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Properties

Label 1080.6.w
Level $1080$
Weight $6$
Character orbit 1080.w
Rep. character $\chi_{1080}(163,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $960$
Sturm bound $1296$

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Defining parameters

Level: \( N \) \(=\) \( 1080 = 2^{3} \cdot 3^{3} \cdot 5 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 1080.w (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 40 \)
Character field: \(\Q(i)\)
Sturm bound: \(1296\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(1080, [\chi])\).

Total New Old
Modular forms 2184 960 1224
Cusp forms 2136 960 1176
Eisenstein series 48 0 48

Trace form

\( 960 q + O(q^{10}) \) \( 960 q - 568 q^{10} + 1220 q^{16} - 2792 q^{22} - 11216 q^{28} - 43388 q^{40} + 1312 q^{43} - 42420 q^{46} - 89988 q^{52} + 27800 q^{58} - 567716 q^{70} + 299740 q^{76} - 253756 q^{82} - 708200 q^{88} + 132176 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(1080, [\chi])\) into newform subspaces

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

Decomposition of \(S_{6}^{\mathrm{old}}(1080, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(1080, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 3}\)