Properties

Label 1350.2.z
Level 1350
Weight 2
Character orbit z
Rep. character \(\chi_{1350}(19,\cdot)\)
Character field \(\Q(\zeta_{30})\)
Dimension 240
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.z (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 225 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(540\)

Dimensions

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

Total New Old
Modular forms 2256 240 2016
Cusp forms 2064 240 1824
Eisenstein series 192 0 192

Trace form

\( 240q - 30q^{4} + 8q^{5} + O(q^{10}) \) \( 240q - 30q^{4} + 8q^{5} + 4q^{11} - 8q^{14} + 30q^{16} + 2q^{20} + 24q^{25} + 96q^{26} - 12q^{29} + 12q^{31} + 32q^{35} + 16q^{41} + 8q^{44} + 50q^{47} + 120q^{49} + 4q^{50} + 24q^{55} + 8q^{56} - 18q^{59} + 60q^{62} + 60q^{64} + 64q^{65} - 30q^{67} + 24q^{70} - 76q^{71} + 80q^{74} - 80q^{77} + 12q^{79} + 4q^{80} + 140q^{83} + 12q^{85} + 20q^{86} + 28q^{89} + 40q^{92} - 36q^{95} + O(q^{100}) \)

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