Properties

Label 8.16.a.b
Level 8
Weight 16
Character orbit 8.a
Self dual Yes
Analytic conductor 11.415
Analytic rank 1
Dimension 1
CM No
Inner twists 1

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 8 = 2^{3} \)
Weight: \( k \) = \( 16 \)
Character orbit: \([\chi]\) = 8.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(11.415480408\)
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

\(f(q)\) \(=\) \(q \) \(\mathstrut +\mathstrut 2700q^{3} \) \(\mathstrut -\mathstrut 251890q^{5} \) \(\mathstrut +\mathstrut 1374072q^{7} \) \(\mathstrut -\mathstrut 7058907q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(q \) \(\mathstrut +\mathstrut 2700q^{3} \) \(\mathstrut -\mathstrut 251890q^{5} \) \(\mathstrut +\mathstrut 1374072q^{7} \) \(\mathstrut -\mathstrut 7058907q^{9} \) \(\mathstrut -\mathstrut 43286716q^{11} \) \(\mathstrut -\mathstrut 323161466q^{13} \) \(\mathstrut -\mathstrut 680103000q^{15} \) \(\mathstrut -\mathstrut 191653646q^{17} \) \(\mathstrut -\mathstrut 6515456644q^{19} \) \(\mathstrut +\mathstrut 3709994400q^{21} \) \(\mathstrut +\mathstrut 23880801512q^{23} \) \(\mathstrut +\mathstrut 32930993975q^{25} \) \(\mathstrut -\mathstrut 57801097800q^{27} \) \(\mathstrut +\mathstrut 176820596982q^{29} \) \(\mathstrut -\mathstrut 152007193888q^{31} \) \(\mathstrut -\mathstrut 116874133200q^{33} \) \(\mathstrut -\mathstrut 346114996080q^{35} \) \(\mathstrut +\mathstrut 21581233902q^{37} \) \(\mathstrut -\mathstrut 872535958200q^{39} \) \(\mathstrut -\mathstrut 245334499686q^{41} \) \(\mathstrut +\mathstrut 2769961534756q^{43} \) \(\mathstrut +\mathstrut 1778068084230q^{45} \) \(\mathstrut +\mathstrut 2811771943248q^{47} \) \(\mathstrut -\mathstrut 2859487648759q^{49} \) \(\mathstrut -\mathstrut 517464844200q^{51} \) \(\mathstrut -\mathstrut 3491413730722q^{53} \) \(\mathstrut +\mathstrut 10903490893240q^{55} \) \(\mathstrut -\mathstrut 17591732938800q^{57} \) \(\mathstrut -\mathstrut 15827800893676q^{59} \) \(\mathstrut -\mathstrut 24609047974442q^{61} \) \(\mathstrut -\mathstrut 9699446459304q^{63} \) \(\mathstrut +\mathstrut 81401141670740q^{65} \) \(\mathstrut -\mathstrut 20706233653684q^{67} \) \(\mathstrut +\mathstrut 64478164082400q^{69} \) \(\mathstrut -\mathstrut 719982528200q^{71} \) \(\mathstrut +\mathstrut 29883036220282q^{73} \) \(\mathstrut +\mathstrut 88913683732500q^{75} \) \(\mathstrut -\mathstrut 59479064427552q^{77} \) \(\mathstrut -\mathstrut 148100908648400q^{79} \) \(\mathstrut -\mathstrut 54775363995351q^{81} \) \(\mathstrut -\mathstrut 302806756982468q^{83} \) \(\mathstrut +\mathstrut 48275636890940q^{85} \) \(\mathstrut +\mathstrut 477415611851400q^{87} \) \(\mathstrut -\mathstrut 496150966996374q^{89} \) \(\mathstrut -\mathstrut 444047121909552q^{91} \) \(\mathstrut -\mathstrut 410419423497600q^{93} \) \(\mathstrut +\mathstrut 1641178374057160q^{95} \) \(\mathstrut +\mathstrut 309183128990882q^{97} \) \(\mathstrut +\mathstrut 305556902579412q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
0 2700.00 0 −251890. 0 1.37407e6 0 −7.05891e6 0
\(n\): 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 \(T_{3} \) \(\mathstrut -\mathstrut 2700 \) acting on \(S_{16}^{\mathrm{new}}(\Gamma_0(8))\).