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Properties

Label 1764.3.u
Level $1764$
Weight $3$
Character orbit 1764.u
Rep. character $\chi_{1764}(655,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $944$
Sturm bound $1008$

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Defining parameters

Level: \( N \) \(=\) \( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1764.u (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 252 \)
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 976 400
Cusp forms 1312 944 368
Eisenstein series 64 32 32

Trace form

\( 944 q + 2 q^{2} + 2 q^{4} - 2 q^{5} - 16 q^{8} + 2 q^{9} + O(q^{10}) \) \( 944 q + 2 q^{2} + 2 q^{4} - 2 q^{5} - 16 q^{8} + 2 q^{9} + 10 q^{10} - 30 q^{12} + 4 q^{13} + 2 q^{16} + 4 q^{17} - 56 q^{18} + 34 q^{20} - 12 q^{22} + 62 q^{24} - 2202 q^{25} - 2 q^{26} - 32 q^{29} - 69 q^{30} - 58 q^{32} + 38 q^{33} - 2 q^{34} - 112 q^{36} + 4 q^{37} - 39 q^{38} - 26 q^{40} + 4 q^{41} + 99 q^{44} - 138 q^{45} + 18 q^{46} + 25 q^{48} + 339 q^{50} + 31 q^{52} + 4 q^{53} - 41 q^{54} - 12 q^{57} + 7 q^{58} + 183 q^{60} + 4 q^{61} + 396 q^{62} - 16 q^{64} - 4 q^{65} - 6 q^{66} + 106 q^{68} - 90 q^{69} + 436 q^{72} + 4 q^{73} - 185 q^{74} + 18 q^{76} + 141 q^{78} + 109 q^{80} - 238 q^{81} - 2 q^{82} - 58 q^{85} + 237 q^{86} + 63 q^{88} + 124 q^{89} - 485 q^{90} - 390 q^{92} + 66 q^{93} - 30 q^{94} + 365 q^{96} + 4 q^{97} + O(q^{100}) \)

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

\( S_{3}^{\mathrm{old}}(1764, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(252, [\chi])\)\(^{\oplus 2}\)