Properties

Level $15$
Weight $0$
Character 15.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 15 = 3 \cdot 5 \)
Weight: \( 0 \)
Character: 15.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 5.11720516411 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.695002194\) \(a_{3}=+0.577350269\) \(a_{4}=+1.873032438\) \(a_{5}=-0.447213595\)
\(a_{6}=+0.978609973\) \(a_{7}=+1.591967918\) \(a_{8}=+1.479791898\) \(a_{9}=+0.333333333\) \(a_{10}=-0.758028026\)
\(a_{11}=-1.196060758\) \(a_{12}=+1.081395782\) \(a_{13}=-0.818304640\) \(a_{14}=+2.698389113\) \(a_{15}=-0.258198890\)
\(a_{16}=+0.635218075\) \(a_{17}=-0.684128371\) \(a_{18}=+0.565000731\) \(a_{19}=+0.042129641\) \(a_{20}=-0.837645571\)
\(a_{21}=+0.919123106\) \(a_{22}=-2.027325609\) \(a_{23}=-0.625995667\) \(a_{24}=+0.854358250\) \(a_{25}=+0.199951172\)
\(a_{26}=-1.387028160\) \(a_{27}=+0.192450090\) \(a_{28}=+2.981807550\) \(a_{29}=+0.919193912\) \(a_{30}=-0.437647685\)
\(a_{31}=+0.234692901\) \(a_{32}=-0.403095866\) \(a_{33}=-0.690546001\) \(a_{34}=-1.159599089\) \(a_{35}=-0.711949696\)
\(a_{36}=+0.624344146\) \(a_{37}=+0.106590278\) \(a_{38}=+0.071409834\) \(a_{39}=-0.472448404\) \(a_{40}=-0.661783056\)
\(a_{41}=+1.801741361\) \(a_{42}=+1.557915682\) \(a_{43}=+0.807721556\) \(a_{44}=-2.240260600\) \(a_{45}=-0.149071198\)
\(a_{46}=-1.061064030\) \(a_{47}=-1.418016845\) \(a_{48}=+0.366743327\) \(a_{49}=+1.534361851\) \(a_{50}=+0.339000439\)
\(a_{51}=-0.394981699\) \(a_{52}=-1.532711134\) \(a_{53}=+0.322102689\) \(a_{54}=+0.326203324\) \(a_{55}=+0.534894632\)
\(a_{56}=+2.355781226\) \(a_{57}=+0.024323559\) \(a_{58}=+1.558035697\) \(a_{59}=-1.298323326\) \(a_{60}=-0.483614896\)
\(a_{61}=-0.701835152\) \(a_{62}=+0.397804982\) \(a_{63}=+0.530655972\) \(a_{64}=-1.318466453\) \(a_{65}=+0.365956960\)
\(a_{66}=-1.170476987\) \(a_{67}=+0.966792277\) \(a_{68}=-1.281394630\) \(a_{69}=-0.361418767\) \(a_{70}=-1.206756296\)
\(a_{71}=+0.357201303\) \(a_{72}=+0.493263972\) \(a_{73}=+1.026646626\) \(a_{74}=+0.180670747\) \(a_{75}=+0.115470069\)
\(a_{76}=+0.078910185\) \(a_{77}=-1.904090375\) \(a_{78}=-0.800801058\) \(a_{79}=+0.297208241\) \(a_{80}=-0.284078185\)
\(a_{81}=+0.111111152\) \(a_{82}=+3.053955511\) \(a_{83}=-0.017925567\) \(a_{84}=+1.721547410\) \(a_{85}=+0.305951382\)
\(a_{86}=+1.369089938\) \(a_{87}=+0.530696853\) \(a_{88}=-1.769921019\) \(a_{89}=+1.220711649\) \(a_{90}=-0.252676008\)
\(a_{91}=-1.302714733\) \(a_{92}=-1.172510192\) \(a_{93}=+0.135500010\) \(a_{94}=-2.403541662\) \(a_{95}=-0.018840947\)
\(a_{96}=-0.232727509\) \(a_{97}=-1.303773251\) \(a_{98}=+2.600746709\) \(a_{99}=-0.398686924\) \(a_{100}=+0.374606486\)

Showing 100 of 1500 available coefficients

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