Properties

Label 1350.2.bf
Level 1350
Weight 2
Character orbit bf
Rep. character \(\chi_{1350}(79,\cdot)\)
Character field \(\Q(\zeta_{90})\)
Dimension 2160
Sturm bound 540

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 1350 = 2 \cdot 3^{3} \cdot 5^{2} \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 1350.bf (of order \(90\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 675 \)
Character field: \(\Q(\zeta_{90})\)
Sturm bound: \(540\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1350, [\chi])\).

Total New Old
Modular forms 6576 2160 4416
Cusp forms 6384 2160 4224
Eisenstein series 192 0 192

Trace form

\( 2160q + 24q^{5} + O(q^{10}) \) \( 2160q + 24q^{5} + 42q^{15} - 12q^{20} + 72q^{21} - 72q^{25} - 288q^{26} - 36q^{30} - 36q^{31} - 18q^{35} + 24q^{36} + 60q^{39} + 12q^{44} - 114q^{45} + 150q^{47} + 30q^{48} + 12q^{50} + 36q^{54} - 18q^{59} - 18q^{60} - 270q^{64} + 6q^{65} - 180q^{67} - 12q^{75} + 480q^{77} + 36q^{81} + 150q^{87} + 132q^{89} - 30q^{90} - 120q^{92} + 18q^{95} + 60q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1350, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1350, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1350, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(675, [\chi])\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database