↑

Properties

Label 1656.2.bf
Level $1656$
Weight $2$
Character orbit 1656.bf
Rep. character $\chi_{1656}(965,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $568$
Sturm bound $576$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1656 = 2^{3} \cdot 3^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1656.bf (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1656 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(576\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1656, [\chi])\).

Total New Old
Modular forms 584 584 0
Cusp forms 568 568 0
Eisenstein series 16 16 0

Trace form

\( 568 q - 6 q^{2} - 2 q^{4} + 3 q^{6} - 8 q^{9} + O(q^{10}) \) \( 568 q - 6 q^{2} - 2 q^{4} + 3 q^{6} - 8 q^{9} - 16 q^{12} - 2 q^{16} - 5 q^{18} - 6 q^{23} - 16 q^{24} + 264 q^{25} - 4 q^{31} - 6 q^{32} + 47 q^{36} - 32 q^{39} - 12 q^{41} - 20 q^{46} - 12 q^{47} - 50 q^{48} + 256 q^{49} - 114 q^{50} - 27 q^{52} + 26 q^{54} - 56 q^{55} + 15 q^{58} + 34 q^{64} - 12 q^{70} + 58 q^{72} - 16 q^{73} - 37 q^{78} - 24 q^{81} - 34 q^{82} + 28 q^{87} - 30 q^{92} - 19 q^{94} - 72 q^{95} + 61 q^{96} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1656, [\chi])\) into newform subspaces

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