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: \( 23.319948556 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=-0.633537535\) \(a_{4}=+0.000000000\) \(a_{5}=+0.307002051\)
\(a_{6}=+0.000000000\) \(a_{7}=-1.849222537\) \(a_{8}=+0.000000000\) \(a_{9}=-0.598630191\) \(a_{10}=+0.000000000\)
\(a_{11}=+0.447716182\) \(a_{12}=+0.000000000\) \(a_{13}=+0.204981493\) \(a_{14}=+0.000000000\) \(a_{15}=-0.194497323\)
\(a_{16}=+0.000000000\) \(a_{17}=-1.044328231\) \(a_{18}=+0.000000000\) \(a_{19}=-0.766593284\) \(a_{20}=+0.000000000\)
\(a_{21}=+1.171551889\) \(a_{22}=+0.000000000\) \(a_{23}=-0.937941779\) \(a_{24}=+0.000000000\) \(a_{25}=-0.905749741\)
\(a_{26}=+0.000000000\) \(a_{27}=+1.012792233\) \(a_{28}=+0.000000000\) \(a_{29}=-0.314758167\) \(a_{30}=+0.000000000\)
\(a_{31}=+1.317119230\) \(a_{32}=+0.000000000\) \(a_{33}=-0.283644298\) \(a_{34}=+0.000000000\) \(a_{35}=-0.567711986\)
\(a_{36}=+0.000000000\) \(a_{37}=-1.739168742\) \(a_{38}=+0.000000000\) \(a_{39}=-0.129724469\) \(a_{40}=+0.000000000\)
\(a_{41}=+0.267803143\) \(a_{42}=+0.000000000\) \(a_{43}=+0.871553580\) \(a_{44}=+0.000000000\)

Showing all 44 available coefficients

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