Properties

Label 6001.2.a.a
Level 6001
Weight 2
Character orbit 6001.a
Self dual Yes
Analytic conductor 47.918
Analytic rank 1
Dimension 113
CM No

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Newspace parameters

Level: \( N \) = \( 6001 = 17 \cdot 353 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6001.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(47.918226253\)
Analytic rank: \(1\)
Dimension: \(113\)
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.

\(\operatorname{Tr}(f)(q) = \) \(113q \) \(\mathstrut -\mathstrut 11q^{2} \) \(\mathstrut -\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 103q^{4} \) \(\mathstrut -\mathstrut 19q^{5} \) \(\mathstrut -\mathstrut 13q^{6} \) \(\mathstrut +\mathstrut 11q^{7} \) \(\mathstrut -\mathstrut 36q^{8} \) \(\mathstrut +\mathstrut 94q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \(113q \) \(\mathstrut -\mathstrut 11q^{2} \) \(\mathstrut -\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 103q^{4} \) \(\mathstrut -\mathstrut 19q^{5} \) \(\mathstrut -\mathstrut 13q^{6} \) \(\mathstrut +\mathstrut 11q^{7} \) \(\mathstrut -\mathstrut 36q^{8} \) \(\mathstrut +\mathstrut 94q^{9} \) \(\mathstrut -\mathstrut 5q^{10} \) \(\mathstrut -\mathstrut 40q^{11} \) \(\mathstrut -\mathstrut 19q^{12} \) \(\mathstrut -\mathstrut 18q^{13} \) \(\mathstrut -\mathstrut 48q^{14} \) \(\mathstrut -\mathstrut 63q^{15} \) \(\mathstrut +\mathstrut 79q^{16} \) \(\mathstrut -\mathstrut 113q^{17} \) \(\mathstrut -\mathstrut 32q^{18} \) \(\mathstrut -\mathstrut 46q^{19} \) \(\mathstrut -\mathstrut 56q^{20} \) \(\mathstrut -\mathstrut 46q^{21} \) \(\mathstrut +\mathstrut 14q^{22} \) \(\mathstrut -\mathstrut 35q^{23} \) \(\mathstrut -\mathstrut 42q^{24} \) \(\mathstrut +\mathstrut 88q^{25} \) \(\mathstrut -\mathstrut 89q^{26} \) \(\mathstrut -\mathstrut 41q^{27} \) \(\mathstrut +\mathstrut 20q^{28} \) \(\mathstrut -\mathstrut 51q^{29} \) \(\mathstrut -\mathstrut 18q^{30} \) \(\mathstrut -\mathstrut 57q^{31} \) \(\mathstrut -\mathstrut 93q^{32} \) \(\mathstrut -\mathstrut 40q^{33} \) \(\mathstrut +\mathstrut 11q^{34} \) \(\mathstrut -\mathstrut 69q^{35} \) \(\mathstrut +\mathstrut 18q^{36} \) \(\mathstrut +\mathstrut 16q^{37} \) \(\mathstrut -\mathstrut 74q^{38} \) \(\mathstrut -\mathstrut 51q^{39} \) \(\mathstrut +\mathstrut 2q^{40} \) \(\mathstrut -\mathstrut 87q^{41} \) \(\mathstrut -\mathstrut 23q^{42} \) \(\mathstrut -\mathstrut 32q^{43} \) \(\mathstrut -\mathstrut 110q^{44} \) \(\mathstrut -\mathstrut 17q^{45} \) \(\mathstrut -\mathstrut 17q^{46} \) \(\mathstrut -\mathstrut 161q^{47} \) \(\mathstrut -\mathstrut 36q^{48} \) \(\mathstrut +\mathstrut 56q^{49} \) \(\mathstrut -\mathstrut 69q^{50} \) \(\mathstrut +\mathstrut 11q^{51} \) \(\mathstrut -\mathstrut 49q^{52} \) \(\mathstrut -\mathstrut 48q^{53} \) \(\mathstrut -\mathstrut 38q^{54} \) \(\mathstrut -\mathstrut 79q^{55} \) \(\mathstrut -\mathstrut 171q^{56} \) \(\mathstrut +\mathstrut 20q^{57} \) \(\mathstrut +\mathstrut 13q^{58} \) \(\mathstrut -\mathstrut 174q^{59} \) \(\mathstrut -\mathstrut 146q^{60} \) \(\mathstrut -\mathstrut 34q^{61} \) \(\mathstrut -\mathstrut 34q^{62} \) \(\mathstrut -\mathstrut 14q^{63} \) \(\mathstrut +\mathstrut 62q^{64} \) \(\mathstrut -\mathstrut 22q^{65} \) \(\mathstrut -\mathstrut 60q^{66} \) \(\mathstrut -\mathstrut 50q^{67} \) \(\mathstrut -\mathstrut 103q^{68} \) \(\mathstrut -\mathstrut 59q^{69} \) \(\mathstrut -\mathstrut 58q^{70} \) \(\mathstrut -\mathstrut 189q^{71} \) \(\mathstrut -\mathstrut 123q^{72} \) \(\mathstrut -\mathstrut 4q^{73} \) \(\mathstrut -\mathstrut 24q^{74} \) \(\mathstrut -\mathstrut 106q^{75} \) \(\mathstrut -\mathstrut 92q^{76} \) \(\mathstrut -\mathstrut 78q^{77} \) \(\mathstrut -\mathstrut 42q^{78} \) \(\mathstrut +\mathstrut 8q^{79} \) \(\mathstrut -\mathstrut 150q^{80} \) \(\mathstrut +\mathstrut 13q^{81} \) \(\mathstrut +\mathstrut 6q^{82} \) \(\mathstrut -\mathstrut 109q^{83} \) \(\mathstrut -\mathstrut 114q^{84} \) \(\mathstrut +\mathstrut 19q^{85} \) \(\mathstrut -\mathstrut 116q^{86} \) \(\mathstrut -\mathstrut 106q^{87} \) \(\mathstrut +\mathstrut 54q^{88} \) \(\mathstrut -\mathstrut 170q^{89} \) \(\mathstrut -\mathstrut q^{90} \) \(\mathstrut -\mathstrut 43q^{91} \) \(\mathstrut -\mathstrut 94q^{92} \) \(\mathstrut -\mathstrut 69q^{93} \) \(\mathstrut -\mathstrut 35q^{94} \) \(\mathstrut -\mathstrut 78q^{95} \) \(\mathstrut -\mathstrut 44q^{96} \) \(\mathstrut -\mathstrut 3q^{97} \) \(\mathstrut -\mathstrut 68q^{98} \) \(\mathstrut -\mathstrut 119q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 −2.78095 −2.69588 5.73371 2.30800 7.49712 4.50681 −10.3833 4.26777 −6.41845
1.2 −2.76448 −0.301476 5.64235 −1.88471 0.833425 2.57260 −10.0692 −2.90911 5.21024
1.3 −2.72078 −0.920111 5.40267 −2.98260 2.50342 −1.43517 −9.25792 −2.15340 8.11501
1.4 −2.69808 2.45523 5.27961 −1.37053 −6.62441 5.08280 −8.84865 3.02818 3.69780
1.5 −2.64384 −0.876989 4.98991 2.40505 2.31862 1.36446 −7.90487 −2.23089 −6.35858
1.6 −2.63611 2.68277 4.94905 −3.99469 −7.07208 −3.60242 −7.77401 4.19728 10.5304
1.7 −2.63080 1.97535 4.92113 2.13953 −5.19675 1.65541 −7.68492 0.902000 −5.62867
1.8 −2.58651 −0.844986 4.69006 −0.771482 2.18557 −2.98561 −6.95787 −2.28600 1.99545
1.9 −2.50694 0.525806 4.28474 −1.87738 −1.31816 4.48031 −5.72770 −2.72353 4.70647
1.10 −2.49624 1.48745 4.23122 −3.58200 −3.71302 1.79069 −5.56966 −0.787505 8.94153
1.11 −2.49146 −2.38691 4.20738 −2.02282 5.94689 1.32918 −5.49960 2.69734 5.03978
1.12 −2.49070 2.79631 4.20359 2.44678 −6.96477 −1.91297 −5.48850 4.81934 −6.09421
1.13 −2.30912 −2.56184 3.33205 −3.64906 5.91560 −1.49745 −3.07586 3.56301 8.42614
1.14 −2.26295 −1.98147 3.12095 3.45141 4.48397 −1.45595 −2.53665 0.926221 −7.81036
1.15 −2.22225 −0.120604 2.93840 1.74504 0.268012 −3.61581 −2.08537 −2.98545 −3.87792
1.16 −2.20707 2.35834 2.87116 2.79748 −5.20501 −1.23289 −1.92271 2.56174 −6.17423
1.17 −2.18121 0.0139647 2.75766 −0.236603 −0.0304599 2.78463 −1.65261 −2.99980 0.516079
1.18 −2.15299 2.37258 2.63537 −0.231510 −5.10813 3.32403 −1.36794 2.62912 0.498439
1.19 −2.14256 −2.11238 2.59055 1.25903 4.52589 1.44603 −1.26528 1.46215 −2.69753
1.20 −2.09226 2.92082 2.37755 −1.12068 −6.11112 −1.50686 −0.789928 5.53120 2.34475
See next 80 embeddings (of 113 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.113
Significant digits:
Format:

Inner twists

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

Atkin-Lehner signs

\( p \) Sign
\(17\) \(1\)
\(353\) \(1\)