↑

Properties

Label 825.4.f
Level $825$
Weight $4$
Character orbit 825.f
Rep. character $\chi_{825}(626,\cdot)$
Character field $\Q$
Dimension $222$
Sturm bound $480$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 825.f (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 33 \)
Character field: \(\Q\)
Sturm bound: \(480\)

Dimensions

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

Total New Old
Modular forms 372 234 138
Cusp forms 348 222 126
Eisenstein series 24 12 12

Trace form

\( 222 q + 6 q^{3} + 868 q^{4} + 80 q^{9} + O(q^{10}) \) \( 222 q + 6 q^{3} + 868 q^{4} + 80 q^{9} + 128 q^{12} + 2972 q^{16} - 72 q^{22} + 168 q^{27} + 84 q^{31} + 16 q^{33} + 424 q^{34} + 116 q^{36} + 280 q^{37} - 2272 q^{42} + 660 q^{48} - 7790 q^{49} + 3048 q^{58} + 6884 q^{64} + 246 q^{66} - 836 q^{67} - 3754 q^{69} - 1168 q^{78} - 1056 q^{81} - 3312 q^{82} + 4800 q^{88} - 6952 q^{91} - 282 q^{93} + 4768 q^{97} + 540 q^{99} + O(q^{100}) \)

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

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