Properties

Label 2.14.a.b
Level 2
Weight 14
Character orbit 2.a
Self dual Yes
Analytic conductor 2.145
Analytic rank 0
Dimension 1
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 2 \)
Weight: \( k \) = \( 14 \)
Character orbit: \([\chi]\) = 2.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(2.14461857904\)
Analytic rank: \(0\)
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

\(f(q)\) \(=\) \(q \) \(\mathstrut +\mathstrut 64q^{2} \) \(\mathstrut +\mathstrut 1236q^{3} \) \(\mathstrut +\mathstrut 4096q^{4} \) \(\mathstrut -\mathstrut 57450q^{5} \) \(\mathstrut +\mathstrut 79104q^{6} \) \(\mathstrut +\mathstrut 64232q^{7} \) \(\mathstrut +\mathstrut 262144q^{8} \) \(\mathstrut -\mathstrut 66627q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(q \) \(\mathstrut +\mathstrut 64q^{2} \) \(\mathstrut +\mathstrut 1236q^{3} \) \(\mathstrut +\mathstrut 4096q^{4} \) \(\mathstrut -\mathstrut 57450q^{5} \) \(\mathstrut +\mathstrut 79104q^{6} \) \(\mathstrut +\mathstrut 64232q^{7} \) \(\mathstrut +\mathstrut 262144q^{8} \) \(\mathstrut -\mathstrut 66627q^{9} \) \(\mathstrut -\mathstrut 3676800q^{10} \) \(\mathstrut +\mathstrut 2464572q^{11} \) \(\mathstrut +\mathstrut 5062656q^{12} \) \(\mathstrut +\mathstrut 8032766q^{13} \) \(\mathstrut +\mathstrut 4110848q^{14} \) \(\mathstrut -\mathstrut 71008200q^{15} \) \(\mathstrut +\mathstrut 16777216q^{16} \) \(\mathstrut +\mathstrut 71112402q^{17} \) \(\mathstrut -\mathstrut 4264128q^{18} \) \(\mathstrut +\mathstrut 136337060q^{19} \) \(\mathstrut -\mathstrut 235315200q^{20} \) \(\mathstrut +\mathstrut 79390752q^{21} \) \(\mathstrut +\mathstrut 157732608q^{22} \) \(\mathstrut -\mathstrut 1186563144q^{23} \) \(\mathstrut +\mathstrut 324009984q^{24} \) \(\mathstrut +\mathstrut 2079799375q^{25} \) \(\mathstrut +\mathstrut 514097024q^{26} \) \(\mathstrut -\mathstrut 2052934200q^{27} \) \(\mathstrut +\mathstrut 263094272q^{28} \) \(\mathstrut -\mathstrut 890583090q^{29} \) \(\mathstrut -\mathstrut 4544524800q^{30} \) \(\mathstrut +\mathstrut 4595552672q^{31} \) \(\mathstrut +\mathstrut 1073741824q^{32} \) \(\mathstrut +\mathstrut 3046210992q^{33} \) \(\mathstrut +\mathstrut 4551193728q^{34} \) \(\mathstrut -\mathstrut 3690128400q^{35} \) \(\mathstrut -\mathstrut 272904192q^{36} \) \(\mathstrut -\mathstrut 19585053898q^{37} \) \(\mathstrut +\mathstrut 8725571840q^{38} \) \(\mathstrut +\mathstrut 9928498776q^{39} \) \(\mathstrut -\mathstrut 15060172800q^{40} \) \(\mathstrut -\mathstrut 2724170358q^{41} \) \(\mathstrut +\mathstrut 5081008128q^{42} \) \(\mathstrut +\mathstrut 51762321116q^{43} \) \(\mathstrut +\mathstrut 10094886912q^{44} \) \(\mathstrut +\mathstrut 3827721150q^{45} \) \(\mathstrut -\mathstrut 75940041216q^{46} \) \(\mathstrut -\mathstrut 53572833168q^{47} \) \(\mathstrut +\mathstrut 20736638976q^{48} \) \(\mathstrut -\mathstrut 92763260583q^{49} \) \(\mathstrut +\mathstrut 133107160000q^{50} \) \(\mathstrut +\mathstrut 87894928872q^{51} \) \(\mathstrut +\mathstrut 32902209536q^{52} \) \(\mathstrut +\mathstrut 82633440006q^{53} \) \(\mathstrut -\mathstrut 131387788800q^{54} \) \(\mathstrut -\mathstrut 141589661400q^{55} \) \(\mathstrut +\mathstrut 16838033408q^{56} \) \(\mathstrut +\mathstrut 168512606160q^{57} \) \(\mathstrut -\mathstrut 56997317760q^{58} \) \(\mathstrut -\mathstrut 394266352980q^{59} \) \(\mathstrut -\mathstrut 290849587200q^{60} \) \(\mathstrut +\mathstrut 671061772142q^{61} \) \(\mathstrut +\mathstrut 294115371008q^{62} \) \(\mathstrut -\mathstrut 4279585464q^{63} \) \(\mathstrut +\mathstrut 68719476736q^{64} \) \(\mathstrut -\mathstrut 461482406700q^{65} \) \(\mathstrut +\mathstrut 194957503488q^{66} \) \(\mathstrut +\mathstrut 388156449812q^{67} \) \(\mathstrut +\mathstrut 291276398592q^{68} \) \(\mathstrut -\mathstrut 1466592045984q^{69} \) \(\mathstrut -\mathstrut 236168217600q^{70} \) \(\mathstrut -\mathstrut 388772243928q^{71} \) \(\mathstrut -\mathstrut 17465868288q^{72} \) \(\mathstrut +\mathstrut 1540972938026q^{73} \) \(\mathstrut -\mathstrut 1253443449472q^{74} \) \(\mathstrut +\mathstrut 2570632027500q^{75} \) \(\mathstrut +\mathstrut 558436597760q^{76} \) \(\mathstrut +\mathstrut 158304388704q^{77} \) \(\mathstrut +\mathstrut 635423921664q^{78} \) \(\mathstrut -\mathstrut 3306509559280q^{79} \) \(\mathstrut -\mathstrut 963851059200q^{80} \) \(\mathstrut -\mathstrut 2431201712679q^{81} \) \(\mathstrut -\mathstrut 174346902912q^{82} \) \(\mathstrut +\mathstrut 4931756967396q^{83} \) \(\mathstrut +\mathstrut 325184520192q^{84} \) \(\mathstrut -\mathstrut 4085407494900q^{85} \) \(\mathstrut +\mathstrut 3312788551424q^{86} \) \(\mathstrut -\mathstrut 1100760699240q^{87} \) \(\mathstrut +\mathstrut 646072762368q^{88} \) \(\mathstrut +\mathstrut 3502949738490q^{89} \) \(\mathstrut +\mathstrut 244974153600q^{90} \) \(\mathstrut +\mathstrut 515960625712q^{91} \) \(\mathstrut -\mathstrut 4860162637824q^{92} \) \(\mathstrut +\mathstrut 5680103102592q^{93} \) \(\mathstrut -\mathstrut 3428661322752q^{94} \) \(\mathstrut -\mathstrut 7832564097000q^{95} \) \(\mathstrut +\mathstrut 1327144894464q^{96} \) \(\mathstrut -\mathstrut 388932598558q^{97} \) \(\mathstrut -\mathstrut 5936848677312q^{98} \) \(\mathstrut -\mathstrut 164207038644q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
64.0000 1236.00 4096.00 −57450.0 79104.0 64232.0 262144. −66627.0 −3.67680e6
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Inner twists

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

Atkin-Lehner signs

\( p \) Sign
\(2\) \(-1\)

Hecke kernels

This newform can be constructed as the kernel of the linear operator \(T_{3} \) \(\mathstrut -\mathstrut 1236 \) acting on \(S_{14}^{\mathrm{new}}(\Gamma_0(2))\).