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Properties

Label 1620.3.w
Level $1620$
Weight $3$
Character orbit 1620.w
Rep. character $\chi_{1620}(107,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $1136$
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.w (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 180 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(972\)

Dimensions

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

Total New Old
Modular forms 2688 1168 1520
Cusp forms 2496 1136 1360
Eisenstein series 192 32 160

Trace form

\( 1136 q + O(q^{10}) \) \( 1136 q - 8 q^{10} + 8 q^{13} + 8 q^{16} + 20 q^{22} + 8 q^{25} - 136 q^{28} - 16 q^{37} + 4 q^{40} - 856 q^{46} - 60 q^{52} + 20 q^{58} + 16 q^{61} + 104 q^{70} - 16 q^{73} - 644 q^{76} + 24 q^{82} + 8 q^{85} + 140 q^{88} + 8 q^{97} + O(q^{100}) \)

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

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