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Properties

Label 1620.3.bq
Level $1620$
Weight $3$
Character orbit 1620.bq
Rep. character $\chi_{1620}(41,\cdot)$
Character field $\Q(\zeta_{54})$
Dimension $1296$
Sturm bound $972$

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Defining parameters

Level: \( N \) \(=\) \( 1620 = 2^{2} \cdot 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1620.bq (of order \(54\) and degree \(18\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 81 \)
Character field: \(\Q(\zeta_{54})\)
Sturm bound: \(972\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(1620, [\chi])\).

Total New Old
Modular forms 11772 1296 10476
Cusp forms 11556 1296 10260
Eisenstein series 216 0 216

Trace form

\( 1296 q + O(q^{10}) \) \( 1296 q + 162 q^{23} - 54 q^{27} - 162 q^{29} - 378 q^{33} - 216 q^{41} - 648 q^{47} - 36 q^{51} + 432 q^{57} + 108 q^{59} + 1080 q^{63} - 540 q^{65} - 504 q^{69} - 1296 q^{71} + 54 q^{79} + 144 q^{81} + 432 q^{83} - 270 q^{85} - 324 q^{89} + 1872 q^{93} + 1080 q^{95} - 180 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(1620, [\chi])\) into newform subspaces

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

Decomposition of \(S_{3}^{\mathrm{old}}(1620, [\chi])\) into lower level spaces

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