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Properties

Label 825.4.cw
Level $825$
Weight $4$
Character orbit 825.cw
Rep. character $\chi_{825}(7,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $864$
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.cw (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 55 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(480\)

Dimensions

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

Total New Old
Modular forms 2976 864 2112
Cusp forms 2784 864 1920
Eisenstein series 192 0 192

Trace form

\( 864 q + 40 q^{7} + O(q^{10}) \) \( 864 q + 40 q^{7} + 112 q^{11} - 48 q^{12} + 3232 q^{16} + 640 q^{17} - 356 q^{22} + 224 q^{23} - 480 q^{26} - 720 q^{28} + 864 q^{31} + 228 q^{33} + 7776 q^{36} + 1104 q^{37} + 2072 q^{38} - 8880 q^{41} - 1224 q^{42} + 3000 q^{46} + 2280 q^{47} + 576 q^{48} + 3360 q^{51} + 8520 q^{52} + 1872 q^{53} + 28880 q^{56} + 1920 q^{57} - 2152 q^{58} + 960 q^{61} - 160 q^{62} - 360 q^{63} - 2256 q^{66} - 5504 q^{67} - 10240 q^{68} + 448 q^{71} + 7380 q^{73} - 3312 q^{77} + 288 q^{78} + 17496 q^{81} + 5616 q^{82} - 13400 q^{83} + 7760 q^{86} - 7188 q^{88} - 19856 q^{91} - 12340 q^{92} - 4104 q^{93} - 9744 q^{97} + O(q^{100}) \)

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

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