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: \( 22.2343087571 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=+1.639437434\) \(a_{4}=+0.000000000\) \(a_{5}=+1.072717597\)
\(a_{6}=+0.000000000\) \(a_{7}=-1.012445476\) \(a_{8}=+0.000000000\) \(a_{9}=+1.687755098\) \(a_{10}=+0.000000000\)
\(a_{11}=-0.944111335\) \(a_{12}=+0.000000000\) \(a_{13}=+1.176683317\) \(a_{14}=+0.000000000\) \(a_{15}=+1.758653384\)
\(a_{16}=+0.000000000\) \(a_{17}=+0.907933070\) \(a_{18}=+0.000000000\) \(a_{19}=+1.834590279\) \(a_{20}=+0.000000000\)
\(a_{21}=-1.659841013\) \(a_{22}=+0.000000000\) \(a_{23}=+0.552317255\) \(a_{24}=+0.000000000\) \(a_{25}=+0.150723036\)
\(a_{26}=+0.000000000\) \(a_{27}=+1.127531397\) \(a_{28}=+0.000000000\) \(a_{29}=-0.574762985\) \(a_{30}=+0.000000000\)
\(a_{31}=+0.247251693\) \(a_{32}=+0.000000000\) \(a_{33}=-1.547842918\) \(a_{34}=+0.000000000\) \(a_{35}=-1.086308600\)
\(a_{36}=+0.000000000\) \(a_{37}=+0.403537157\) \(a_{38}=+0.000000000\) \(a_{39}=+1.916538895\) \(a_{40}=+0.000000000\)
\(a_{41}=-1.099383683\) \(a_{42}=+0.000000000\) \(a_{43}=+1.254810647\)

Showing all 43 available coefficients

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