Properties

Label 6023.2.a.d
Level 6023
Weight 2
Character orbit 6023.a
Self dual Yes
Analytic conductor 48.094
Analytic rank 0
Dimension 140
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: \(0\)
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.

\(\operatorname{Tr}(f)(q) = \) \(140q \) \(\mathstrut +\mathstrut 4q^{2} \) \(\mathstrut +\mathstrut 3q^{3} \) \(\mathstrut +\mathstrut 162q^{4} \) \(\mathstrut +\mathstrut 13q^{5} \) \(\mathstrut +\mathstrut 12q^{6} \) \(\mathstrut +\mathstrut 25q^{7} \) \(\mathstrut +\mathstrut 12q^{8} \) \(\mathstrut +\mathstrut 181q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \(140q \) \(\mathstrut +\mathstrut 4q^{2} \) \(\mathstrut +\mathstrut 3q^{3} \) \(\mathstrut +\mathstrut 162q^{4} \) \(\mathstrut +\mathstrut 13q^{5} \) \(\mathstrut +\mathstrut 12q^{6} \) \(\mathstrut +\mathstrut 25q^{7} \) \(\mathstrut +\mathstrut 12q^{8} \) \(\mathstrut +\mathstrut 181q^{9} \) \(\mathstrut +\mathstrut 8q^{10} \) \(\mathstrut +\mathstrut 19q^{11} \) \(\mathstrut +\mathstrut 17q^{12} \) \(\mathstrut +\mathstrut 28q^{13} \) \(\mathstrut +\mathstrut 5q^{14} \) \(\mathstrut +\mathstrut 14q^{15} \) \(\mathstrut +\mathstrut 202q^{16} \) \(\mathstrut +\mathstrut 38q^{17} \) \(\mathstrut +\mathstrut 26q^{18} \) \(\mathstrut -\mathstrut 140q^{19} \) \(\mathstrut +\mathstrut 36q^{20} \) \(\mathstrut +\mathstrut 4q^{21} \) \(\mathstrut +\mathstrut 53q^{22} \) \(\mathstrut +\mathstrut 58q^{23} \) \(\mathstrut +\mathstrut 47q^{24} \) \(\mathstrut +\mathstrut 279q^{25} \) \(\mathstrut +\mathstrut 29q^{26} \) \(\mathstrut +\mathstrut 21q^{27} \) \(\mathstrut +\mathstrut 69q^{28} \) \(\mathstrut +\mathstrut 18q^{29} \) \(\mathstrut +\mathstrut 50q^{30} \) \(\mathstrut +\mathstrut 20q^{31} \) \(\mathstrut +\mathstrut 13q^{32} \) \(\mathstrut +\mathstrut 47q^{33} \) \(\mathstrut +\mathstrut 6q^{34} \) \(\mathstrut +\mathstrut 35q^{35} \) \(\mathstrut +\mathstrut 230q^{36} \) \(\mathstrut +\mathstrut 88q^{37} \) \(\mathstrut -\mathstrut 4q^{38} \) \(\mathstrut +\mathstrut 32q^{39} \) \(\mathstrut +\mathstrut 32q^{40} \) \(\mathstrut +\mathstrut 24q^{41} \) \(\mathstrut +\mathstrut 75q^{42} \) \(\mathstrut +\mathstrut 100q^{43} \) \(\mathstrut +\mathstrut 63q^{44} \) \(\mathstrut +\mathstrut 87q^{45} \) \(\mathstrut +\mathstrut 23q^{46} \) \(\mathstrut +\mathstrut 35q^{47} \) \(\mathstrut +\mathstrut 46q^{48} \) \(\mathstrut +\mathstrut 255q^{49} \) \(\mathstrut +\mathstrut 11q^{50} \) \(\mathstrut -\mathstrut 6q^{51} \) \(\mathstrut +\mathstrut 47q^{52} \) \(\mathstrut +\mathstrut 77q^{53} \) \(\mathstrut +\mathstrut 16q^{54} \) \(\mathstrut +\mathstrut 63q^{55} \) \(\mathstrut +\mathstrut 21q^{56} \) \(\mathstrut -\mathstrut 3q^{57} \) \(\mathstrut +\mathstrut 165q^{58} \) \(\mathstrut +\mathstrut 18q^{59} \) \(\mathstrut +\mathstrut 28q^{60} \) \(\mathstrut +\mathstrut 99q^{61} \) \(\mathstrut +\mathstrut 34q^{62} \) \(\mathstrut +\mathstrut 89q^{63} \) \(\mathstrut +\mathstrut 298q^{64} \) \(\mathstrut +\mathstrut 78q^{65} \) \(\mathstrut -\mathstrut 3q^{66} \) \(\mathstrut +\mathstrut 28q^{67} \) \(\mathstrut +\mathstrut 93q^{68} \) \(\mathstrut +\mathstrut 19q^{69} \) \(\mathstrut +\mathstrut 16q^{70} \) \(\mathstrut +\mathstrut q^{71} \) \(\mathstrut +\mathstrut 43q^{72} \) \(\mathstrut +\mathstrut 201q^{73} \) \(\mathstrut +\mathstrut 32q^{74} \) \(\mathstrut +\mathstrut 22q^{75} \) \(\mathstrut -\mathstrut 162q^{76} \) \(\mathstrut +\mathstrut 86q^{77} \) \(\mathstrut +\mathstrut 122q^{78} \) \(\mathstrut +\mathstrut 58q^{79} \) \(\mathstrut +\mathstrut 92q^{80} \) \(\mathstrut +\mathstrut 288q^{81} \) \(\mathstrut +\mathstrut 143q^{82} \) \(\mathstrut +\mathstrut 57q^{83} \) \(\mathstrut +\mathstrut q^{84} \) \(\mathstrut +\mathstrut 136q^{85} \) \(\mathstrut -\mathstrut 6q^{86} \) \(\mathstrut +\mathstrut 43q^{87} \) \(\mathstrut +\mathstrut 198q^{88} \) \(\mathstrut +\mathstrut 46q^{89} \) \(\mathstrut +\mathstrut 30q^{90} \) \(\mathstrut +\mathstrut 26q^{91} \) \(\mathstrut +\mathstrut 129q^{92} \) \(\mathstrut +\mathstrut 111q^{93} \) \(\mathstrut +\mathstrut 44q^{94} \) \(\mathstrut -\mathstrut 13q^{95} \) \(\mathstrut +\mathstrut 32q^{96} \) \(\mathstrut +\mathstrut 110q^{97} \) \(\mathstrut -\mathstrut 34q^{98} \) \(\mathstrut +\mathstrut 62q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 −2.81146 3.38830 5.90432 1.31579 −9.52607 1.88433 −10.9768 8.48057 −3.69930
1.2 −2.77997 −2.09006 5.72822 0.541434 5.81030 4.43063 −10.3643 1.36835 −1.50517
1.3 −2.76348 −3.02907 5.63680 4.42510 8.37075 −1.32943 −10.0502 6.17524 −12.2287
1.4 −2.74325 1.84551 5.52540 −2.64274 −5.06270 −2.21393 −9.67106 0.405925 7.24969
1.5 −2.71272 −1.70174 5.35887 −3.51340 4.61635 3.49913 −9.11167 −0.104083 9.53088
1.6 −2.67904 −0.649743 5.17727 −3.70919 1.74069 −4.64503 −8.51205 −2.57783 9.93707
1.7 −2.62272 0.254820 4.87868 4.28261 −0.668323 3.95531 −7.54997 −2.93507 −11.2321
1.8 −2.59629 2.14678 4.74071 −3.36546 −5.57365 2.25359 −7.11569 1.60865 8.73769
1.9 −2.57318 −1.88947 4.62125 −0.577572 4.86195 −3.88708 −6.74496 0.570108 1.48620
1.10 −2.56765 0.729440 4.59285 −3.21691 −1.87295 3.04493 −6.65754 −2.46792 8.25992
1.11 −2.54565 1.89511 4.48036 0.316502 −4.82430 4.66425 −6.31414 0.591450 −0.805706
1.12 −2.51714 −1.59250 4.33600 3.04640 4.00854 0.234755 −5.88004 −0.463957 −7.66821
1.13 −2.50460 −0.513198 4.27304 1.36674 1.28536 −1.89861 −5.69306 −2.73663 −3.42314
1.14 −2.48608 −2.16516 4.18058 −0.720530 5.38275 −0.0570474 −5.42110 1.68791 1.79129
1.15 −2.46064 3.05601 4.05473 4.13558 −7.51973 −4.22732 −5.05594 6.33922 −10.1762
1.16 −2.37815 0.382823 3.65560 3.62895 −0.910412 −2.15818 −3.93728 −2.85345 −8.63020
1.17 −2.34544 0.814980 3.50107 0.397454 −1.91148 −3.87514 −3.52066 −2.33581 −0.932204
1.18 −2.24180 −2.80359 3.02567 1.63656 6.28509 0.514582 −2.29934 4.86012 −3.66885
1.19 −2.20474 −3.27519 2.86088 −2.46837 7.22094 4.00346 −1.89803 7.72686 5.44211
1.20 −2.12238 2.91250 2.50448 1.81666 −6.18142 0.226771 −1.07071 5.48264 −3.85564
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
\(19\) \(1\)
\(317\) \(-1\)