Properties

Label 1620.3.p
Level $1620$
Weight $3$
Character orbit 1620.p
Rep. character $\chi_{1620}(379,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $568$
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.p (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 180 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(972\)

Dimensions

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

Total New Old
Modular forms 1344 584 760
Cusp forms 1248 568 680
Eisenstein series 96 16 80

Trace form

\( 568 q + 4 q^{4} + O(q^{10}) \) \( 568 q + 4 q^{4} + 12 q^{10} + 4 q^{16} + 4 q^{25} - 42 q^{34} - 48 q^{40} + 380 q^{46} - 1812 q^{49} + 8 q^{61} + 652 q^{64} + 158 q^{70} - 450 q^{76} - 96 q^{85} + 620 q^{94} + O(q^{100}) \)

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

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