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Properties

Label 1620.2.bg
Level $1620$
Weight $2$
Character orbit 1620.bg
Rep. character $\chi_{1620}(61,\cdot)$
Character field $\Q(\zeta_{27})$
Dimension $648$
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.bg (of order \(27\) and degree \(18\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 81 \)
Character field: \(\Q(\zeta_{27})\)
Sturm bound: \(648\)

Dimensions

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

Total New Old
Modular forms 5940 648 5292
Cusp forms 5724 648 5076
Eisenstein series 216 0 216

Trace form

\( 648 q + O(q^{10}) \) \( 648 q - 54 q^{23} - 54 q^{27} - 54 q^{29} - 54 q^{33} + 18 q^{41} + 108 q^{47} + 18 q^{51} + 108 q^{53} + 108 q^{57} + 18 q^{59} + 108 q^{63} + 36 q^{65} + 90 q^{69} + 144 q^{71} - 54 q^{79} + 144 q^{81} + 144 q^{83} - 54 q^{85} + 18 q^{89} + 144 q^{93} + 72 q^{95} + 144 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1620, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(81, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(162, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(324, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(405, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(810, [\chi])\)\(^{\oplus 2}\)