Properties

Label 1350.2.r
Level 1350
Weight 2
Character orbit r
Rep. character \(\chi_{1350}(91,\cdot)\)
Character field \(\Q(\zeta_{15})\)
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.r (of order \(15\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 225 \)
Character field: \(\Q(\zeta_{15})\)
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

\( 240q + 30q^{4} - 8q^{5} + O(q^{10}) \) \( 240q + 30q^{4} - 8q^{5} - 4q^{11} - 8q^{14} + 30q^{16} - 24q^{17} + 2q^{20} + 24q^{25} - 96q^{26} - 12q^{29} - 12q^{31} - 8q^{35} + 24q^{37} + 12q^{38} - 16q^{41} + 8q^{44} - 26q^{47} - 120q^{49} + 12q^{50} + 72q^{53} - 8q^{56} + 12q^{58} - 18q^{59} + 36q^{62} - 60q^{64} + 104q^{65} + 18q^{67} - 48q^{68} - 24q^{70} - 4q^{71} + 80q^{74} - 32q^{77} + 12q^{79} - 4q^{80} - 48q^{82} + 104q^{83} + 12q^{85} - 20q^{86} + 188q^{89} - 8q^{95} + 12q^{97} - 48q^{98} + O(q^{100}) \)

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