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Properties

Label 1620.3.f
Level $1620$
Weight $3$
Character orbit 1620.f
Rep. character $\chi_{1620}(1459,\cdot)$
Character field $\Q$
Dimension $280$
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.f (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 20 \)
Character field: \(\Q\)
Sturm bound: \(972\)

Dimensions

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

Total New Old
Modular forms 672 296 376
Cusp forms 624 280 344
Eisenstein series 48 16 32

Trace form

\( 280 q + 4 q^{4} + O(q^{10}) \) \( 280 q + 4 q^{4} - 12 q^{10} + 4 q^{16} + 4 q^{25} - 48 q^{40} + 92 q^{46} + 1632 q^{49} - 232 q^{61} + 124 q^{64} + 44 q^{70} + 456 q^{76} - 264 q^{85} - 268 q^{94} + O(q^{100}) \)

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

\( S_{3}^{\mathrm{old}}(1620, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(540, [\chi])\)\(^{\oplus 2}\)