Properties

Label 27.2.a
Level $27$
Weight $2$
Character orbit 27.a
Rep. character $\chi_{27}(1,\cdot)$
Character field $\Q$
Dimension $1$
Newform subspaces $1$
Sturm bound $6$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 27 = 3^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 27.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(6\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(27))\).

Total New Old
Modular forms 6 1 5
Cusp forms 1 1 0
Eisenstein series 5 0 5

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(3\)Dim.
\(-\)\(1\)

Trace form

\( q - 2 q^{4} - q^{7} + O(q^{10}) \) \( q - 2 q^{4} - q^{7} + 5 q^{13} + 4 q^{16} - 7 q^{19} - 5 q^{25} + 2 q^{28} - 4 q^{31} + 11 q^{37} + 8 q^{43} - 6 q^{49} - 10 q^{52} - q^{61} - 8 q^{64} + 5 q^{67} - 7 q^{73} + 14 q^{76} + 17 q^{79} - 5 q^{91} - 19 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(27))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 3
27.2.a.a 27.a 1.a $1$ $0.216$ \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(-1\) $-$ $N(\mathrm{U}(1))$ \(q-2q^{4}-q^{7}+5q^{13}+4q^{16}-7q^{19}+\cdots\)