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Properties

Label 1764.4.bb
Level $1764$
Weight $4$
Character orbit 1764.bb
Rep. character $\chi_{1764}(263,\cdot)$
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.bb (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

\( 1424 q + 2 q^{4} + 6 q^{5} + 12 q^{6} + 2 q^{9} + O(q^{10}) \) \( 1424 q + 2 q^{4} + 6 q^{5} + 12 q^{6} + 2 q^{9} - 14 q^{10} - 162 q^{12} + 4 q^{13} + 2 q^{16} + 100 q^{18} + 6 q^{20} + 12 q^{22} + 278 q^{24} + 16998 q^{25} - 24 q^{26} + 60 q^{29} - 429 q^{30} - 106 q^{33} + 10 q^{34} + 536 q^{36} + 4 q^{37} - 819 q^{38} + 124 q^{40} + 12 q^{41} + 1923 q^{44} + 282 q^{45} - 30 q^{46} - 509 q^{48} - 387 q^{50} + 127 q^{52} + 2011 q^{54} - 756 q^{57} - 17 q^{58} - 2817 q^{60} + 4 q^{61} - 16 q^{64} - 564 q^{66} - 1968 q^{68} + 2118 q^{69} + 5896 q^{72} + 4 q^{73} + 5559 q^{74} + 66 q^{76} + 2847 q^{78} - 3297 q^{80} - 3382 q^{81} + 10 q^{82} + 242 q^{85} - 4179 q^{86} - 513 q^{88} - 3180 q^{89} - 1199 q^{90} - 4002 q^{92} + 378 q^{93} + 66 q^{94} + 2669 q^{96} + 4 q^{97} + O(q^{100}) \)

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

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