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Properties

Label 1080.2.cg
Level $1080$
Weight $2$
Character orbit 1080.cg
Rep. character $\chi_{1080}(49,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $324$
Sturm bound $432$

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Defining parameters

Level: \( N \) \(=\) \( 1080 = 2^{3} \cdot 3^{3} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1080.cg (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 135 \)
Character field: \(\Q(\zeta_{18})\)
Sturm bound: \(432\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1080, [\chi])\).

Total New Old
Modular forms 1344 324 1020
Cusp forms 1248 324 924
Eisenstein series 96 0 96

Trace form

\( 324 q + O(q^{10}) \) \( 324 q - 12 q^{15} + 18 q^{29} + 36 q^{39} - 12 q^{41} + 36 q^{45} - 18 q^{49} - 72 q^{51} + 72 q^{59} + 18 q^{61} + 12 q^{69} + 18 q^{75} + 96 q^{81} + 72 q^{89} - 78 q^{95} + 60 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1080, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1080, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1080, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(135, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(270, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(540, [\chi])\)\(^{\oplus 2}\)