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Properties

Label 1620.2.bm
Level $1620$
Weight $2$
Character orbit 1620.bm
Rep. character $\chi_{1620}(59,\cdot)$
Character field $\Q(\zeta_{54})$
Dimension $5760$
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.bm (of order \(54\) and degree \(18\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1620 \)
Character field: \(\Q(\zeta_{54})\)
Sturm bound: \(648\)

Dimensions

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

Total New Old
Modular forms 5904 5904 0
Cusp forms 5760 5760 0
Eisenstein series 144 144 0

Trace form

\( 5760 q - 36 q^{4} - 36 q^{5} - 36 q^{6} - 72 q^{9} + O(q^{10}) \) \( 5760 q - 36 q^{4} - 36 q^{5} - 36 q^{6} - 72 q^{9} - 18 q^{10} - 36 q^{14} - 36 q^{16} - 18 q^{20} - 72 q^{21} - 36 q^{24} - 36 q^{25} - 54 q^{26} - 72 q^{29} - 18 q^{30} - 36 q^{34} - 36 q^{36} - 18 q^{40} - 72 q^{41} + 36 q^{44} - 36 q^{45} - 36 q^{46} - 72 q^{49} + 99 q^{50} + 90 q^{54} - 162 q^{56} + 99 q^{60} - 72 q^{61} - 36 q^{64} - 36 q^{65} - 108 q^{66} - 72 q^{69} - 18 q^{70} - 36 q^{74} - 36 q^{76} - 72 q^{81} + 18 q^{84} - 36 q^{85} - 36 q^{86} - 72 q^{89} - 81 q^{90} - 36 q^{94} - 36 q^{96} + O(q^{100}) \)

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.