Properties

Label 1350.2.bc
Level 1350
Weight 2
Character orbit bc
Rep. character \(\chi_{1350}(31,\cdot)\)
Character field \(\Q(\zeta_{45})\)
Dimension 2160
Sturm bound 540

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Defining parameters

Level: \( N \) = \( 1350 = 2 \cdot 3^{3} \cdot 5^{2} \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 1350.bc (of order \(45\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 675 \)
Character field: \(\Q(\zeta_{45})\)
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

\( 2160q - 24q^{5} + O(q^{10}) \) \( 2160q - 24q^{5} - 42q^{15} - 12q^{20} - 72q^{21} + 24q^{23} - 72q^{25} + 288q^{26} + 12q^{27} - 36q^{30} + 36q^{31} + 12q^{33} - 18q^{35} - 24q^{36} + 36q^{38} + 60q^{39} + 48q^{42} + 12q^{44} + 174q^{45} - 78q^{47} - 18q^{48} + 36q^{50} + 120q^{53} + 36q^{54} + 36q^{57} - 18q^{59} + 18q^{60} + 84q^{63} + 270q^{64} + 18q^{65} + 108q^{67} - 144q^{68} - 48q^{72} + 48q^{75} + 336q^{77} + 24q^{78} - 36q^{81} + 60q^{83} - 282q^{87} + 12q^{89} + 30q^{90} + 72q^{92} + 48q^{93} + 42q^{95} - 72q^{97} + 60q^{99} + O(q^{100}) \)

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