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Properties

Label 1764.2.o
Level $1764$
Weight $2$
Character orbit 1764.o
Rep. character $\chi_{1764}(851,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $464$
Sturm bound $672$

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Defining parameters

Level: \( N \) \(=\) \( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1764.o (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 252 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(672\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1764, [\chi])\).

Total New Old
Modular forms 704 496 208
Cusp forms 640 464 176
Eisenstein series 64 32 32

Trace form

\( 464 q + 3 q^{2} - q^{4} + 6 q^{6} + 2 q^{9} + O(q^{10}) \) \( 464 q + 3 q^{2} - q^{4} + 6 q^{6} + 2 q^{9} - 2 q^{10} - 3 q^{12} + 4 q^{13} - q^{16} - 17 q^{18} + 6 q^{20} + 14 q^{24} - 396 q^{25} + 6 q^{26} - 12 q^{29} - 60 q^{30} - 57 q^{32} + 26 q^{33} + 4 q^{34} - 4 q^{36} + 4 q^{37} - 8 q^{40} + 12 q^{41} - 15 q^{44} - 42 q^{45} - 6 q^{46} + 43 q^{48} - 27 q^{50} - 14 q^{52} + 22 q^{54} + 12 q^{57} + 10 q^{58} + 18 q^{60} - 2 q^{61} - 16 q^{64} - 42 q^{65} + 93 q^{66} + 6 q^{69} - 77 q^{72} + 4 q^{73} + 6 q^{76} - 45 q^{78} - 87 q^{80} - 34 q^{81} + 4 q^{82} + 2 q^{85} + 18 q^{88} - 60 q^{89} - 41 q^{90} - 42 q^{92} - 6 q^{93} - 9 q^{94} + 20 q^{96} + 4 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1764, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1764, [\chi])\) into lower level spaces

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