Properties

Level $26$
Weight $0$
Character 26.1
Symmetry even
Fricke sign $+1$

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The Maass form of level 26 with the smallest eigenvalue. This Maass form is even, and for all smaller levels the Maass form with the smallest eigenvalue is odd. The prevalence of odd Maass forms among those with smallest eigenvalue can be explained by the location of the trivial zeros of the associated L-function and the effect of those zeros on the explicit formula.

Level 26 is also the smallest squarefree level where the smallest newform eigenvalue is larger than the smallest oldform eigenvalue.

Maass form invariants

Level: \( 26 = 2 \cdot 13 \)
Weight: \( 0 \)
Character: 26.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 1.37694606445 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=-1.265244528\) \(a_{4}=+0.500000000\) \(a_{5}=+1.498439086\)
\(a_{6}=+0.894662985\) \(a_{7}=-0.581915820\) \(a_{8}=-0.353553391\) \(a_{9}=+0.600843715\) \(a_{10}=-1.059556439\)
\(a_{11}=+1.137716411\) \(a_{12}=-0.632622264\) \(a_{13}=-0.277350098\) \(a_{14}=+0.411476622\) \(a_{15}=-1.895891854\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.388171150\) \(a_{18}=-0.424860665\) \(a_{19}=-0.167549667\) \(a_{20}=+0.749219543\)
\(a_{21}=+0.736265807\) \(a_{22}=-0.804486989\) \(a_{23}=+0.052350121\) \(a_{24}=+0.447331493\) \(a_{25}=+1.245319695\)
\(a_{26}=+0.196116135\) \(a_{27}=+0.505030306\) \(a_{28}=-0.290957910\) \(a_{29}=-0.715419308\) \(a_{30}=+1.340597985\)
\(a_{31}=-0.661817901\) \(a_{32}=-0.176776695\) \(a_{33}=-1.439489463\) \(a_{34}=-0.274478451\) \(a_{35}=-0.871965409\)
\(a_{36}=+0.300421854\) \(a_{37}=+0.992792569\) \(a_{38}=+0.118475507\) \(a_{39}=+0.350915698\) \(a_{40}=-0.529778216\)
\(a_{41}=-0.317925691\) \(a_{42}=-0.520618546\) \(a_{43}=-0.861710305\) \(a_{44}=+0.568858222\) \(a_{45}=+0.900327711\)
\(a_{46}=-0.037017144\) \(a_{47}=+1.730035807\) \(a_{48}=-0.316311093\) \(a_{49}=-0.661373942\) \(a_{50}=-0.880573963\)
\(a_{51}=-0.491131397\) \(a_{52}=-0.138675054\) \(a_{53}=-1.390458127\) \(a_{54}=-0.357110311\) \(a_{55}=+1.704798692\)
\(a_{56}=+0.205738343\) \(a_{57}=+0.211991333\) \(a_{58}=+0.505877849\) \(a_{59}=+1.095254048\) \(a_{60}=-0.947945921\)
\(a_{61}=+1.580045726\) \(a_{62}=+0.467975929\) \(a_{63}=-0.349640465\) \(a_{64}=+0.124999990\) \(a_{65}=-0.415592204\)
\(a_{66}=+1.017872748\) \(a_{67}=+0.360113448\) \(a_{68}=+0.194085611\) \(a_{69}=-0.066235699\) \(a_{70}=+0.616572561\)
\(a_{71}=-0.786143568\) \(a_{72}=-0.212430314\) \(a_{73}=-1.336792672\) \(a_{74}=-0.702010367\) \(a_{75}=-1.575633940\)
\(a_{76}=-0.083774835\) \(a_{77}=-0.662055190\) \(a_{78}=-0.248134872\) \(a_{79}=-0.297921773\) \(a_{80}=+0.374609792\)
\(a_{81}=-1.239830569\) \(a_{82}=+0.224807393\) \(a_{83}=+0.555202769\) \(a_{84}=+0.368132845\) \(a_{85}=+0.581650830\)
\(a_{86}=+0.609321230\) \(a_{87}=+0.905180343\) \(a_{88}=-0.402243527\) \(a_{89}=+0.149090244\) \(a_{90}=-0.636627831\)
\(a_{91}=+0.161394381\) \(a_{92}=+0.026175054\) \(a_{93}=+0.837361563\) \(a_{94}=-1.223320121\) \(a_{95}=-0.251062998\)
\(a_{96}=+0.223665805\) \(a_{97}=-0.357723338\) \(a_{98}=+0.467662079\) \(a_{99}=+0.683589726\) \(a_{100}=+0.622659784\)

Showing 100 of 1500 available coefficients

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