Properties

Label 1350.2.bi
Level 1350
Weight 2
Character orbit bi
Rep. character \(\chi_{1350}(23,\cdot)\)
Character field \(\Q(\zeta_{180})\)
Dimension 4320
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.bi (of order \(180\) and degree \(48\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 675 \)
Character field: \(\Q(\zeta_{180})\)
Sturm bound: \(540\)

Dimensions

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

Total New Old
Modular forms 13152 4320 8832
Cusp forms 12768 4320 8448
Eisenstein series 384 0 384

Trace form

\( 4320q + O(q^{10}) \) \( 4320q + 24q^{20} - 24q^{23} + 144q^{25} - 12q^{27} + 72q^{30} + 12q^{33} + 108q^{35} + 36q^{38} + 48q^{42} + 60q^{45} + 48q^{47} + 12q^{48} + 48q^{50} + 36q^{57} + 60q^{59} - 84q^{63} - 24q^{65} + 72q^{67} + 144q^{68} + 48q^{72} + 36q^{75} - 720q^{77} - 24q^{78} + 60q^{83} + 252q^{87} + 48q^{92} + 96q^{93} + 60q^{95} + 72q^{97} + O(q^{100}) \)

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