Properties

Label 1350.2.bd
Level 1350
Weight 2
Character orbit bd
Rep. character \(\chi_{1350}(17,\cdot)\)
Character field \(\Q(\zeta_{60})\)
Dimension 480
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.bd (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 225 \)
Character field: \(\Q(\zeta_{60})\)
Sturm bound: \(540\)

Dimensions

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

Total New Old
Modular forms 4512 480 4032
Cusp forms 4128 480 3648
Eisenstein series 384 0 384

Trace form

\( 480q + O(q^{10}) \) \( 480q - 60q^{16} - 12q^{20} - 24q^{23} - 48q^{25} + 24q^{37} + 36q^{38} + 48q^{47} + 48q^{50} + 24q^{55} - 12q^{58} + 60q^{59} - 24q^{65} + 12q^{67} + 144q^{68} + 432q^{77} + 48q^{82} + 60q^{83} + 24q^{85} - 24q^{92} + 60q^{95} + 36q^{97} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1350, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(225, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(450, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(675, [\chi])\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database