Properties

Label 1350.2.w
Level 1350
Weight 2
Character orbit w
Rep. character \(\chi_{1350}(53,\cdot)\)
Character field \(\Q(\zeta_{20})\)
Dimension 320
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.w (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 75 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(540\)

Dimensions

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

Total New Old
Modular forms 2256 320 1936
Cusp forms 2064 320 1744
Eisenstein series 192 0 192

Trace form

\( 320q + 4q^{7} + O(q^{10}) \) \( 320q + 4q^{7} - 4q^{10} - 24q^{13} + 80q^{16} - 40q^{19} - 36q^{22} - 8q^{25} - 16q^{28} + 80q^{34} - 24q^{37} + 16q^{40} + 72q^{43} + 24q^{52} + 12q^{55} - 16q^{58} + 72q^{67} + 76q^{70} + 28q^{73} + 80q^{79} + 48q^{82} + 176q^{85} + 4q^{88} - 8q^{97} + O(q^{100}) \)

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

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

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database