Properties

Label 8021.2.a.b
Level 8021
Weight 2
Character orbit 8021.a
Self dual Yes
Analytic conductor 64.048
Analytic rank 1
Dimension 140
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: \(1\)
Dimension: \(140\)
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.

\(\operatorname{Tr}(f)(q) = \) \(140q \) \(\mathstrut -\mathstrut 6q^{2} \) \(\mathstrut -\mathstrut 9q^{3} \) \(\mathstrut +\mathstrut 112q^{4} \) \(\mathstrut -\mathstrut 12q^{5} \) \(\mathstrut -\mathstrut 18q^{6} \) \(\mathstrut -\mathstrut 32q^{7} \) \(\mathstrut -\mathstrut 15q^{8} \) \(\mathstrut +\mathstrut 111q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \(140q \) \(\mathstrut -\mathstrut 6q^{2} \) \(\mathstrut -\mathstrut 9q^{3} \) \(\mathstrut +\mathstrut 112q^{4} \) \(\mathstrut -\mathstrut 12q^{5} \) \(\mathstrut -\mathstrut 18q^{6} \) \(\mathstrut -\mathstrut 32q^{7} \) \(\mathstrut -\mathstrut 15q^{8} \) \(\mathstrut +\mathstrut 111q^{9} \) \(\mathstrut -\mathstrut q^{10} \) \(\mathstrut -\mathstrut 47q^{11} \) \(\mathstrut -\mathstrut 11q^{12} \) \(\mathstrut -\mathstrut 140q^{13} \) \(\mathstrut -\mathstrut 12q^{14} \) \(\mathstrut -\mathstrut 30q^{15} \) \(\mathstrut +\mathstrut 64q^{16} \) \(\mathstrut +\mathstrut 3q^{17} \) \(\mathstrut -\mathstrut 22q^{18} \) \(\mathstrut -\mathstrut 91q^{19} \) \(\mathstrut -\mathstrut 24q^{20} \) \(\mathstrut -\mathstrut 28q^{21} \) \(\mathstrut -\mathstrut 12q^{22} \) \(\mathstrut -\mathstrut 10q^{23} \) \(\mathstrut -\mathstrut 42q^{24} \) \(\mathstrut +\mathstrut 84q^{25} \) \(\mathstrut +\mathstrut 6q^{26} \) \(\mathstrut -\mathstrut 33q^{27} \) \(\mathstrut -\mathstrut 71q^{28} \) \(\mathstrut -\mathstrut 32q^{29} \) \(\mathstrut -\mathstrut 45q^{30} \) \(\mathstrut -\mathstrut 90q^{31} \) \(\mathstrut -\mathstrut 31q^{32} \) \(\mathstrut -\mathstrut 32q^{33} \) \(\mathstrut -\mathstrut 78q^{34} \) \(\mathstrut -\mathstrut 50q^{35} \) \(\mathstrut +\mathstrut 10q^{36} \) \(\mathstrut -\mathstrut 67q^{37} \) \(\mathstrut -\mathstrut 8q^{38} \) \(\mathstrut +\mathstrut 9q^{39} \) \(\mathstrut -\mathstrut 10q^{40} \) \(\mathstrut -\mathstrut 22q^{41} \) \(\mathstrut -\mathstrut 30q^{42} \) \(\mathstrut -\mathstrut 40q^{43} \) \(\mathstrut -\mathstrut 88q^{44} \) \(\mathstrut -\mathstrut 36q^{45} \) \(\mathstrut -\mathstrut 77q^{46} \) \(\mathstrut -\mathstrut 29q^{47} \) \(\mathstrut -\mathstrut 4q^{48} \) \(\mathstrut +\mathstrut 66q^{49} \) \(\mathstrut -\mathstrut 45q^{50} \) \(\mathstrut -\mathstrut 87q^{51} \) \(\mathstrut -\mathstrut 112q^{52} \) \(\mathstrut -\mathstrut 19q^{53} \) \(\mathstrut -\mathstrut 82q^{54} \) \(\mathstrut -\mathstrut 28q^{55} \) \(\mathstrut -\mathstrut 63q^{56} \) \(\mathstrut -\mathstrut 41q^{57} \) \(\mathstrut -\mathstrut 96q^{58} \) \(\mathstrut -\mathstrut 84q^{59} \) \(\mathstrut -\mathstrut 106q^{60} \) \(\mathstrut -\mathstrut 58q^{61} \) \(\mathstrut -\mathstrut 3q^{62} \) \(\mathstrut -\mathstrut 76q^{63} \) \(\mathstrut -\mathstrut 55q^{64} \) \(\mathstrut +\mathstrut 12q^{65} \) \(\mathstrut -\mathstrut 56q^{66} \) \(\mathstrut -\mathstrut 140q^{67} \) \(\mathstrut -\mathstrut 4q^{68} \) \(\mathstrut -\mathstrut 41q^{69} \) \(\mathstrut -\mathstrut 106q^{70} \) \(\mathstrut -\mathstrut 104q^{71} \) \(\mathstrut -\mathstrut 52q^{72} \) \(\mathstrut -\mathstrut 57q^{73} \) \(\mathstrut -\mathstrut 24q^{74} \) \(\mathstrut -\mathstrut 62q^{75} \) \(\mathstrut -\mathstrut 184q^{76} \) \(\mathstrut +\mathstrut 8q^{77} \) \(\mathstrut +\mathstrut 18q^{78} \) \(\mathstrut -\mathstrut 104q^{79} \) \(\mathstrut -\mathstrut 102q^{80} \) \(\mathstrut +\mathstrut 4q^{81} \) \(\mathstrut -\mathstrut 37q^{82} \) \(\mathstrut -\mathstrut 52q^{83} \) \(\mathstrut -\mathstrut 94q^{84} \) \(\mathstrut -\mathstrut 93q^{85} \) \(\mathstrut -\mathstrut 79q^{86} \) \(\mathstrut +\mathstrut 51q^{87} \) \(\mathstrut -\mathstrut 47q^{88} \) \(\mathstrut -\mathstrut 64q^{89} \) \(\mathstrut +\mathstrut 22q^{90} \) \(\mathstrut +\mathstrut 32q^{91} \) \(\mathstrut -\mathstrut 42q^{92} \) \(\mathstrut -\mathstrut 115q^{93} \) \(\mathstrut -\mathstrut 43q^{94} \) \(\mathstrut -\mathstrut 25q^{95} \) \(\mathstrut -\mathstrut 116q^{96} \) \(\mathstrut -\mathstrut 92q^{97} \) \(\mathstrut -\mathstrut 36q^{98} \) \(\mathstrut -\mathstrut 223q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 −2.74251 −0.873664 5.52139 −0.639723 2.39604 −2.37570 −9.65746 −2.23671 1.75445
1.2 −2.72092 2.93492 5.40338 −0.339682 −7.98568 −0.916249 −9.26032 5.61377 0.924245
1.3 −2.66546 1.20306 5.10470 −3.76588 −3.20671 −2.98135 −8.27547 −1.55265 10.0378
1.4 −2.62889 1.78605 4.91107 1.43411 −4.69533 3.37960 −7.65290 0.189969 −3.77012
1.5 −2.61802 −0.518785 4.85402 −1.93655 1.35819 1.44000 −7.47189 −2.73086 5.06994
1.6 −2.58382 −0.446323 4.67613 3.71919 1.15322 −4.18348 −6.91464 −2.80080 −9.60973
1.7 −2.55171 −0.135477 4.51121 −1.86622 0.345697 −2.01089 −6.40787 −2.98165 4.76206
1.8 −2.51611 −0.357802 4.33083 1.59960 0.900270 0.472398 −5.86464 −2.87198 −4.02477
1.9 −2.49455 −1.79114 4.22277 −0.0823474 4.46808 3.62956 −5.54480 0.208181 0.205419
1.10 −2.49397 −2.62257 4.21989 0.472078 6.54061 1.90995 −5.53635 3.87786 −1.17735
1.11 −2.47091 2.70447 4.10542 −1.18660 −6.68251 −3.35758 −5.20231 4.31416 2.93198
1.12 −2.46538 −1.17968 4.07807 2.88368 2.90835 −1.57366 −5.12323 −1.60835 −7.10935
1.13 −2.42591 −2.98941 3.88502 −2.94726 7.25203 −3.20190 −4.57289 5.93657 7.14978
1.14 −2.40289 0.734522 3.77388 0.776538 −1.76498 4.43052 −4.26243 −2.46048 −1.86594
1.15 −2.35872 2.44520 3.56358 2.52211 −5.76755 2.39189 −3.68804 2.97900 −5.94896
1.16 −2.33878 −3.04534 3.46990 −1.89662 7.12240 2.91891 −3.43778 6.27412 4.43579
1.17 −2.27005 2.30637 3.15311 −4.44364 −5.23557 0.498318 −2.61762 2.31934 10.0873
1.18 −2.16089 1.85142 2.66943 −2.55060 −4.00072 2.44468 −1.44657 0.427768 5.51156
1.19 −2.13500 1.79448 2.55821 1.65943 −3.83121 −2.70571 −1.19178 0.220161 −3.54288
1.20 −2.13485 −1.44998 2.55757 −1.78016 3.09549 −0.238675 −1.19032 −0.897552 3.80036
See next 80 embeddings (of 140 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.140
Significant digits:
Format:

Inner twists

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

Atkin-Lehner signs

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