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Properties

Label 1620.2.bb
Level $1620$
Weight $2$
Character orbit 1620.bb
Rep. character $\chi_{1620}(179,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $624$
Sturm bound $648$

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Defining parameters

Level: \( N \) \(=\) \( 1620 = 2^{2} \cdot 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1620.bb (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 540 \)
Character field: \(\Q(\zeta_{18})\)
Sturm bound: \(648\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1620, [\chi])\).

Total New Old
Modular forms 2016 672 1344
Cusp forms 1872 624 1248
Eisenstein series 144 48 96

Trace form

\( 624 q - 12 q^{4} + 12 q^{5} + O(q^{10}) \) \( 624 q - 12 q^{4} + 12 q^{5} - 3 q^{10} + 12 q^{14} - 12 q^{16} - 15 q^{20} - 12 q^{25} + 12 q^{29} + 9 q^{40} + 24 q^{41} + 90 q^{44} - 6 q^{46} - 24 q^{49} + 84 q^{50} - 30 q^{56} - 24 q^{61} - 6 q^{64} - 12 q^{65} + 9 q^{70} + 66 q^{74} - 36 q^{76} + 18 q^{85} + 126 q^{86} + 36 q^{89} - 12 q^{94} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1620, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1620, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1620, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(540, [\chi])\)\(^{\oplus 2}\)