Properties

Label 27.2.a
Level 27
Weight 2
Character orbit a
Rep. character \(\chi_{27}(1,\cdot)\)
Character field \(\Q\)
Dimension 1
Newforms 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: \(\Q\)
Newforms: \( 1 \)
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

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

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(27))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 3
27.2.a.a \(1\) \(0.216\) \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(-1\) \(-\) \(q-2q^{4}-q^{7}+5q^{13}+4q^{16}-7q^{19}+\cdots\)