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Properties

Label 1764.4.o
Level $1764$
Weight $4$
Character orbit 1764.o
Rep. character $\chi_{1764}(851,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $1424$
Sturm bound $1344$

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Defining parameters

Level: \( N \) \(=\) \( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1764.o (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 252 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(1344\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1764, [\chi])\).

Total New Old
Modular forms 2048 1456 592
Cusp forms 1984 1424 560
Eisenstein series 64 32 32

Trace form

\( 1424 q + 3 q^{2} - q^{4} + 12 q^{6} + 2 q^{9} + O(q^{10}) \) \( 1424 q + 3 q^{2} - q^{4} + 12 q^{6} + 2 q^{9} - 14 q^{10} + 165 q^{12} + 4 q^{13} - q^{16} - 101 q^{18} + 6 q^{20} + 12 q^{22} + 278 q^{24} - 33996 q^{25} + 24 q^{26} + 60 q^{29} + 912 q^{30} + 1383 q^{32} + 218 q^{33} + 10 q^{34} + 536 q^{36} + 4 q^{37} - 248 q^{40} + 12 q^{41} - 1923 q^{44} - 1218 q^{45} - 30 q^{46} - 509 q^{48} - 387 q^{50} - 254 q^{52} - 68 q^{54} - 756 q^{57} + 34 q^{58} + 426 q^{60} - 2 q^{61} - 16 q^{64} + 1398 q^{65} + 435 q^{66} + 2118 q^{69} - 1541 q^{72} + 4 q^{73} + 66 q^{76} + 2847 q^{78} + 3297 q^{80} + 1238 q^{81} + 10 q^{82} + 242 q^{85} + 1026 q^{88} + 3180 q^{89} - 1199 q^{90} - 4002 q^{92} - 102 q^{93} - 33 q^{94} - 5404 q^{96} + 4 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(1764, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(1764, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1764, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(252, [\chi])\)\(^{\oplus 2}\)