↑

Properties

Label 1620.3.bt
Level $1620$
Weight $3$
Character orbit 1620.bt
Rep. character $\chi_{1620}(23,\cdot)$
Character field $\Q(\zeta_{108})$
Dimension $23184$
Sturm bound $972$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1620 = 2^{2} \cdot 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1620.bt (of order \(108\) and degree \(36\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1620 \)
Character field: \(\Q(\zeta_{108})\)
Sturm bound: \(972\)

Dimensions

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

Total New Old
Modular forms 23472 23472 0
Cusp forms 23184 23184 0
Eisenstein series 288 288 0

Trace form

\( 23184 q - 36 q^{2} - 72 q^{5} - 72 q^{6} - 36 q^{8} + O(q^{10}) \) \( 23184 q - 36 q^{2} - 72 q^{5} - 72 q^{6} - 36 q^{8} - 36 q^{10} - 36 q^{12} - 72 q^{13} - 72 q^{16} - 72 q^{17} - 36 q^{18} - 36 q^{20} - 144 q^{21} - 36 q^{22} - 72 q^{25} - 108 q^{26} - 18 q^{28} - 36 q^{30} - 36 q^{32} - 72 q^{33} - 72 q^{36} - 72 q^{37} - 36 q^{38} - 36 q^{40} - 144 q^{41} - 36 q^{42} - 72 q^{45} - 72 q^{46} - 36 q^{48} - 36 q^{50} - 36 q^{52} - 108 q^{53} + 684 q^{56} - 72 q^{57} - 36 q^{58} - 36 q^{60} - 144 q^{61} - 36 q^{62} - 72 q^{65} + 1800 q^{66} - 36 q^{68} - 36 q^{70} - 36 q^{72} - 72 q^{73} - 72 q^{76} - 72 q^{77} + 126 q^{78} - 144 q^{81} - 72 q^{82} - 72 q^{85} - 72 q^{86} - 36 q^{88} - 36 q^{90} - 36 q^{92} - 3096 q^{93} - 72 q^{96} - 72 q^{97} + 3042 q^{98} + O(q^{100}) \)

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.