Properties

Label 6023.2.a.b
Level 6023
Weight 2
Character orbit 6023.a
Self dual Yes
Analytic conductor 48.094
Analytic rank 1
Dimension 99
CM No

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Newspace parameters

Level: \( N \) = \( 6023 = 19 \cdot 317 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6023.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.0938971374\)
Analytic rank: \(1\)
Dimension: \(99\)
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.

\(\operatorname{Tr}(f)(q) = \) \(99q \) \(\mathstrut -\mathstrut 4q^{2} \) \(\mathstrut -\mathstrut 3q^{3} \) \(\mathstrut +\mathstrut 80q^{4} \) \(\mathstrut -\mathstrut 15q^{5} \) \(\mathstrut -\mathstrut 12q^{6} \) \(\mathstrut -\mathstrut 19q^{7} \) \(\mathstrut -\mathstrut 12q^{8} \) \(\mathstrut +\mathstrut 58q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \(99q \) \(\mathstrut -\mathstrut 4q^{2} \) \(\mathstrut -\mathstrut 3q^{3} \) \(\mathstrut +\mathstrut 80q^{4} \) \(\mathstrut -\mathstrut 15q^{5} \) \(\mathstrut -\mathstrut 12q^{6} \) \(\mathstrut -\mathstrut 19q^{7} \) \(\mathstrut -\mathstrut 12q^{8} \) \(\mathstrut +\mathstrut 58q^{9} \) \(\mathstrut -\mathstrut 6q^{10} \) \(\mathstrut -\mathstrut 9q^{11} \) \(\mathstrut -\mathstrut 27q^{12} \) \(\mathstrut -\mathstrut 28q^{13} \) \(\mathstrut -\mathstrut 13q^{14} \) \(\mathstrut -\mathstrut 10q^{15} \) \(\mathstrut +\mathstrut 38q^{16} \) \(\mathstrut -\mathstrut 36q^{17} \) \(\mathstrut -\mathstrut 14q^{18} \) \(\mathstrut -\mathstrut 99q^{19} \) \(\mathstrut -\mathstrut 34q^{20} \) \(\mathstrut -\mathstrut 20q^{21} \) \(\mathstrut -\mathstrut 53q^{22} \) \(\mathstrut -\mathstrut 38q^{23} \) \(\mathstrut -\mathstrut 25q^{24} \) \(\mathstrut -\mathstrut 8q^{25} \) \(\mathstrut -\mathstrut 3q^{26} \) \(\mathstrut -\mathstrut 3q^{27} \) \(\mathstrut -\mathstrut 63q^{28} \) \(\mathstrut -\mathstrut 34q^{29} \) \(\mathstrut -\mathstrut 30q^{30} \) \(\mathstrut -\mathstrut 16q^{31} \) \(\mathstrut -\mathstrut 43q^{32} \) \(\mathstrut -\mathstrut 41q^{33} \) \(\mathstrut -\mathstrut 14q^{34} \) \(\mathstrut -\mathstrut 25q^{35} \) \(\mathstrut -\mathstrut 16q^{36} \) \(\mathstrut -\mathstrut 80q^{37} \) \(\mathstrut +\mathstrut 4q^{38} \) \(\mathstrut -\mathstrut 48q^{39} \) \(\mathstrut -\mathstrut 10q^{40} \) \(\mathstrut -\mathstrut 32q^{41} \) \(\mathstrut -\mathstrut 37q^{42} \) \(\mathstrut -\mathstrut 76q^{43} \) \(\mathstrut -\mathstrut 21q^{44} \) \(\mathstrut -\mathstrut 53q^{45} \) \(\mathstrut -\mathstrut 23q^{46} \) \(\mathstrut -\mathstrut 31q^{47} \) \(\mathstrut -\mathstrut 74q^{48} \) \(\mathstrut -\mathstrut 32q^{49} \) \(\mathstrut -\mathstrut 29q^{50} \) \(\mathstrut -\mathstrut 30q^{51} \) \(\mathstrut -\mathstrut 71q^{52} \) \(\mathstrut -\mathstrut 35q^{53} \) \(\mathstrut -\mathstrut 80q^{54} \) \(\mathstrut -\mathstrut 45q^{55} \) \(\mathstrut -\mathstrut 33q^{56} \) \(\mathstrut +\mathstrut 3q^{57} \) \(\mathstrut -\mathstrut 91q^{58} \) \(\mathstrut +\mathstrut 12q^{59} \) \(\mathstrut -\mathstrut 56q^{60} \) \(\mathstrut -\mathstrut 61q^{61} \) \(\mathstrut -\mathstrut 46q^{62} \) \(\mathstrut -\mathstrut 43q^{63} \) \(\mathstrut -\mathstrut 30q^{64} \) \(\mathstrut -\mathstrut 46q^{65} \) \(\mathstrut -\mathstrut 75q^{66} \) \(\mathstrut -\mathstrut 26q^{67} \) \(\mathstrut -\mathstrut 55q^{68} \) \(\mathstrut -\mathstrut 45q^{69} \) \(\mathstrut -\mathstrut 76q^{70} \) \(\mathstrut -\mathstrut 41q^{71} \) \(\mathstrut -\mathstrut 77q^{72} \) \(\mathstrut -\mathstrut 143q^{73} \) \(\mathstrut -\mathstrut 64q^{74} \) \(\mathstrut -\mathstrut 8q^{75} \) \(\mathstrut -\mathstrut 80q^{76} \) \(\mathstrut -\mathstrut 58q^{77} \) \(\mathstrut -\mathstrut 34q^{78} \) \(\mathstrut -\mathstrut 22q^{79} \) \(\mathstrut -\mathstrut 36q^{80} \) \(\mathstrut -\mathstrut 81q^{81} \) \(\mathstrut -\mathstrut 109q^{82} \) \(\mathstrut -\mathstrut 7q^{83} \) \(\mathstrut -\mathstrut 6q^{84} \) \(\mathstrut -\mathstrut 80q^{85} \) \(\mathstrut +\mathstrut 32q^{86} \) \(\mathstrut -\mathstrut 57q^{87} \) \(\mathstrut -\mathstrut 120q^{88} \) \(\mathstrut -\mathstrut 28q^{89} \) \(\mathstrut -\mathstrut 12q^{90} \) \(\mathstrut -\mathstrut 30q^{91} \) \(\mathstrut -\mathstrut 107q^{92} \) \(\mathstrut -\mathstrut 121q^{93} \) \(\mathstrut +\mathstrut 8q^{94} \) \(\mathstrut +\mathstrut 15q^{95} \) \(\mathstrut +\mathstrut 4q^{96} \) \(\mathstrut -\mathstrut 128q^{97} \) \(\mathstrut +\mathstrut 54q^{98} \) \(\mathstrut -\mathstrut 34q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 −2.79086 −1.66708 5.78891 1.47477 4.65258 −1.60538 −10.5743 −0.220852 −4.11587
1.2 −2.66510 −2.16013 5.10274 −2.11668 5.75694 −1.28803 −8.26911 1.66614 5.64116
1.3 −2.63080 −0.151619 4.92110 −0.321250 0.398879 −0.565304 −7.68484 −2.97701 0.845143
1.4 −2.62992 1.18387 4.91650 1.04484 −3.11349 0.263404 −7.67017 −1.59845 −2.74784
1.5 −2.57189 2.00338 4.61464 2.67910 −5.15249 −0.0453210 −6.72459 1.01355 −6.89035
1.6 −2.56636 2.86321 4.58620 −1.49629 −7.34803 −1.31440 −6.63713 5.19797 3.84001
1.7 −2.48734 −0.305991 4.18686 −0.333485 0.761103 2.33440 −5.43948 −2.90637 0.829491
1.8 −2.33180 −3.18012 3.43727 0.827568 7.41539 −0.00201560 −3.35142 7.11317 −1.92972
1.9 −2.32426 −2.85691 3.40220 −3.59754 6.64022 −1.30166 −3.25907 5.16196 8.36162
1.10 −2.31886 2.08746 3.37709 −2.67469 −4.84053 −2.80565 −3.19328 1.35751 6.20222
1.11 −2.31836 −0.700819 3.37481 −1.53243 1.62475 2.29352 −3.18731 −2.50885 3.55272
1.12 −2.30551 2.60917 3.31537 −2.40173 −6.01546 3.07987 −3.03260 3.80775 5.53721
1.13 −2.20989 −1.74865 2.88361 1.63174 3.86432 4.01021 −1.95267 0.0577689 −3.60597
1.14 −2.20648 −1.66546 2.86855 2.85921 3.67480 −0.996345 −1.91643 −0.226251 −6.30878
1.15 −2.19313 1.00492 2.80981 −2.58247 −2.20392 −2.47276 −1.77602 −1.99014 5.66370
1.16 −2.15033 −0.758271 2.62390 −3.61423 1.63053 −3.46519 −1.34159 −2.42502 7.77178
1.17 −1.96796 −0.967508 1.87288 0.188751 1.90402 −4.91446 0.250172 −2.06393 −0.371455
1.18 −1.95928 1.09252 1.83878 1.35010 −2.14055 3.30535 0.315883 −1.80641 −2.64522
1.19 −1.90532 0.192511 1.63023 0.483590 −0.366795 3.15438 0.704532 −2.96294 −0.921392
1.20 −1.88369 2.22834 1.54829 0.640943 −4.19751 −4.86422 0.850890 1.96551 −1.20734
See all 99 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.99
Significant digits:
Format:

Inner twists

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

Atkin-Lehner signs

\( p \) Sign
\(19\) \(1\)
\(317\) \(1\)