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Properties

Label 1620.4.k
Level $1620$
Weight $4$
Character orbit 1620.k
Rep. character $\chi_{1620}(163,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $848$
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.k (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 20 \)
Character field: \(\Q(i)\)
Sturm bound: \(1296\)

Dimensions

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

Total New Old
Modular forms 1992 880 1112
Cusp forms 1896 848 1048
Eisenstein series 96 32 64

Trace form

\( 848 q + O(q^{10}) \) \( 848 q - 8 q^{10} + 8 q^{13} + 8 q^{16} + 68 q^{22} + 8 q^{25} + 248 q^{28} + 776 q^{37} + 4 q^{40} + 56 q^{46} + 516 q^{52} + 68 q^{58} + 16 q^{61} - 3964 q^{70} - 16 q^{73} - 1712 q^{76} - 2352 q^{82} + 2672 q^{85} + 2132 q^{88} + 8 q^{97} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(1620, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(540, [\chi])\)\(^{\oplus 2}\)