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Properties

Label 825.4.bi
Level $825$
Weight $4$
Character orbit 825.bi
Rep. character $\chi_{825}(101,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $888$
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.bi (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 33 \)
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 936 552
Cusp forms 1392 888 504
Eisenstein series 96 48 48

Trace form

\( 888 q - q^{3} - 858 q^{4} + 35 q^{6} + 10 q^{7} + 5 q^{9} + O(q^{10}) \) \( 888 q - q^{3} - 858 q^{4} + 35 q^{6} + 10 q^{7} + 5 q^{9} + 42 q^{12} + 10 q^{13} - 3182 q^{16} + 235 q^{18} - 440 q^{19} - 548 q^{22} - 475 q^{24} - 133 q^{27} + 490 q^{28} - 504 q^{31} + 194 q^{33} + 196 q^{34} + 49 q^{36} - 150 q^{37} + 775 q^{39} - 1098 q^{42} - 470 q^{46} - 1600 q^{48} + 8760 q^{49} - 1260 q^{51} + 4270 q^{52} + 2370 q^{57} + 262 q^{58} + 1110 q^{61} + 3955 q^{63} - 12334 q^{64} + 2604 q^{66} - 4724 q^{67} + 1544 q^{69} - 5080 q^{72} - 3500 q^{73} - 6332 q^{78} + 1150 q^{79} + 1861 q^{81} - 608 q^{82} - 2180 q^{84} + 6430 q^{88} - 98 q^{91} + 37 q^{93} - 8930 q^{94} - 14910 q^{96} - 648 q^{97} - 4505 q^{99} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(825, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(33, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(165, [\chi])\)\(^{\oplus 2}\)