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Properties

Label 828.3.t
Level $828$
Weight $3$
Character orbit 828.t
Rep. character $\chi_{828}(55,\cdot)$
Character field $\Q(\zeta_{22})$
Dimension $1180$
Sturm bound $432$

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Defining parameters

Level: \( N \) \(=\) \( 828 = 2^{2} \cdot 3^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 828.t (of order \(22\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 92 \)
Character field: \(\Q(\zeta_{22})\)
Sturm bound: \(432\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(828, [\chi])\).

Total New Old
Modular forms 2960 1220 1740
Cusp forms 2800 1180 1620
Eisenstein series 160 40 120

Trace form

\( 1180 q + 7 q^{2} - 19 q^{4} + 18 q^{5} + 28 q^{8} + O(q^{10}) \) \( 1180 q + 7 q^{2} - 19 q^{4} + 18 q^{5} + 28 q^{8} + 19 q^{10} - 18 q^{13} + 31 q^{14} + 21 q^{16} + 18 q^{17} - 13 q^{20} - 26 q^{22} - 568 q^{25} - 32 q^{26} - 101 q^{28} - 62 q^{29} - 33 q^{32} + 269 q^{34} + 78 q^{37} - 358 q^{38} + 43 q^{40} + 34 q^{41} + 4 q^{44} - 3 q^{46} + 676 q^{49} + 280 q^{50} - 732 q^{52} - 286 q^{53} + 414 q^{56} - 187 q^{58} + 46 q^{61} - 44 q^{62} - 70 q^{64} + 94 q^{65} + 22 q^{68} - 250 q^{70} - 18 q^{73} + 292 q^{74} + 798 q^{76} - 938 q^{77} + 950 q^{80} + 1078 q^{82} - 214 q^{85} + 615 q^{86} - 215 q^{88} + 74 q^{89} + 104 q^{92} - 697 q^{94} + 198 q^{97} - 781 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(828, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{3}^{\mathrm{old}}(828, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(828, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(92, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(276, [\chi])\)\(^{\oplus 2}\)