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: \( 18.5182349935 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=-0.639592890\) \(a_{4}=+0.000000000\) \(a_{5}=+0.745687636\)
\(a_{6}=+0.000000000\) \(a_{7}=+1.153062773\) \(a_{8}=+0.000000000\) \(a_{9}=-0.590920935\) \(a_{10}=+0.000000000\)
\(a_{11}=-0.323496757\) \(a_{12}=+0.000000000\) \(a_{13}=-0.663253756\) \(a_{14}=+0.000000000\) \(a_{15}=-0.476936510\)
\(a_{16}=+0.000000000\) \(a_{17}=+1.663115240\) \(a_{18}=+0.000000000\) \(a_{19}=-0.923326167\) \(a_{20}=+0.000000000\)
\(a_{21}=-0.737490750\) \(a_{22}=+0.000000000\) \(a_{23}=-0.318520077\) \(a_{24}=+0.000000000\) \(a_{25}=-0.443949933\)
\(a_{26}=+0.000000000\) \(a_{27}=+1.017541747\) \(a_{28}=+0.000000000\) \(a_{29}=+1.652128496\) \(a_{30}=+0.000000000\)
\(a_{31}=+1.422576246\) \(a_{32}=+0.000000000\) \(a_{33}=+0.207019062\) \(a_{34}=+0.000000000\) \(a_{35}=+0.861432663\)
\(a_{36}=+0.000000000\)

Showing all 36 available coefficients

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