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Properties

Label 825.4.k
Level $825$
Weight $4$
Character orbit 825.k
Rep. character $\chi_{825}(518,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $360$
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.k (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 15 \)
Character field: \(\Q(i)\)
Sturm bound: \(480\)

Dimensions

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

Total New Old
Modular forms 744 360 384
Cusp forms 696 360 336
Eisenstein series 48 0 48

Trace form

\( 360 q - 4 q^{3} - 32 q^{6} + O(q^{10}) \) \( 360 q - 4 q^{3} - 32 q^{6} + 64 q^{12} + 48 q^{13} - 4848 q^{16} - 444 q^{18} - 1504 q^{21} + 1112 q^{27} + 864 q^{28} + 912 q^{31} - 176 q^{33} - 1344 q^{36} - 1728 q^{37} + 808 q^{42} + 2400 q^{46} - 3848 q^{48} + 64 q^{51} - 456 q^{52} + 1040 q^{57} + 1176 q^{58} + 4800 q^{61} + 2648 q^{63} + 216 q^{67} - 456 q^{72} - 3600 q^{73} - 16896 q^{76} - 5240 q^{78} - 6448 q^{81} + 1944 q^{82} - 2032 q^{87} + 792 q^{88} + 2448 q^{91} + 4436 q^{93} + 10352 q^{96} + 5568 q^{97} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(825, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(165, [\chi])\)\(^{\oplus 2}\)