Properties

Label 1620.4.y
Level $1620$
Weight $4$
Character orbit 1620.y
Rep. character $\chi_{1620}(703,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $1712$
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.y (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 180 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(1296\)

Dimensions

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

Total New Old
Modular forms 3984 1744 2240
Cusp forms 3792 1712 2080
Eisenstein series 192 32 160

Trace form

\( 1712 q + O(q^{10}) \) \( 1712 q - 8 q^{10} + 8 q^{13} + 8 q^{16} - 28 q^{22} + 8 q^{25} - 520 q^{28} - 16 q^{37} + 4 q^{40} + 344 q^{46} - 252 q^{52} - 28 q^{58} + 16 q^{61} - 496 q^{70} - 16 q^{73} + 6100 q^{76} - 72 q^{82} + 8 q^{85} - 12484 q^{88} + 8 q^{97} + O(q^{100}) \)

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

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