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Properties

Label 1080.6.k
Level $1080$
Weight $6$
Character orbit 1080.k
Rep. character $\chi_{1080}(541,\cdot)$
Character field $\Q$
Dimension $320$
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.k (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 8 \)
Character field: \(\Q\)
Sturm bound: \(1296\)

Dimensions

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

Total New Old
Modular forms 1092 320 772
Cusp forms 1068 320 748
Eisenstein series 24 0 24

Trace form

\( 320 q - 10 q^{4} + O(q^{10}) \) \( 320 q - 10 q^{4} - 50 q^{10} - 6078 q^{16} - 12284 q^{22} - 200000 q^{25} - 38084 q^{28} + 7160 q^{31} + 41082 q^{34} - 12400 q^{40} + 54762 q^{46} + 739056 q^{49} - 27508 q^{52} - 36432 q^{58} - 27568 q^{64} - 3300 q^{70} - 105136 q^{73} - 169466 q^{76} - 529528 q^{79} - 131516 q^{82} - 444308 q^{88} + 138504 q^{94} + 147376 q^{97} + O(q^{100}) \)

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

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