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Properties

Label 1620.2.bd
Level $1620$
Weight $2$
Character orbit 1620.bd
Rep. character $\chi_{1620}(289,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $108$
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.bd (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 135 \)
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 2052 108 1944
Cusp forms 1836 108 1728
Eisenstein series 216 0 216

Trace form

\( 108 q + 3 q^{5} + O(q^{10}) \) \( 108 q + 3 q^{5} - 6 q^{11} + 9 q^{25} - 6 q^{29} - 18 q^{31} + 9 q^{35} - 24 q^{41} + 18 q^{49} + 66 q^{59} - 18 q^{61} + 69 q^{65} + 36 q^{79} + 42 q^{89} + 90 q^{95} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1620, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(135, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(270, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(405, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(540, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(810, [\chi])\)\(^{\oplus 2}\)