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Properties

Label 1620.3.c
Level $1620$
Weight $3$
Character orbit 1620.c
Rep. character $\chi_{1620}(811,\cdot)$
Character field $\Q$
Dimension $192$
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.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 4 \)
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 672 192 480
Cusp forms 624 192 432
Eisenstein series 48 0 48

Trace form

\( 192 q + O(q^{10}) \) \( 192 q + 24 q^{16} - 120 q^{22} + 960 q^{25} - 168 q^{28} + 12 q^{34} - 60 q^{40} + 180 q^{46} - 1344 q^{49} - 36 q^{52} - 132 q^{58} + 384 q^{64} - 48 q^{73} - 156 q^{76} - 396 q^{82} + 408 q^{88} + 468 q^{94} - 240 q^{97} + O(q^{100}) \)

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

\( S_{3}^{\mathrm{old}}(1620, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(108, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(324, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(540, [\chi])\)\(^{\oplus 2}\)