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: \( 16.4782589777 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=-0.478492548\) \(a_{4}=+0.000000000\) \(a_{5}=+1.601057465\)
\(a_{6}=+0.000000000\) \(a_{7}=+0.229649089\) \(a_{8}=+0.000000000\) \(a_{9}=-0.771044882\) \(a_{10}=+0.000000000\)
\(a_{11}=-0.255835801\) \(a_{12}=+0.000000000\) \(a_{13}=+1.021450818\) \(a_{14}=+0.000000000\) \(a_{15}=-0.766094066\)
\(a_{16}=+0.000000000\) \(a_{17}=-1.368398755\) \(a_{18}=+0.000000000\) \(a_{19}=+0.994901989\) \(a_{20}=+0.000000000\)
\(a_{21}=-0.109885378\) \(a_{22}=+0.000000000\) \(a_{23}=+1.804525030\) \(a_{24}=+0.000000000\) \(a_{25}=+1.563385006\)
\(a_{26}=+0.000000000\) \(a_{27}=+0.847431778\) \(a_{28}=+0.000000000\) \(a_{29}=-0.252870000\) \(a_{30}=+0.000000000\)
\(a_{31}=+1.436996460\) \(a_{32}=+0.000000000\) \(a_{33}=+0.122415524\) \(a_{34}=+0.000000000\) \(a_{35}=+0.367681389\)
\(a_{36}=+0.000000000\)

Showing all 36 available coefficients

Rows: Cols: