Properties

Label 1350.2.h
Level 1350
Weight 2
Character orbit h
Rep. character \(\chi_{1350}(271,\cdot)\)
Character field \(\Q(\zeta_{5})\)
Dimension 160
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.h (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 25 \)
Character field: \(\Q(\zeta_{5})\)
Sturm bound: \(540\)

Dimensions

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

Total New Old
Modular forms 1128 160 968
Cusp forms 1032 160 872
Eisenstein series 96 0 96

Trace form

\( 160q - 40q^{4} - 4q^{7} + O(q^{10}) \) \( 160q - 40q^{4} - 4q^{7} + 6q^{10} + 8q^{13} - 40q^{16} + 12q^{19} + 8q^{22} + 18q^{25} + 6q^{28} + 6q^{31} - 24q^{34} - 32q^{37} + 6q^{40} + 56q^{43} + 12q^{46} + 220q^{49} + 8q^{52} + 30q^{55} + 48q^{58} + 40q^{61} - 40q^{64} - 46q^{70} + 124q^{73} - 8q^{76} + 56q^{79} + 80q^{82} - 160q^{85} - 2q^{88} + 20q^{91} - 16q^{94} - 18q^{97} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1350, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(150, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(225, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(450, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(675, [\chi])\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database