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Properties

Label 1080.4.x
Level $1080$
Weight $4$
Character orbit 1080.x
Rep. character $\chi_{1080}(53,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $576$
Sturm bound $864$

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Defining parameters

Level: \( N \) \(=\) \( 1080 = 2^{3} \cdot 3^{3} \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1080.x (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 120 \)
Character field: \(\Q(i)\)
Sturm bound: \(864\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1080, [\chi])\).

Total New Old
Modular forms 1320 576 744
Cusp forms 1272 576 696
Eisenstein series 48 0 48

Trace form

\( 576 q + O(q^{10}) \) \( 576 q + 72 q^{10} + 132 q^{16} - 216 q^{22} - 432 q^{28} - 528 q^{31} - 132 q^{40} + 396 q^{46} + 876 q^{52} - 360 q^{58} + 7644 q^{70} + 4476 q^{76} + 3252 q^{82} - 6360 q^{88} - 1488 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(1080, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{4}^{\mathrm{old}}(1080, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1080, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(360, [\chi])\)\(^{\oplus 2}\)