Properties

Label 9.4.a
Level 9
Weight 4
Character orbit a
Rep. character \(\chi_{9}(1,\cdot)\)
Character field \(\Q\)
Dimension 1
Newforms 1
Sturm bound 4
Trace bound 0

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Defining parameters

Level: \( N \) = \( 9 = 3^{2} \)
Weight: \( k \) = \( 4 \)
Character orbit: \([\chi]\) = 9.a (trivial)
Character field: \(\Q\)
Newforms: \( 1 \)
Sturm bound: \(4\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(9))\).

Total New Old
Modular forms 5 2 3
Cusp forms 1 1 0
Eisenstein series 4 1 3

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

\(q \) \(\mathstrut -\mathstrut 8q^{4} \) \(\mathstrut +\mathstrut 20q^{7} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(q \) \(\mathstrut -\mathstrut 8q^{4} \) \(\mathstrut +\mathstrut 20q^{7} \) \(\mathstrut -\mathstrut 70q^{13} \) \(\mathstrut +\mathstrut 64q^{16} \) \(\mathstrut +\mathstrut 56q^{19} \) \(\mathstrut -\mathstrut 125q^{25} \) \(\mathstrut -\mathstrut 160q^{28} \) \(\mathstrut +\mathstrut 308q^{31} \) \(\mathstrut +\mathstrut 110q^{37} \) \(\mathstrut -\mathstrut 520q^{43} \) \(\mathstrut +\mathstrut 57q^{49} \) \(\mathstrut +\mathstrut 560q^{52} \) \(\mathstrut +\mathstrut 182q^{61} \) \(\mathstrut -\mathstrut 512q^{64} \) \(\mathstrut -\mathstrut 880q^{67} \) \(\mathstrut +\mathstrut 1190q^{73} \) \(\mathstrut -\mathstrut 448q^{76} \) \(\mathstrut +\mathstrut 884q^{79} \) \(\mathstrut -\mathstrut 1400q^{91} \) \(\mathstrut -\mathstrut 1330q^{97} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(9))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 3
9.4.a.a \(1\) \(0.531\) \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(20\) \(+\) \(q-8q^{4}+20q^{7}-70q^{13}+2^{6}q^{16}+\cdots\)