Properties

Label 1080.6.bt
Level $1080$
Weight $6$
Character orbit 1080.bt
Rep. character $\chi_{1080}(17,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $360$
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.bt (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 45 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(1296\)

Dimensions

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

Total New Old
Modular forms 4416 360 4056
Cusp forms 4224 360 3864
Eisenstein series 192 0 192

Trace form

\( 360 q + O(q^{10}) \) \( 360 q + 15816 q^{23} - 56460 q^{41} + 95076 q^{47} - 46740 q^{61} - 107928 q^{65} - 316752 q^{77} - 46740 q^{83} + 81624 q^{85} + 3660 q^{95} - 122856 q^{97} + O(q^{100}) \)

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

\( S_{6}^{\mathrm{old}}(1080, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(135, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(270, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(360, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(540, [\chi])\)\(^{\oplus 2}\)