Properties

Label 1.26.a.a
Level 1
Weight 26
Character orbit 1.a
Self dual Yes
Analytic conductor 3.960
Analytic rank 1
Dimension 1
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 1 \)
Weight: \( k \) = \( 26 \)
Character orbit: \([\chi]\) = 1.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(3.95996779952\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \(q \) \(\mathstrut -\mathstrut 48q^{2} \) \(\mathstrut -\mathstrut 195804q^{3} \) \(\mathstrut -\mathstrut 33552128q^{4} \) \(\mathstrut -\mathstrut 741989850q^{5} \) \(\mathstrut +\mathstrut 9398592q^{6} \) \(\mathstrut +\mathstrut 39080597192q^{7} \) \(\mathstrut +\mathstrut 3221114880q^{8} \) \(\mathstrut -\mathstrut 808949403027q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(q \) \(\mathstrut -\mathstrut 48q^{2} \) \(\mathstrut -\mathstrut 195804q^{3} \) \(\mathstrut -\mathstrut 33552128q^{4} \) \(\mathstrut -\mathstrut 741989850q^{5} \) \(\mathstrut +\mathstrut 9398592q^{6} \) \(\mathstrut +\mathstrut 39080597192q^{7} \) \(\mathstrut +\mathstrut 3221114880q^{8} \) \(\mathstrut -\mathstrut 808949403027q^{9} \) \(\mathstrut +\mathstrut 35615512800q^{10} \) \(\mathstrut +\mathstrut 8419515299052q^{11} \) \(\mathstrut +\mathstrut 6569640870912q^{12} \) \(\mathstrut -\mathstrut 81651045335314q^{13} \) \(\mathstrut -\mathstrut 1875868665216q^{14} \) \(\mathstrut +\mathstrut 145284580589400q^{15} \) \(\mathstrut +\mathstrut 1125667983917056q^{16} \) \(\mathstrut -\mathstrut 2519900028948078q^{17} \) \(\mathstrut +\mathstrut 38829571345296q^{18} \) \(\mathstrut -\mathstrut 6082056370308940q^{19} \) \(\mathstrut +\mathstrut 24895338421900800q^{20} \) \(\mathstrut -\mathstrut 7652137252582368q^{21} \) \(\mathstrut -\mathstrut 404136734354496q^{22} \) \(\mathstrut -\mathstrut 94995280296320424q^{23} \) \(\mathstrut -\mathstrut 630707177963520q^{24} \) \(\mathstrut +\mathstrut 252525713626069375q^{25} \) \(\mathstrut +\mathstrut 3919250176095072q^{26} \) \(\mathstrut +\mathstrut 324298027793675880q^{27} \) \(\mathstrut -\mathstrut 1311237199302424576q^{28} \) \(\mathstrut -\mathstrut 271246959476737410q^{29} \) \(\mathstrut -\mathstrut 6973659868291200q^{30} \) \(\mathstrut +\mathstrut 4291666067521509152q^{31} \) \(\mathstrut -\mathstrut 162114743433166848q^{32} \) \(\mathstrut -\mathstrut 1648574773615577808q^{33} \) \(\mathstrut +\mathstrut 120955201389507744q^{34} \) \(\mathstrut -\mathstrut 28997406448402501200q^{35} \) \(\mathstrut +\mathstrut 27141973915885491456q^{36} \) \(\mathstrut +\mathstrut 20301484446109126982q^{37} \) \(\mathstrut +\mathstrut 291938705774829120q^{38} \) \(\mathstrut +\mathstrut 15987601280835822456q^{39} \) \(\mathstrut -\mathstrut 2390034546643968000q^{40} \) \(\mathstrut -\mathstrut 183744249574071224598q^{41} \) \(\mathstrut +\mathstrut 367302588123953664q^{42} \) \(\mathstrut +\mathstrut 300901824185586335756q^{43} \) \(\mathstrut -\mathstrut 282492655011750982656q^{44} \) \(\mathstrut +\mathstrut 600232246209593275950q^{45} \) \(\mathstrut +\mathstrut 4559773454223380352q^{46} \) \(\mathstrut -\mathstrut 924361048064704868688q^{47} \) \(\mathstrut -\mathstrut 220410293922895233024q^{48} \) \(\mathstrut +\mathstrut 186224457219393384057q^{49} \) \(\mathstrut -\mathstrut 12121234254051330000q^{50} \) \(\mathstrut +\mathstrut 493406505268149464712q^{51} \) \(\mathstrut +\mathstrut 2739566324424258248192q^{52} \) \(\mathstrut -\mathstrut 990292205554990470954q^{53} \) \(\mathstrut -\mathstrut 15566305334096442240q^{54} \) \(\mathstrut -\mathstrut 6247194893816298622200q^{55} \) \(\mathstrut +\mathstrut 125883093134437416960q^{56} \) \(\mathstrut +\mathstrut 1190890965531971687760q^{57} \) \(\mathstrut +\mathstrut 13019854054883395680q^{58} \) \(\mathstrut +\mathstrut 13052569416454201837980q^{59} \) \(\mathstrut -\mathstrut 4874606844361864243200q^{60} \) \(\mathstrut +\mathstrut 9015451224701414617502q^{61} \) \(\mathstrut -\mathstrut 205999971241032439296q^{62} \) \(\mathstrut -\mathstrut 31614225768407052500184q^{63} \) \(\mathstrut -\mathstrut 37763368313237157183488q^{64} \) \(\mathstrut +\mathstrut 60584246880692834562900q^{65} \) \(\mathstrut +\mathstrut 79131589133547734784q^{66} \) \(\mathstrut -\mathstrut 26689067808908579702428q^{67} \) \(\mathstrut +\mathstrut 84548008318469618409984q^{68} \) \(\mathstrut +\mathstrut 18600455863140724300896q^{69} \) \(\mathstrut +\mathstrut 1391875509523320057600q^{70} \) \(\mathstrut -\mathstrut 192390516186217637440248q^{71} \) \(\mathstrut -\mathstrut 2605718959257386741760q^{72} \) \(\mathstrut +\mathstrut 42404584838092453858826q^{73} \) \(\mathstrut -\mathstrut 974471253413238095136q^{74} \) \(\mathstrut -\mathstrut 49445544830838887902500q^{75} \) \(\mathstrut +\mathstrut 204065933839820954424320q^{76} \) \(\mathstrut +\mathstrut 329039685954132631461984q^{77} \) \(\mathstrut -\mathstrut 767404861480119477888q^{78} \) \(\mathstrut -\mathstrut 271681055025772277197360q^{79} \) \(\mathstrut -\mathstrut 835234218536418793881600q^{80} \) \(\mathstrut +\mathstrut 621914763766378892976441q^{81} \) \(\mathstrut +\mathstrut 8819723979555418780704q^{82} \) \(\mathstrut -\mathstrut 931454457307013524361484q^{83} \) \(\mathstrut +\mathstrut 256745488572211941679104q^{84} \) \(\mathstrut +\mathstrut 1869740244494180053008300q^{85} \) \(\mathstrut -\mathstrut 14443287560908144116288q^{86} \) \(\mathstrut +\mathstrut 53111239653383091827640q^{87} \) \(\mathstrut +\mathstrut 27120226012164047093760q^{88} \) \(\mathstrut -\mathstrut 1763635518049807316502630q^{89} \) \(\mathstrut -\mathstrut 28811147818060477245600q^{90} \) \(\mathstrut -\mathstrut 3190971613055137006838288q^{91} \) \(\mathstrut +\mathstrut 3187293803898020795062272q^{92} \) \(\mathstrut -\mathstrut 840325382684981577998208q^{93} \) \(\mathstrut +\mathstrut 44369330307105833697024q^{94} \) \(\mathstrut +\mathstrut 4512824093897074844259000q^{95} \) \(\mathstrut +\mathstrut 31742715223187801505792q^{96} \) \(\mathstrut +\mathstrut 2829240869926872086187362q^{97} \) \(\mathstrut -\mathstrut 8938773946530882434736q^{98} \) \(\mathstrut -\mathstrut 6810961874944808779030404q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Embeddings

For each embedding \(\iota_m\) of the coefficient field, the values \(\iota_m(a_n)\) are shown below.

For more information on an embedded modular form you can click on its label.

Label \(\iota_m(\nu)\) \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1.1
0
−48.0000 −195804. −3.35521e7 −7.41990e8 9.39859e6 3.90806e10 3.22111e9 −8.08949e11 3.56155e10
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Inner twists

This newform does not admit any (nontrivial) inner twists.

Hecke kernels

There are no other newforms in \(S_{26}^{\mathrm{new}}(\Gamma_0(1))\).