 q^{39} + 3048 q^{41} - 1380 q^{44} - 324 q^{46} + 6636 q^{49} + 1824 q^{51} + 864 q^{54} - 24 q^{56} + 408 q^{59} + 4296 q^{61} + 1016 q^{64} - 5136 q^{66} - 2064 q^{69} - 3360 q^{71} - 6096 q^{74} - 16920 q^{76} - 856 q^{79} - 8748 q^{81} - 1872 q^{84} + 2080 q^{86} - 2800 q^{89} + 640 q^{91} - 19020 q^{94} + 2688 q^{96} + 1008 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

\( S_{4}^{\mathrm{old}}(825, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(165, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(275, [\chi])\)\(^{\oplus 2}\)