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: \( 15.8093206166 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=+1.223116943\) \(a_{4}=+0.000000000\) \(a_{5}=-1.629182079\)
\(a_{6}=+0.000000000\) \(a_{7}=+1.329049994\) \(a_{8}=+0.000000000\) \(a_{9}=+0.496015057\) \(a_{10}=+0.000000000\)
\(a_{11}=+0.713337837\) \(a_{12}=+0.000000000\) \(a_{13}=+0.354696737\) \(a_{14}=+0.000000000\) \(a_{15}=-1.992680204\)
\(a_{16}=+0.000000000\) \(a_{17}=+0.937888769\) \(a_{18}=+0.000000000\) \(a_{19}=+0.090922718\) \(a_{20}=+0.000000000\)
\(a_{21}=+1.625583566\) \(a_{22}=+0.000000000\) \(a_{23}=+1.176455280\) \(a_{24}=+0.000000000\) \(a_{25}=+1.654234246\)
\(a_{26}=+0.000000000\) \(a_{27}=-0.616432523\) \(a_{28}=+0.000000000\) \(a_{29}=+0.876299858\) \(a_{30}=+0.000000000\)
\(a_{31}=+0.591003418\) \(a_{32}=+0.000000000\) \(a_{33}=+0.872495595\) \(a_{34}=+0.000000000\) \(a_{35}=-2.165264432\)
\(a_{36}=+0.000000000\)

Showing all 36 available coefficients

Rows: Cols: