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Properties

Label 1764.2.bf
Level $1764$
Weight $2$
Character orbit 1764.bf
Rep. character $\chi_{1764}(19,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $192$
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.bf (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 28 \)
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 736 208 528
Cusp forms 608 192 416
Eisenstein series 128 16 112

Trace form

\( 192 q + q^{2} - q^{4} - 6 q^{5} + 10 q^{8} + O(q^{10}) \) \( 192 q + q^{2} - q^{4} - 6 q^{5} + 10 q^{8} - 6 q^{10} - 5 q^{16} - 6 q^{17} + 8 q^{22} + 86 q^{25} + 18 q^{26} - 8 q^{29} + 31 q^{32} + 22 q^{37} + 36 q^{38} + 48 q^{40} + 18 q^{44} + 20 q^{46} + 58 q^{50} + 36 q^{52} - 14 q^{53} - 10 q^{58} + 18 q^{61} + 50 q^{64} + 28 q^{65} - 36 q^{68} + 42 q^{73} - 78 q^{74} - 96 q^{80} - 24 q^{82} + 12 q^{85} - 48 q^{86} - 26 q^{88} + 54 q^{89} + 20 q^{92} - 78 q^{94} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1764, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(252, [\chi])\)\(^{\oplus 2}\)