Properties

Label 8011.2.a.a
Level 8011
Weight 2
Character orbit 8011.a
Self dual Yes
Analytic conductor 63.968
Analytic rank 1
Dimension 309
CM No

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Newspace parameters

Level: \( N \) = \( 8011 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8011.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.9681570592\)
Analytic rank: \(1\)
Dimension: \(309\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

The dimension is sufficiently large that we do not compute an algebraic \(q\)-expansion, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \(309q \) \(\mathstrut -\mathstrut 33q^{2} \) \(\mathstrut -\mathstrut 15q^{3} \) \(\mathstrut +\mathstrut 273q^{4} \) \(\mathstrut -\mathstrut 74q^{5} \) \(\mathstrut -\mathstrut 32q^{6} \) \(\mathstrut -\mathstrut 19q^{7} \) \(\mathstrut -\mathstrut 93q^{8} \) \(\mathstrut +\mathstrut 214q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \(309q \) \(\mathstrut -\mathstrut 33q^{2} \) \(\mathstrut -\mathstrut 15q^{3} \) \(\mathstrut +\mathstrut 273q^{4} \) \(\mathstrut -\mathstrut 74q^{5} \) \(\mathstrut -\mathstrut 32q^{6} \) \(\mathstrut -\mathstrut 19q^{7} \) \(\mathstrut -\mathstrut 93q^{8} \) \(\mathstrut +\mathstrut 214q^{9} \) \(\mathstrut -\mathstrut 23q^{10} \) \(\mathstrut -\mathstrut 72q^{11} \) \(\mathstrut -\mathstrut 42q^{12} \) \(\mathstrut -\mathstrut 57q^{13} \) \(\mathstrut -\mathstrut 77q^{14} \) \(\mathstrut -\mathstrut 44q^{15} \) \(\mathstrut +\mathstrut 205q^{16} \) \(\mathstrut -\mathstrut 86q^{17} \) \(\mathstrut -\mathstrut 82q^{18} \) \(\mathstrut -\mathstrut 58q^{19} \) \(\mathstrut -\mathstrut 134q^{20} \) \(\mathstrut -\mathstrut 123q^{21} \) \(\mathstrut -\mathstrut 31q^{22} \) \(\mathstrut -\mathstrut 94q^{23} \) \(\mathstrut -\mathstrut 84q^{24} \) \(\mathstrut +\mathstrut 225q^{25} \) \(\mathstrut -\mathstrut 92q^{26} \) \(\mathstrut -\mathstrut 48q^{27} \) \(\mathstrut -\mathstrut 36q^{28} \) \(\mathstrut -\mathstrut 345q^{29} \) \(\mathstrut -\mathstrut 85q^{30} \) \(\mathstrut -\mathstrut 36q^{31} \) \(\mathstrut -\mathstrut 199q^{32} \) \(\mathstrut -\mathstrut 56q^{33} \) \(\mathstrut -\mathstrut 28q^{34} \) \(\mathstrut -\mathstrut 168q^{35} \) \(\mathstrut +\mathstrut 65q^{36} \) \(\mathstrut -\mathstrut 79q^{37} \) \(\mathstrut -\mathstrut 66q^{38} \) \(\mathstrut -\mathstrut 145q^{39} \) \(\mathstrut -\mathstrut 54q^{40} \) \(\mathstrut -\mathstrut 176q^{41} \) \(\mathstrut -\mathstrut 48q^{42} \) \(\mathstrut -\mathstrut 58q^{43} \) \(\mathstrut -\mathstrut 194q^{44} \) \(\mathstrut -\mathstrut 192q^{45} \) \(\mathstrut -\mathstrut 44q^{46} \) \(\mathstrut -\mathstrut 82q^{47} \) \(\mathstrut -\mathstrut 81q^{48} \) \(\mathstrut +\mathstrut 186q^{49} \) \(\mathstrut -\mathstrut 206q^{50} \) \(\mathstrut -\mathstrut 145q^{51} \) \(\mathstrut -\mathstrut 86q^{52} \) \(\mathstrut -\mathstrut 223q^{53} \) \(\mathstrut -\mathstrut 117q^{54} \) \(\mathstrut -\mathstrut 58q^{55} \) \(\mathstrut -\mathstrut 216q^{56} \) \(\mathstrut -\mathstrut 124q^{57} \) \(\mathstrut -\mathstrut 151q^{59} \) \(\mathstrut -\mathstrut 91q^{60} \) \(\mathstrut -\mathstrut 184q^{61} \) \(\mathstrut -\mathstrut 124q^{62} \) \(\mathstrut -\mathstrut 78q^{63} \) \(\mathstrut +\mathstrut 101q^{64} \) \(\mathstrut -\mathstrut 194q^{65} \) \(\mathstrut -\mathstrut 112q^{66} \) \(\mathstrut -\mathstrut 53q^{67} \) \(\mathstrut -\mathstrut 182q^{68} \) \(\mathstrut -\mathstrut 243q^{69} \) \(\mathstrut -\mathstrut 193q^{71} \) \(\mathstrut -\mathstrut 208q^{72} \) \(\mathstrut -\mathstrut 69q^{73} \) \(\mathstrut -\mathstrut 236q^{74} \) \(\mathstrut -\mathstrut 62q^{75} \) \(\mathstrut -\mathstrut 142q^{76} \) \(\mathstrut -\mathstrut 324q^{77} \) \(\mathstrut -\mathstrut 20q^{78} \) \(\mathstrut -\mathstrut 91q^{79} \) \(\mathstrut -\mathstrut 223q^{80} \) \(\mathstrut -\mathstrut 27q^{81} \) \(\mathstrut +\mathstrut 2q^{82} \) \(\mathstrut -\mathstrut 117q^{83} \) \(\mathstrut -\mathstrut 157q^{84} \) \(\mathstrut -\mathstrut 171q^{85} \) \(\mathstrut -\mathstrut 203q^{86} \) \(\mathstrut -\mathstrut 69q^{87} \) \(\mathstrut -\mathstrut 36q^{88} \) \(\mathstrut -\mathstrut 172q^{89} \) \(\mathstrut -\mathstrut 10q^{90} \) \(\mathstrut -\mathstrut 84q^{91} \) \(\mathstrut -\mathstrut 226q^{92} \) \(\mathstrut -\mathstrut 220q^{93} \) \(\mathstrut -\mathstrut 96q^{94} \) \(\mathstrut -\mathstrut 166q^{95} \) \(\mathstrut -\mathstrut 118q^{96} \) \(\mathstrut -\mathstrut 12q^{97} \) \(\mathstrut -\mathstrut 116q^{98} \) \(\mathstrut -\mathstrut 154q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1.1 −2.81833 1.84881 5.94296 −3.66460 −5.21056 −0.909168 −11.1126 0.418106 10.3280
1.2 −2.78702 −1.95051 5.76751 −0.484177 5.43612 0.734493 −10.5001 0.804484 1.34941
1.3 −2.76917 0.105018 5.66833 −1.01486 −0.290815 4.45070 −10.1582 −2.98897 2.81033
1.4 −2.75364 −0.00102412 5.58256 −3.57698 0.00282007 1.05818 −9.86509 −3.00000 9.84973
1.5 −2.74707 2.55044 5.54642 3.00412 −7.00626 1.74411 −9.74228 3.50477 −8.25255
1.6 −2.74693 2.61520 5.54560 −1.49229 −7.18376 4.10131 −9.73951 3.83927 4.09920
1.7 −2.74292 −0.194612 5.52364 4.36086 0.533805 −1.38725 −9.66507 −2.96213 −11.9615
1.8 −2.69623 −0.432527 5.26965 2.72420 1.16619 −0.628855 −8.81573 −2.81292 −7.34507
1.9 −2.68837 −2.21810 5.22734 1.47525 5.96309 −1.22716 −8.67630 1.91998 −3.96602
1.10 −2.67443 −1.89818 5.15257 −2.43152 5.07654 2.86566 −8.43133 0.603070 6.50294
1.11 −2.67381 −2.54689 5.14927 −3.71609 6.80992 3.32085 −8.42057 3.48667 9.93612
1.12 −2.67151 −0.346621 5.13696 1.63571 0.926001 −0.275244 −8.38042 −2.87985 −4.36981
1.13 −2.65734 −0.429161 5.06145 2.18236 1.14043 3.77949 −8.13530 −2.81582 −5.79927
1.14 −2.64340 2.84192 4.98759 0.696294 −7.51235 −3.08264 −7.89741 5.07651 −1.84059
1.15 −2.61747 −3.23549 4.85115 −2.81151 8.46879 −1.74803 −7.46281 7.46837 7.35905
1.16 −2.61660 −0.249789 4.84659 −1.85842 0.653599 −0.258344 −7.44839 −2.93761 4.86274
1.17 −2.58476 −1.81476 4.68100 2.17232 4.69073 −4.47910 −6.92974 0.293363 −5.61492
1.18 −2.57419 1.43469 4.62646 0.684490 −3.69317 3.09372 −6.76100 −0.941663 −1.76201
1.19 −2.56976 2.00808 4.60368 −0.878358 −5.16030 1.06025 −6.69084 1.03240 2.25717
1.20 −2.56050 2.53687 4.55617 −3.00342 −6.49566 2.39644 −6.54508 3.43571 7.69027
See next 80 embeddings (of 309 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.309
Significant digits:
Format:

Inner twists

This newform does not have CM; other inner twists have not been computed.

Atkin-Lehner signs

\( p \) Sign
\(8011\) \(1\)