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Properties

Label 1620.4.e
Level $1620$
Weight $4$
Character orbit 1620.e
Rep. character $\chi_{1620}(971,\cdot)$
Character field $\Q$
Dimension $288$
Sturm bound $1296$

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Defining parameters

Level: \( N \) \(=\) \( 1620 = 2^{2} \cdot 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1620.e (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 12 \)
Character field: \(\Q\)
Sturm bound: \(1296\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1620, [\chi])\).

Total New Old
Modular forms 996 288 708
Cusp forms 948 288 660
Eisenstein series 48 0 48

Trace form

\( 288 q + O(q^{10}) \) \( 288 q + 360 q^{16} - 72 q^{22} - 7200 q^{25} + 504 q^{28} + 396 q^{34} + 180 q^{40} + 1836 q^{46} - 14112 q^{49} - 1836 q^{52} + 1476 q^{58} + 1224 q^{64} + 1656 q^{73} + 1116 q^{76} - 1404 q^{82} + 4824 q^{88} - 2700 q^{94} + 72 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(1620, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{4}^{\mathrm{old}}(1620, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1620, [\chi]) \cong \)