↑

Properties

Label 1620.4.bi
Level $1620$
Weight $4$
Character orbit 1620.bi
Rep. character $\chi_{1620}(127,\cdot)$
Character field $\Q(\zeta_{36})$
Dimension $3840$
Sturm bound $1296$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1620 = 2^{2} \cdot 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1620.bi (of order \(36\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 540 \)
Character field: \(\Q(\zeta_{36})\)
Sturm bound: \(1296\)

Dimensions

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

Total New Old
Modular forms 11808 3936 7872
Cusp forms 11520 3840 7680
Eisenstein series 288 96 192

Trace form

\( 3840 q + 12 q^{2} + 24 q^{5} + 6 q^{8} + O(q^{10}) \) \( 3840 q + 12 q^{2} + 24 q^{5} + 6 q^{8} - 6 q^{10} - 24 q^{13} - 24 q^{16} + 12 q^{17} + 12 q^{20} - 12 q^{22} - 24 q^{25} + 48 q^{26} - 24 q^{28} - 1368 q^{32} - 12 q^{37} - 36 q^{38} - 12 q^{40} + 48 q^{41} - 12 q^{46} + 12 q^{50} - 12 q^{52} + 48 q^{53} - 7872 q^{56} - 12 q^{58} - 48 q^{61} + 6 q^{62} - 1368 q^{65} + 396 q^{68} - 12 q^{70} - 12 q^{73} + 744 q^{76} + 24 q^{77} + 204 q^{80} - 24 q^{82} - 24 q^{85} - 8292 q^{86} - 3084 q^{88} - 9450 q^{92} - 24 q^{97} + 1944 q^{98} + O(q^{100}) \)

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

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