Properties

Label 14.8.a.a
Level 14
Weight 8
Character orbit 14.a
Self dual Yes
Analytic conductor 4.373
Analytic rank 0
Dimension 1
CM No
Inner twists 1

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 14 = 2 \cdot 7 \)
Weight: \( k \) = \( 8 \)
Character orbit: \([\chi]\) = 14.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(4.37339035678\)
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

\(f(q)\) \(=\) \(q \) \(\mathstrut -\mathstrut 8q^{2} \) \(\mathstrut -\mathstrut 82q^{3} \) \(\mathstrut +\mathstrut 64q^{4} \) \(\mathstrut +\mathstrut 448q^{5} \) \(\mathstrut +\mathstrut 656q^{6} \) \(\mathstrut -\mathstrut 343q^{7} \) \(\mathstrut -\mathstrut 512q^{8} \) \(\mathstrut +\mathstrut 4537q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(q \) \(\mathstrut -\mathstrut 8q^{2} \) \(\mathstrut -\mathstrut 82q^{3} \) \(\mathstrut +\mathstrut 64q^{4} \) \(\mathstrut +\mathstrut 448q^{5} \) \(\mathstrut +\mathstrut 656q^{6} \) \(\mathstrut -\mathstrut 343q^{7} \) \(\mathstrut -\mathstrut 512q^{8} \) \(\mathstrut +\mathstrut 4537q^{9} \) \(\mathstrut -\mathstrut 3584q^{10} \) \(\mathstrut +\mathstrut 2408q^{11} \) \(\mathstrut -\mathstrut 5248q^{12} \) \(\mathstrut +\mathstrut 7116q^{13} \) \(\mathstrut +\mathstrut 2744q^{14} \) \(\mathstrut -\mathstrut 36736q^{15} \) \(\mathstrut +\mathstrut 4096q^{16} \) \(\mathstrut +\mathstrut 2486q^{17} \) \(\mathstrut -\mathstrut 36296q^{18} \) \(\mathstrut +\mathstrut 36482q^{19} \) \(\mathstrut +\mathstrut 28672q^{20} \) \(\mathstrut +\mathstrut 28126q^{21} \) \(\mathstrut -\mathstrut 19264q^{22} \) \(\mathstrut -\mathstrut 12880q^{23} \) \(\mathstrut +\mathstrut 41984q^{24} \) \(\mathstrut +\mathstrut 122579q^{25} \) \(\mathstrut -\mathstrut 56928q^{26} \) \(\mathstrut -\mathstrut 192700q^{27} \) \(\mathstrut -\mathstrut 21952q^{28} \) \(\mathstrut -\mathstrut 88094q^{29} \) \(\mathstrut +\mathstrut 293888q^{30} \) \(\mathstrut +\mathstrut 282636q^{31} \) \(\mathstrut -\mathstrut 32768q^{32} \) \(\mathstrut -\mathstrut 197456q^{33} \) \(\mathstrut -\mathstrut 19888q^{34} \) \(\mathstrut -\mathstrut 153664q^{35} \) \(\mathstrut +\mathstrut 290368q^{36} \) \(\mathstrut -\mathstrut 214534q^{37} \) \(\mathstrut -\mathstrut 291856q^{38} \) \(\mathstrut -\mathstrut 583512q^{39} \) \(\mathstrut -\mathstrut 229376q^{40} \) \(\mathstrut -\mathstrut 140874q^{41} \) \(\mathstrut -\mathstrut 225008q^{42} \) \(\mathstrut +\mathstrut 36464q^{43} \) \(\mathstrut +\mathstrut 154112q^{44} \) \(\mathstrut +\mathstrut 2032576q^{45} \) \(\mathstrut +\mathstrut 103040q^{46} \) \(\mathstrut +\mathstrut 716868q^{47} \) \(\mathstrut -\mathstrut 335872q^{48} \) \(\mathstrut +\mathstrut 117649q^{49} \) \(\mathstrut -\mathstrut 980632q^{50} \) \(\mathstrut -\mathstrut 203852q^{51} \) \(\mathstrut +\mathstrut 455424q^{52} \) \(\mathstrut -\mathstrut 56946q^{53} \) \(\mathstrut +\mathstrut 1541600q^{54} \) \(\mathstrut +\mathstrut 1078784q^{55} \) \(\mathstrut +\mathstrut 175616q^{56} \) \(\mathstrut -\mathstrut 2991524q^{57} \) \(\mathstrut +\mathstrut 704752q^{58} \) \(\mathstrut -\mathstrut 2149862q^{59} \) \(\mathstrut -\mathstrut 2351104q^{60} \) \(\mathstrut +\mathstrut 3084360q^{61} \) \(\mathstrut -\mathstrut 2261088q^{62} \) \(\mathstrut -\mathstrut 1556191q^{63} \) \(\mathstrut +\mathstrut 262144q^{64} \) \(\mathstrut +\mathstrut 3187968q^{65} \) \(\mathstrut +\mathstrut 1579648q^{66} \) \(\mathstrut -\mathstrut 3034364q^{67} \) \(\mathstrut +\mathstrut 159104q^{68} \) \(\mathstrut +\mathstrut 1056160q^{69} \) \(\mathstrut +\mathstrut 1229312q^{70} \) \(\mathstrut -\mathstrut 106624q^{71} \) \(\mathstrut -\mathstrut 2322944q^{72} \) \(\mathstrut +\mathstrut 988930q^{73} \) \(\mathstrut +\mathstrut 1716272q^{74} \) \(\mathstrut -\mathstrut 10051478q^{75} \) \(\mathstrut +\mathstrut 2334848q^{76} \) \(\mathstrut -\mathstrut 825944q^{77} \) \(\mathstrut +\mathstrut 4668096q^{78} \) \(\mathstrut +\mathstrut 3415896q^{79} \) \(\mathstrut +\mathstrut 1835008q^{80} \) \(\mathstrut +\mathstrut 5878981q^{81} \) \(\mathstrut +\mathstrut 1126992q^{82} \) \(\mathstrut -\mathstrut 15142q^{83} \) \(\mathstrut +\mathstrut 1800064q^{84} \) \(\mathstrut +\mathstrut 1113728q^{85} \) \(\mathstrut -\mathstrut 291712q^{86} \) \(\mathstrut +\mathstrut 7223708q^{87} \) \(\mathstrut -\mathstrut 1232896q^{88} \) \(\mathstrut +\mathstrut 174810q^{89} \) \(\mathstrut -\mathstrut 16260608q^{90} \) \(\mathstrut -\mathstrut 2440788q^{91} \) \(\mathstrut -\mathstrut 824320q^{92} \) \(\mathstrut -\mathstrut 23176152q^{93} \) \(\mathstrut -\mathstrut 5734944q^{94} \) \(\mathstrut +\mathstrut 16343936q^{95} \) \(\mathstrut +\mathstrut 2686976q^{96} \) \(\mathstrut +\mathstrut 13506790q^{97} \) \(\mathstrut -\mathstrut 941192q^{98} \) \(\mathstrut +\mathstrut 10925096q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
−8.00000 −82.0000 64.0000 448.000 656.000 −343.000 −512.000 4537.00 −3584.00
\(n\): 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
\(2\) \(1\)
\(7\) \(1\)

Hecke kernels

This newform can be constructed as the kernel of the linear operator \(T_{3} \) \(\mathstrut +\mathstrut 82 \) acting on \(S_{8}^{\mathrm{new}}(\Gamma_0(14))\).