# 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 Inner twists 1

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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: $$99$$ Coefficient ring index: multiple of None Twist minimal: yes 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.

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

## 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: Complex embeddings Normalized embeddings Satake parameters Satake angles

## Inner twists

This newform does not admit any (nontrivial) inner twists.

## Twists

By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 6023.2.a.b 99

By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
6023.2.a.b 99 1.a even 1 1 trivial

## Atkin-Lehner signs

$$p$$ Sign
$$19$$ $$1$$
$$317$$ $$1$$