Properties

Label 216.2.c
Level $216$
Weight $2$
Character orbit 216.c
Rep. character $\chi_{216}(215,\cdot)$
Character field $\Q$
Dimension $0$
Newform subspaces $0$
Sturm bound $72$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 216 = 2^{3} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 216.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 12 \)
Character field: \(\Q\)
Newform subspaces: \( 0 \)
Sturm bound: \(72\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(216, [\chi])\).

Total New Old
Modular forms 48 0 48
Cusp forms 24 0 24
Eisenstein series 24 0 24

Decomposition of \(S_{2}^{\mathrm{old}}(216, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(216, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(108, [\chi])\)\(^{\oplus 2}\)

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database