Properties

Label 8021.2.a.d
Level 8021
Weight 2
Character orbit 8021.a
Self dual Yes
Analytic conductor 64.048
Analytic rank 0
Dimension 174
CM No

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Newspace parameters

Level: \( N \) = \( 8021 = 13 \cdot 617 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8021.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0480074613\)
Analytic rank: \(0\)
Dimension: \(174\)
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.

\(\operatorname{Tr}(f)(q) = \) \(174q \) \(\mathstrut +\mathstrut 6q^{2} \) \(\mathstrut +\mathstrut 37q^{3} \) \(\mathstrut +\mathstrut 214q^{4} \) \(\mathstrut +\mathstrut 10q^{5} \) \(\mathstrut +\mathstrut 12q^{6} \) \(\mathstrut +\mathstrut 28q^{7} \) \(\mathstrut +\mathstrut 15q^{8} \) \(\mathstrut +\mathstrut 211q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \(174q \) \(\mathstrut +\mathstrut 6q^{2} \) \(\mathstrut +\mathstrut 37q^{3} \) \(\mathstrut +\mathstrut 214q^{4} \) \(\mathstrut +\mathstrut 10q^{5} \) \(\mathstrut +\mathstrut 12q^{6} \) \(\mathstrut +\mathstrut 28q^{7} \) \(\mathstrut +\mathstrut 15q^{8} \) \(\mathstrut +\mathstrut 211q^{9} \) \(\mathstrut +\mathstrut 47q^{10} \) \(\mathstrut +\mathstrut 47q^{11} \) \(\mathstrut +\mathstrut 81q^{12} \) \(\mathstrut +\mathstrut 174q^{13} \) \(\mathstrut +\mathstrut 22q^{14} \) \(\mathstrut +\mathstrut 26q^{15} \) \(\mathstrut +\mathstrut 286q^{16} \) \(\mathstrut +\mathstrut 27q^{17} \) \(\mathstrut +\mathstrut 22q^{18} \) \(\mathstrut +\mathstrut 91q^{19} \) \(\mathstrut +\mathstrut 18q^{20} \) \(\mathstrut +\mathstrut 8q^{21} \) \(\mathstrut +\mathstrut 58q^{22} \) \(\mathstrut +\mathstrut 62q^{23} \) \(\mathstrut +\mathstrut 24q^{24} \) \(\mathstrut +\mathstrut 244q^{25} \) \(\mathstrut +\mathstrut 6q^{26} \) \(\mathstrut +\mathstrut 139q^{27} \) \(\mathstrut +\mathstrut 43q^{28} \) \(\mathstrut +\mathstrut 42q^{29} \) \(\mathstrut +\mathstrut 31q^{30} \) \(\mathstrut +\mathstrut 82q^{31} \) \(\mathstrut +\mathstrut 11q^{32} \) \(\mathstrut +\mathstrut 12q^{33} \) \(\mathstrut +\mathstrut 50q^{34} \) \(\mathstrut +\mathstrut 74q^{35} \) \(\mathstrut +\mathstrut 310q^{36} \) \(\mathstrut +\mathstrut 47q^{37} \) \(\mathstrut +\mathstrut 10q^{38} \) \(\mathstrut +\mathstrut 37q^{39} \) \(\mathstrut +\mathstrut 118q^{40} \) \(\mathstrut +\mathstrut 16q^{41} \) \(\mathstrut +\mathstrut 26q^{42} \) \(\mathstrut +\mathstrut 136q^{43} \) \(\mathstrut +\mathstrut 74q^{44} \) \(\mathstrut +\mathstrut 18q^{45} \) \(\mathstrut +\mathstrut 53q^{46} \) \(\mathstrut +\mathstrut 15q^{47} \) \(\mathstrut +\mathstrut 132q^{48} \) \(\mathstrut +\mathstrut 254q^{49} \) \(\mathstrut -\mathstrut 5q^{50} \) \(\mathstrut +\mathstrut 121q^{51} \) \(\mathstrut +\mathstrut 214q^{52} \) \(\mathstrut +\mathstrut 39q^{53} \) \(\mathstrut +\mathstrut 30q^{54} \) \(\mathstrut +\mathstrut 188q^{55} \) \(\mathstrut +\mathstrut 55q^{56} \) \(\mathstrut +\mathstrut 11q^{57} \) \(\mathstrut +\mathstrut 32q^{58} \) \(\mathstrut +\mathstrut 58q^{59} \) \(\mathstrut +\mathstrut 16q^{60} \) \(\mathstrut +\mathstrut 128q^{61} \) \(\mathstrut +\mathstrut 27q^{62} \) \(\mathstrut +\mathstrut 42q^{63} \) \(\mathstrut +\mathstrut 423q^{64} \) \(\mathstrut +\mathstrut 10q^{65} \) \(\mathstrut +\mathstrut 4q^{66} \) \(\mathstrut +\mathstrut 132q^{67} \) \(\mathstrut +\mathstrut 52q^{68} \) \(\mathstrut +\mathstrut 63q^{69} \) \(\mathstrut -\mathstrut 8q^{70} \) \(\mathstrut +\mathstrut 78q^{71} \) \(\mathstrut +\mathstrut 2q^{72} \) \(\mathstrut +\mathstrut 21q^{73} \) \(\mathstrut -\mathstrut 16q^{74} \) \(\mathstrut +\mathstrut 188q^{75} \) \(\mathstrut +\mathstrut 160q^{76} \) \(\mathstrut +\mathstrut 20q^{77} \) \(\mathstrut +\mathstrut 12q^{78} \) \(\mathstrut +\mathstrut 232q^{79} \) \(\mathstrut +\mathstrut 2q^{80} \) \(\mathstrut +\mathstrut 302q^{81} \) \(\mathstrut +\mathstrut 115q^{82} \) \(\mathstrut +\mathstrut 18q^{83} \) \(\mathstrut -\mathstrut 26q^{84} \) \(\mathstrut +\mathstrut 47q^{85} \) \(\mathstrut +\mathstrut 27q^{86} \) \(\mathstrut +\mathstrut 127q^{87} \) \(\mathstrut +\mathstrut 163q^{88} \) \(\mathstrut +\mathstrut 14q^{90} \) \(\mathstrut +\mathstrut 28q^{91} \) \(\mathstrut +\mathstrut 68q^{92} \) \(\mathstrut +\mathstrut 15q^{93} \) \(\mathstrut +\mathstrut 91q^{94} \) \(\mathstrut +\mathstrut 75q^{95} \) \(\mathstrut -\mathstrut 26q^{96} \) \(\mathstrut +\mathstrut 34q^{97} \) \(\mathstrut -\mathstrut 60q^{98} \) \(\mathstrut +\mathstrut 181q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 −2.81586 1.36738 5.92908 −2.81839 −3.85036 −0.890414 −11.0638 −1.13027 7.93620
1.2 −2.77267 1.50862 5.68769 1.04517 −4.18289 −5.21770 −10.2247 −0.724079 −2.89792
1.3 −2.75277 3.20644 5.57777 3.17240 −8.82662 4.29647 −9.84879 7.28128 −8.73291
1.4 −2.74939 −3.36521 5.55917 −2.17409 9.25228 0.588042 −9.78555 8.32462 5.97744
1.5 −2.69931 −1.31016 5.28630 −0.0823096 3.53653 −3.58591 −8.87075 −1.28348 0.222180
1.6 −2.69663 −1.80678 5.27183 −0.883800 4.87223 4.78301 −8.82294 0.264464 2.38328
1.7 −2.66552 1.95620 5.10502 −0.546887 −5.21429 5.08856 −8.27650 0.826707 1.45774
1.8 −2.65450 3.02354 5.04638 −2.29392 −8.02600 −0.907848 −8.08663 6.14182 6.08922
1.9 −2.65348 3.32664 5.04093 −4.27882 −8.82716 −1.52713 −8.06904 8.06653 11.3537
1.10 −2.64790 −2.80956 5.01138 2.16330 7.43944 3.49626 −7.97383 4.89364 −5.72819
1.11 −2.64300 −0.434399 4.98547 −0.633166 1.14812 1.76480 −7.89059 −2.81130 1.67346
1.12 −2.64088 0.716800 4.97424 −3.63503 −1.89298 1.69747 −7.85462 −2.48620 9.59969
1.13 −2.63723 −2.22050 4.95500 3.72301 5.85596 −3.62454 −7.79302 1.93060 −9.81845
1.14 −2.63597 −1.22103 4.94831 −4.05948 3.21858 −2.69195 −7.77165 −1.50910 10.7007
1.15 −2.62193 2.84190 4.87451 3.72911 −7.45125 −2.25507 −7.53678 5.07638 −9.77745
1.16 −2.58537 −0.157570 4.68414 0.713446 0.407377 −2.31899 −6.93951 −2.97517 −1.84452
1.17 −2.55071 −1.16628 4.50614 1.55643 2.97485 2.04272 −6.39246 −1.63979 −3.97002
1.18 −2.41415 1.51661 3.82811 −1.37172 −3.66132 −4.25980 −4.41333 −0.699894 3.31154
1.19 −2.39849 2.44398 3.75277 −3.07733 −5.86187 3.93094 −4.20400 2.97305 7.38096
1.20 −2.31194 −2.08272 3.34506 −3.48244 4.81513 3.73510 −3.10970 1.33774 8.05119
See next 80 embeddings (of 174 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.174
Significant digits:
Format:

Inner twists

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

Atkin-Lehner signs

\( p \) Sign
\(13\) \(-1\)
\(617\) \(1\)