Properties

Label 32.2.a
Level $32$
Weight $2$
Character orbit 32.a
Rep. character $\chi_{32}(1,\cdot)$
Character field $\Q$
Dimension $1$
Newform subspaces $1$
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: \(\Q\)
Newform subspaces: \( 1 \)
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

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

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(32))\) into newform subspaces

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