Properties

Label 32.2.a
Level 32
Weight 2
Character orbit a
Rep. character \(\chi_{32}(1,\cdot)\)
Character field \(\Q\)
Dimension 1
Newforms 1
Sturm bound 8
Trace bound 0

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Defining parameters

Level: \( N \) = \( 32 = 2^{5} \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 32.a (trivial)
Character field: \(\Q\)
Newforms: \( 1 \)
Sturm bound: \(8\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(32))\).

Total New Old
Modular forms 8 1 7
Cusp forms 1 1 0
Eisenstein series 7 0 7

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

\(2\)Dim.
\(-\)\(1\)

Trace form

\(q \) \(\mathstrut -\mathstrut 2q^{5} \) \(\mathstrut -\mathstrut 3q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(q \) \(\mathstrut -\mathstrut 2q^{5} \) \(\mathstrut -\mathstrut 3q^{9} \) \(\mathstrut +\mathstrut 6q^{13} \) \(\mathstrut +\mathstrut 2q^{17} \) \(\mathstrut -\mathstrut q^{25} \) \(\mathstrut -\mathstrut 10q^{29} \) \(\mathstrut -\mathstrut 2q^{37} \) \(\mathstrut +\mathstrut 10q^{41} \) \(\mathstrut +\mathstrut 6q^{45} \) \(\mathstrut -\mathstrut 7q^{49} \) \(\mathstrut +\mathstrut 14q^{53} \) \(\mathstrut -\mathstrut 10q^{61} \) \(\mathstrut -\mathstrut 12q^{65} \) \(\mathstrut -\mathstrut 6q^{73} \) \(\mathstrut +\mathstrut 9q^{81} \) \(\mathstrut -\mathstrut 4q^{85} \) \(\mathstrut +\mathstrut 10q^{89} \) \(\mathstrut +\mathstrut 18q^{97} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(32))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2
32.2.a.a \(1\) \(0.256\) \(\Q\) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(-2\) \(0\) \(-\) \(q-2q^{5}-3q^{9}+6q^{13}+2q^{17}-q^{25}+\cdots\)