Properties

Level $4$
Weight $0$
Character 4.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 4 = 2^{2} \)
Weight: \( 0 \)
Character: 4.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 17.4053949776 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=-0.683900425\) \(a_{4}=+0.000000000\) \(a_{5}=-1.807168464\)
\(a_{6}=+0.000000000\) \(a_{7}=-0.978081301\) \(a_{8}=+0.000000000\) \(a_{9}=-0.532280209\) \(a_{10}=+0.000000000\)
\(a_{11}=-0.865227305\) \(a_{12}=+0.000000000\) \(a_{13}=-0.125815275\) \(a_{14}=+0.000000000\) \(a_{15}=+1.235923280\)
\(a_{16}=+0.000000000\) \(a_{17}=-1.036404625\) \(a_{18}=+0.000000000\) \(a_{19}=-1.109440130\) \(a_{20}=+0.000000000\)
\(a_{21}=+0.668910217\) \(a_{22}=+0.000000000\) \(a_{23}=-0.643773370\) \(a_{24}=+0.000000000\) \(a_{25}=+2.265857857\)
\(a_{26}=+0.000000000\) \(a_{27}=+1.047927086\) \(a_{28}=+0.000000000\) \(a_{29}=+1.320630000\) \(a_{30}=+0.000000000\)
\(a_{31}=+0.113899946\) \(a_{32}=+0.000000000\) \(a_{33}=+0.591729322\) \(a_{34}=+0.000000000\) \(a_{35}=+1.767557683\)
\(a_{36}=+0.000000000\) \(a_{37}=-1.000000000\) \(a_{38}=+0.000000000\) \(a_{39}=+0.086045120\) \(a_{40}=+0.000000000\)

Showing all 40 available coefficients

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