↑

Properties

Label 1764.3.v
Level $1764$
Weight $3$
Character orbit 1764.v
Rep. character $\chi_{1764}(295,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $964$
Sturm bound $1008$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1764.v (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 36 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(1008\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(1764, [\chi])\).

Total New Old
Modular forms 1376 1004 372
Cusp forms 1312 964 348
Eisenstein series 64 40 24

Trace form

\( 964 q + q^{2} + q^{4} + 2 q^{5} + 3 q^{6} - 38 q^{8} + 8 q^{9} + O(q^{10}) \) \( 964 q + q^{2} + q^{4} + 2 q^{5} + 3 q^{6} - 38 q^{8} + 8 q^{9} - 4 q^{10} - 24 q^{12} + 2 q^{13} + q^{16} - 16 q^{17} + 82 q^{18} - 10 q^{20} + 3 q^{22} - 43 q^{24} - 2208 q^{25} + 152 q^{26} + 14 q^{29} + 210 q^{30} - 119 q^{32} + 2 q^{33} - q^{34} - 145 q^{36} + 8 q^{37} - 99 q^{38} + 56 q^{40} + 62 q^{41} - 378 q^{44} - 150 q^{45} - 120 q^{46} + 49 q^{48} + 153 q^{50} - 40 q^{52} + 152 q^{53} - 11 q^{54} + 84 q^{57} + 38 q^{58} + 150 q^{60} + 2 q^{61} - 204 q^{62} - 14 q^{64} - 146 q^{65} + 180 q^{66} + 215 q^{68} - 186 q^{69} + 109 q^{72} + 32 q^{73} + 170 q^{74} + 63 q^{76} - 144 q^{78} - 712 q^{80} - 16 q^{81} + 194 q^{82} + 40 q^{85} - 21 q^{86} - 51 q^{88} + 104 q^{89} + 364 q^{90} - 318 q^{92} - 390 q^{93} + 66 q^{94} + 20 q^{96} - 58 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(1764, [\chi])\) into newform subspaces

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

Decomposition of \(S_{3}^{\mathrm{old}}(1764, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(1764, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 3}\)