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Properties

Label 1656.2.bb
Level $1656$
Weight $2$
Character orbit 1656.bb
Rep. character $\chi_{1656}(277,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $528$
Sturm bound $576$

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Defining parameters

Level: \( N \) \(=\) \( 1656 = 2^{3} \cdot 3^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1656.bb (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 72 \)
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 584 528 56
Cusp forms 568 528 40
Eisenstein series 16 0 16

Trace form

\( 528 q - 3 q^{6} + 6 q^{8} + O(q^{10}) \) \( 528 q - 3 q^{6} + 6 q^{8} + 16 q^{12} - 10 q^{14} - 35 q^{18} + 14 q^{20} + 12 q^{23} + 18 q^{24} + 264 q^{25} - 44 q^{26} - 66 q^{30} - 40 q^{32} + 16 q^{33} - 7 q^{36} - 28 q^{38} - 12 q^{39} - 8 q^{41} + 2 q^{42} - 108 q^{44} - 40 q^{47} - 36 q^{48} - 264 q^{49} + 40 q^{50} - 9 q^{52} + 60 q^{54} - 28 q^{56} + 8 q^{57} + 9 q^{58} + 28 q^{60} + 142 q^{62} - 80 q^{63} - 18 q^{64} + 120 q^{66} - 10 q^{68} - 112 q^{71} + 12 q^{72} + 42 q^{74} - 41 q^{78} + 164 q^{80} - 8 q^{81} - 18 q^{82} + 138 q^{84} - 16 q^{86} - 80 q^{87} - 24 q^{88} - 56 q^{90} + 15 q^{94} - 64 q^{95} + 87 q^{96} - 108 q^{98} + O(q^{100}) \)

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.

Decomposition of \(S_{2}^{\mathrm{old}}(1656, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1656, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 2}\)