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: \( 19.3266065864 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=+0.796936989\) \(a_{4}=+0.000000000\) \(a_{5}=-0.837566137\)
\(a_{6}=+0.000000000\) \(a_{7}=-1.166815567\) \(a_{8}=+0.000000000\) \(a_{9}=-0.364891435\) \(a_{10}=+0.000000000\)
\(a_{11}=+0.981536178\) \(a_{12}=+0.000000000\) \(a_{13}=+1.016244093\) \(a_{14}=+0.000000000\) \(a_{15}=-0.667487436\)
\(a_{16}=+0.000000000\) \(a_{17}=+0.116812748\) \(a_{18}=+0.000000000\) \(a_{19}=+1.520568680\) \(a_{20}=+0.000000000\)
\(a_{21}=-0.929878486\) \(a_{22}=+0.000000000\) \(a_{23}=-0.593562867\) \(a_{24}=+0.000000000\) \(a_{25}=-0.298482936\)
\(a_{26}=+0.000000000\) \(a_{27}=-1.087732048\) \(a_{28}=+0.000000000\) \(a_{29}=+1.246303646\) \(a_{30}=+0.000000000\)
\(a_{31}=+1.650717142\) \(a_{32}=+0.000000000\) \(a_{33}=+0.782042659\) \(a_{34}=+0.000000000\) \(a_{35}=+0.975720869\)
\(a_{36}=+0.000000000\) \(a_{37}=+0.928738217\) \(a_{38}=+0.000000000\) \(a_{39}=+0.665789492\) \(a_{40}=+0.000000000\)

Showing all 40 available coefficients

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