Properties

Label 8031.2.a.c
Level 8031
Weight 2
Character orbit 8031.a
Self dual Yes
Analytic conductor 64.128
Analytic rank 0
Dimension 121
CM No

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Newspace parameters

Level: \( N \) = \( 8031 = 3 \cdot 2677 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8031.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.1278578633\)
Analytic rank: \(0\)
Dimension: \(121\)
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.

\(\operatorname{Tr}(f)(q) = \) \(121q \) \(\mathstrut +\mathstrut 7q^{2} \) \(\mathstrut -\mathstrut 121q^{3} \) \(\mathstrut +\mathstrut 123q^{4} \) \(\mathstrut +\mathstrut 24q^{5} \) \(\mathstrut -\mathstrut 7q^{6} \) \(\mathstrut -\mathstrut 14q^{7} \) \(\mathstrut +\mathstrut 18q^{8} \) \(\mathstrut +\mathstrut 121q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \(121q \) \(\mathstrut +\mathstrut 7q^{2} \) \(\mathstrut -\mathstrut 121q^{3} \) \(\mathstrut +\mathstrut 123q^{4} \) \(\mathstrut +\mathstrut 24q^{5} \) \(\mathstrut -\mathstrut 7q^{6} \) \(\mathstrut -\mathstrut 14q^{7} \) \(\mathstrut +\mathstrut 18q^{8} \) \(\mathstrut +\mathstrut 121q^{9} \) \(\mathstrut +\mathstrut 18q^{10} \) \(\mathstrut +\mathstrut 32q^{11} \) \(\mathstrut -\mathstrut 123q^{12} \) \(\mathstrut +\mathstrut 2q^{13} \) \(\mathstrut +\mathstrut 37q^{14} \) \(\mathstrut -\mathstrut 24q^{15} \) \(\mathstrut +\mathstrut 131q^{16} \) \(\mathstrut +\mathstrut 87q^{17} \) \(\mathstrut +\mathstrut 7q^{18} \) \(\mathstrut -\mathstrut 10q^{19} \) \(\mathstrut +\mathstrut 60q^{20} \) \(\mathstrut +\mathstrut 14q^{21} \) \(\mathstrut -\mathstrut 22q^{22} \) \(\mathstrut +\mathstrut 31q^{23} \) \(\mathstrut -\mathstrut 18q^{24} \) \(\mathstrut +\mathstrut 147q^{25} \) \(\mathstrut +\mathstrut 37q^{26} \) \(\mathstrut -\mathstrut 121q^{27} \) \(\mathstrut -\mathstrut 29q^{28} \) \(\mathstrut +\mathstrut 68q^{29} \) \(\mathstrut -\mathstrut 18q^{30} \) \(\mathstrut +\mathstrut 25q^{31} \) \(\mathstrut +\mathstrut 43q^{32} \) \(\mathstrut -\mathstrut 32q^{33} \) \(\mathstrut +\mathstrut 27q^{34} \) \(\mathstrut +\mathstrut 51q^{35} \) \(\mathstrut +\mathstrut 123q^{36} \) \(\mathstrut -\mathstrut 4q^{37} \) \(\mathstrut +\mathstrut 36q^{38} \) \(\mathstrut -\mathstrut 2q^{39} \) \(\mathstrut +\mathstrut 61q^{40} \) \(\mathstrut +\mathstrut 132q^{41} \) \(\mathstrut -\mathstrut 37q^{42} \) \(\mathstrut -\mathstrut 91q^{43} \) \(\mathstrut +\mathstrut 94q^{44} \) \(\mathstrut +\mathstrut 24q^{45} \) \(\mathstrut +\mathstrut 39q^{47} \) \(\mathstrut -\mathstrut 131q^{48} \) \(\mathstrut +\mathstrut 217q^{49} \) \(\mathstrut +\mathstrut 54q^{50} \) \(\mathstrut -\mathstrut 87q^{51} \) \(\mathstrut -\mathstrut 12q^{52} \) \(\mathstrut +\mathstrut 55q^{53} \) \(\mathstrut -\mathstrut 7q^{54} \) \(\mathstrut +\mathstrut 7q^{55} \) \(\mathstrut +\mathstrut 104q^{56} \) \(\mathstrut +\mathstrut 10q^{57} \) \(\mathstrut -\mathstrut 3q^{58} \) \(\mathstrut +\mathstrut 58q^{59} \) \(\mathstrut -\mathstrut 60q^{60} \) \(\mathstrut +\mathstrut 126q^{61} \) \(\mathstrut +\mathstrut 74q^{62} \) \(\mathstrut -\mathstrut 14q^{63} \) \(\mathstrut +\mathstrut 122q^{64} \) \(\mathstrut +\mathstrut 128q^{65} \) \(\mathstrut +\mathstrut 22q^{66} \) \(\mathstrut -\mathstrut 139q^{67} \) \(\mathstrut +\mathstrut 190q^{68} \) \(\mathstrut -\mathstrut 31q^{69} \) \(\mathstrut -\mathstrut 18q^{70} \) \(\mathstrut +\mathstrut 37q^{71} \) \(\mathstrut +\mathstrut 18q^{72} \) \(\mathstrut +\mathstrut 84q^{73} \) \(\mathstrut +\mathstrut 79q^{74} \) \(\mathstrut -\mathstrut 147q^{75} \) \(\mathstrut +\mathstrut 23q^{76} \) \(\mathstrut +\mathstrut 95q^{77} \) \(\mathstrut -\mathstrut 37q^{78} \) \(\mathstrut -\mathstrut 14q^{79} \) \(\mathstrut +\mathstrut 145q^{80} \) \(\mathstrut +\mathstrut 121q^{81} \) \(\mathstrut +\mathstrut 9q^{82} \) \(\mathstrut +\mathstrut 58q^{83} \) \(\mathstrut +\mathstrut 29q^{84} \) \(\mathstrut +\mathstrut 32q^{85} \) \(\mathstrut +\mathstrut 28q^{86} \) \(\mathstrut -\mathstrut 68q^{87} \) \(\mathstrut -\mathstrut 84q^{88} \) \(\mathstrut +\mathstrut 198q^{89} \) \(\mathstrut +\mathstrut 18q^{90} \) \(\mathstrut +\mathstrut 5q^{91} \) \(\mathstrut +\mathstrut 98q^{92} \) \(\mathstrut -\mathstrut 25q^{93} \) \(\mathstrut +\mathstrut 9q^{94} \) \(\mathstrut +\mathstrut 42q^{95} \) \(\mathstrut -\mathstrut 43q^{96} \) \(\mathstrut +\mathstrut 73q^{97} \) \(\mathstrut +\mathstrut 69q^{98} \) \(\mathstrut +\mathstrut 32q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 −2.78421 −1.00000 5.75185 0.686525 2.78421 −0.869505 −10.4459 1.00000 −1.91143
1.2 −2.74757 −1.00000 5.54913 2.21252 2.74757 −1.55769 −9.75147 1.00000 −6.07904
1.3 −2.68356 −1.00000 5.20147 −3.95156 2.68356 −4.75750 −8.59132 1.00000 10.6042
1.4 −2.64556 −1.00000 4.99897 −1.40412 2.64556 −0.985442 −7.93394 1.00000 3.71467
1.5 −2.62963 −1.00000 4.91495 3.86074 2.62963 3.78778 −7.66525 1.00000 −10.1523
1.6 −2.60983 −1.00000 4.81123 0.810523 2.60983 −4.83270 −7.33685 1.00000 −2.11533
1.7 −2.47165 −1.00000 4.10906 −0.0868982 2.47165 −4.58387 −5.21287 1.00000 0.214782
1.8 −2.46498 −1.00000 4.07611 3.49515 2.46498 1.81173 −5.11755 1.00000 −8.61546
1.9 −2.44537 −1.00000 3.97985 0.860526 2.44537 −1.02072 −4.84146 1.00000 −2.10431
1.10 −2.41661 −1.00000 3.83999 −2.56069 2.41661 −0.401342 −4.44652 1.00000 6.18818
1.11 −2.39891 −1.00000 3.75476 −1.21800 2.39891 −2.25601 −4.20952 1.00000 2.92186
1.12 −2.36975 −1.00000 3.61573 −1.85498 2.36975 4.52062 −3.82888 1.00000 4.39585
1.13 −2.36162 −1.00000 3.57726 0.566306 2.36162 3.15276 −3.72490 1.00000 −1.33740
1.14 −2.35691 −1.00000 3.55501 3.33677 2.35691 −1.10286 −3.66500 1.00000 −7.86445
1.15 −2.31301 −1.00000 3.35001 −2.44479 2.31301 −2.31166 −3.12259 1.00000 5.65482
1.16 −2.29229 −1.00000 3.25458 1.65455 2.29229 2.03484 −2.87586 1.00000 −3.79270
1.17 −2.27538 −1.00000 3.17734 −2.29093 2.27538 1.46815 −2.67889 1.00000 5.21272
1.18 −2.15810 −1.00000 2.65739 −1.43595 2.15810 1.17187 −1.41872 1.00000 3.09891
1.19 −2.11893 −1.00000 2.48988 3.42435 2.11893 −4.49601 −1.03803 1.00000 −7.25596
1.20 −1.99295 −1.00000 1.97186 0.956056 1.99295 2.24151 0.0560744 1.00000 −1.90538
See next 80 embeddings (of 121 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.121
Significant digits:
Format:

Inner twists

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

Atkin-Lehner signs

\( p \) Sign
\(3\) \(1\)
\(2677\) \(-1\)