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Properties

Label 1620.3.ba
Level $1620$
Weight $3$
Character orbit 1620.ba
Rep. character $\chi_{1620}(91,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $864$
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.ba (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 108 \)
Character field: \(\Q(\zeta_{18})\)
Sturm bound: \(972\)

Dimensions

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

Total New Old
Modular forms 3960 864 3096
Cusp forms 3816 864 2952
Eisenstein series 144 0 144

Trace form

\( 864 q + O(q^{10}) \) \( 864 q + 90 q^{14} - 324 q^{26} + 72 q^{29} + 180 q^{38} - 360 q^{41} - 216 q^{44} - 54 q^{52} + 252 q^{56} + 270 q^{58} + 594 q^{62} + 666 q^{68} + 252 q^{74} + 288 q^{77} + 162 q^{86} - 216 q^{89} + 1800 q^{92} + 702 q^{94} - 360 q^{97} + O(q^{100}) \)

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

\( S_{3}^{\mathrm{old}}(1620, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(108, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(324, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(540, [\chi])\)\(^{\oplus 2}\)