Properties

Label 4019.2.a.a
Level 4019
Weight 2
Character orbit 4019.a
Self dual Yes
Analytic conductor 32.092
Analytic rank 1
Dimension 149
CM No

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Newspace parameters

Level: \( N \) = \( 4019 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4019.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.0918765724\)
Analytic rank: \(1\)
Dimension: \(149\)
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.

\(\operatorname{Tr}(f)(q) = \) \(149q \) \(\mathstrut -\mathstrut 8q^{2} \) \(\mathstrut -\mathstrut 12q^{3} \) \(\mathstrut +\mathstrut 124q^{4} \) \(\mathstrut -\mathstrut 36q^{5} \) \(\mathstrut -\mathstrut 45q^{6} \) \(\mathstrut -\mathstrut 32q^{7} \) \(\mathstrut -\mathstrut 21q^{8} \) \(\mathstrut +\mathstrut 115q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \(149q \) \(\mathstrut -\mathstrut 8q^{2} \) \(\mathstrut -\mathstrut 12q^{3} \) \(\mathstrut +\mathstrut 124q^{4} \) \(\mathstrut -\mathstrut 36q^{5} \) \(\mathstrut -\mathstrut 45q^{6} \) \(\mathstrut -\mathstrut 32q^{7} \) \(\mathstrut -\mathstrut 21q^{8} \) \(\mathstrut +\mathstrut 115q^{9} \) \(\mathstrut -\mathstrut 58q^{10} \) \(\mathstrut -\mathstrut 33q^{11} \) \(\mathstrut -\mathstrut 33q^{12} \) \(\mathstrut -\mathstrut 107q^{13} \) \(\mathstrut -\mathstrut 28q^{14} \) \(\mathstrut -\mathstrut 24q^{15} \) \(\mathstrut +\mathstrut 74q^{16} \) \(\mathstrut -\mathstrut 39q^{17} \) \(\mathstrut -\mathstrut 33q^{18} \) \(\mathstrut -\mathstrut 93q^{19} \) \(\mathstrut -\mathstrut 63q^{20} \) \(\mathstrut -\mathstrut 113q^{21} \) \(\mathstrut -\mathstrut 38q^{22} \) \(\mathstrut -\mathstrut 11q^{23} \) \(\mathstrut -\mathstrut 130q^{24} \) \(\mathstrut +\mathstrut 85q^{25} \) \(\mathstrut -\mathstrut 33q^{26} \) \(\mathstrut -\mathstrut 30q^{27} \) \(\mathstrut -\mathstrut 94q^{28} \) \(\mathstrut -\mathstrut 85q^{29} \) \(\mathstrut -\mathstrut 16q^{30} \) \(\mathstrut -\mathstrut 129q^{31} \) \(\mathstrut -\mathstrut 35q^{32} \) \(\mathstrut -\mathstrut 64q^{33} \) \(\mathstrut -\mathstrut 78q^{34} \) \(\mathstrut -\mathstrut 27q^{35} \) \(\mathstrut +\mathstrut 79q^{36} \) \(\mathstrut -\mathstrut 135q^{37} \) \(\mathstrut -\mathstrut 11q^{38} \) \(\mathstrut -\mathstrut 73q^{39} \) \(\mathstrut -\mathstrut 146q^{40} \) \(\mathstrut -\mathstrut 101q^{41} \) \(\mathstrut +\mathstrut 4q^{42} \) \(\mathstrut -\mathstrut 55q^{43} \) \(\mathstrut -\mathstrut 82q^{44} \) \(\mathstrut -\mathstrut 168q^{45} \) \(\mathstrut -\mathstrut 113q^{46} \) \(\mathstrut -\mathstrut 40q^{47} \) \(\mathstrut -\mathstrut 65q^{48} \) \(\mathstrut +\mathstrut 27q^{49} \) \(\mathstrut -\mathstrut 5q^{50} \) \(\mathstrut -\mathstrut 49q^{51} \) \(\mathstrut -\mathstrut 177q^{52} \) \(\mathstrut -\mathstrut 32q^{53} \) \(\mathstrut -\mathstrut 155q^{54} \) \(\mathstrut -\mathstrut 128q^{55} \) \(\mathstrut -\mathstrut 44q^{56} \) \(\mathstrut -\mathstrut 47q^{57} \) \(\mathstrut -\mathstrut 46q^{58} \) \(\mathstrut -\mathstrut 53q^{59} \) \(\mathstrut -\mathstrut 11q^{60} \) \(\mathstrut -\mathstrut 347q^{61} \) \(\mathstrut -\mathstrut 11q^{62} \) \(\mathstrut -\mathstrut 73q^{63} \) \(\mathstrut +\mathstrut q^{64} \) \(\mathstrut -\mathstrut 31q^{65} \) \(\mathstrut -\mathstrut 37q^{66} \) \(\mathstrut -\mathstrut 40q^{67} \) \(\mathstrut -\mathstrut 80q^{68} \) \(\mathstrut -\mathstrut 175q^{69} \) \(\mathstrut -\mathstrut 61q^{70} \) \(\mathstrut -\mathstrut 31q^{71} \) \(\mathstrut -\mathstrut 68q^{72} \) \(\mathstrut -\mathstrut 193q^{73} \) \(\mathstrut -\mathstrut 33q^{74} \) \(\mathstrut -\mathstrut 56q^{75} \) \(\mathstrut -\mathstrut 248q^{76} \) \(\mathstrut -\mathstrut 84q^{77} \) \(\mathstrut +\mathstrut 40q^{78} \) \(\mathstrut -\mathstrut 111q^{79} \) \(\mathstrut -\mathstrut 54q^{80} \) \(\mathstrut +\mathstrut 49q^{81} \) \(\mathstrut -\mathstrut 74q^{82} \) \(\mathstrut -\mathstrut 24q^{83} \) \(\mathstrut -\mathstrut 159q^{84} \) \(\mathstrut -\mathstrut 258q^{85} \) \(\mathstrut -\mathstrut q^{86} \) \(\mathstrut -\mathstrut 66q^{87} \) \(\mathstrut -\mathstrut 97q^{88} \) \(\mathstrut -\mathstrut 76q^{89} \) \(\mathstrut -\mathstrut 75q^{90} \) \(\mathstrut -\mathstrut 134q^{91} \) \(\mathstrut +\mathstrut 31q^{92} \) \(\mathstrut -\mathstrut 97q^{93} \) \(\mathstrut -\mathstrut 111q^{94} \) \(\mathstrut -\mathstrut 14q^{95} \) \(\mathstrut -\mathstrut 216q^{96} \) \(\mathstrut -\mathstrut 140q^{97} \) \(\mathstrut -\mathstrut 13q^{98} \) \(\mathstrut -\mathstrut 116q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 −2.78495 3.42897 5.75594 1.05066 −9.54951 −0.902468 −10.4601 8.75783 −2.92604
1.2 −2.73191 −1.70544 5.46336 2.32218 4.65913 1.19146 −9.46160 −0.0914604 −6.34400
1.3 −2.70774 1.77949 5.33184 1.68400 −4.81839 −4.00894 −9.02175 0.166582 −4.55984
1.4 −2.68954 1.48905 5.23361 2.84645 −4.00487 −1.97182 −8.69693 −0.782716 −7.65564
1.5 −2.62051 −0.192294 4.86706 −1.97989 0.503908 −4.52578 −7.51315 −2.96302 5.18832
1.6 −2.59547 1.08147 4.73647 0.749609 −2.80691 2.15869 −7.10242 −1.83043 −1.94559
1.7 −2.58406 1.99817 4.67739 −2.81422 −5.16341 −2.01468 −6.91855 0.992695 7.27214
1.8 −2.57089 0.190612 4.60945 −1.40475 −0.490042 1.52623 −6.70860 −2.96367 3.61144
1.9 −2.51991 −1.75801 4.34994 3.61499 4.43004 3.76242 −5.92164 0.0906134 −9.10944
1.10 −2.46575 −2.43164 4.07992 2.59428 5.99581 −0.656341 −5.12858 2.91285 −6.39684
1.11 −2.45850 −1.74268 4.04423 −0.525405 4.28438 −0.912805 −5.02575 0.0369224 1.29171
1.12 −2.45807 −2.34751 4.04212 −0.597755 5.77034 −0.214441 −5.01969 2.51079 1.46933
1.13 −2.42490 −1.02548 3.88013 −4.00476 2.48668 −1.16451 −4.55913 −1.94839 9.71114
1.14 −2.40917 −3.09144 3.80411 −1.16894 7.44782 2.97947 −4.34641 6.55703 2.81617
1.15 −2.36640 0.537231 3.59984 −0.969490 −1.27130 3.20883 −3.78587 −2.71138 2.29420
1.16 −2.35135 2.82086 3.52886 0.184417 −6.63284 2.16509 −3.59489 4.95726 −0.433630
1.17 −2.30650 −1.73394 3.31993 −0.392279 3.99934 −3.42422 −3.04443 0.00656301 0.904791
1.18 −2.27033 2.56855 3.15439 −3.84625 −5.83145 2.23399 −2.62085 3.59745 8.73225
1.19 −2.23088 1.97807 2.97683 1.53013 −4.41285 −1.35303 −2.17920 0.912770 −3.41354
1.20 −2.21437 0.176199 2.90346 3.35713 −0.390170 0.00990688 −2.00059 −2.96895 −7.43394
See next 80 embeddings (of 149 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.149
Significant digits:
Format:

Inner twists

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

Atkin-Lehner signs

\( p \) Sign
\(4019\) \(1\)