Properties

Label 1350.2.bb
Level 1350
Weight 2
Character orbit bb
Rep. character \(\chi_{1350}(257,\cdot)\)
Character field \(\Q(\zeta_{36})\)
Dimension 648
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.bb (of order \(36\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 135 \)
Character field: \(\Q(\zeta_{36})\)
Sturm bound: \(540\)

Dimensions

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

Total New Old
Modular forms 3384 648 2736
Cusp forms 3096 648 2448
Eisenstein series 288 0 288

Trace form

\( 648q - 24q^{6} + O(q^{10}) \) \( 648q - 24q^{6} - 48q^{11} - 24q^{23} - 12q^{27} + 12q^{33} + 24q^{36} + 36q^{38} + 144q^{41} + 48q^{42} + 48q^{47} + 12q^{48} + 24q^{51} + 24q^{56} + 36q^{57} - 72q^{61} - 84q^{63} + 72q^{67} - 36q^{68} + 48q^{72} + 240q^{77} - 24q^{78} + 48q^{81} + 60q^{83} + 36q^{86} + 252q^{87} + 48q^{92} + 96q^{93} + 72q^{97} + O(q^{100}) \)

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

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

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database