Properties

Label 1350.2.u
Level 1350
Weight 2
Character orbit u
Rep. character \(\chi_{1350}(49,\cdot)\)
Character field \(\Q(\zeta_{18})\)
Dimension 324
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.u (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 135 \)
Character field: \(\Q(\zeta_{18})\)
Sturm bound: \(540\)

Dimensions

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

Total New Old
Modular forms 1692 324 1368
Cusp forms 1548 324 1224
Eisenstein series 144 0 144

Trace form

\( 324q + 12q^{6} - 24q^{9} + O(q^{10}) \) \( 324q + 12q^{6} - 24q^{9} + 24q^{11} - 12q^{14} + 72q^{21} + 72q^{26} - 12q^{29} - 36q^{31} + 36q^{36} + 36q^{39} + 24q^{41} + 12q^{44} - 36q^{49} + 84q^{51} + 36q^{54} + 12q^{56} - 24q^{59} + 36q^{61} + 162q^{64} + 120q^{69} + 96q^{74} + 144q^{79} + 48q^{81} - 18q^{86} + 12q^{89} + 72q^{94} + 12q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1350, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(135, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(270, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(675, [\chi])\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database