Properties

Label 6019.2.a.d
Level 6019
Weight 2
Character orbit 6019.a
Self dual Yes
Analytic conductor 48.062
Analytic rank 0
Dimension 123
CM No

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Newspace parameters

Level: \( N \) = \( 6019 = 13 \cdot 463 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6019.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.0619569766\)
Analytic rank: \(0\)
Dimension: \(123\)
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.

\(\operatorname{Tr}(f)(q) = \) \(123q \) \(\mathstrut +\mathstrut 10q^{2} \) \(\mathstrut +\mathstrut q^{3} \) \(\mathstrut +\mathstrut 136q^{4} \) \(\mathstrut +\mathstrut 46q^{5} \) \(\mathstrut +\mathstrut 16q^{6} \) \(\mathstrut +\mathstrut 12q^{7} \) \(\mathstrut +\mathstrut 30q^{8} \) \(\mathstrut +\mathstrut 154q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \(123q \) \(\mathstrut +\mathstrut 10q^{2} \) \(\mathstrut +\mathstrut q^{3} \) \(\mathstrut +\mathstrut 136q^{4} \) \(\mathstrut +\mathstrut 46q^{5} \) \(\mathstrut +\mathstrut 16q^{6} \) \(\mathstrut +\mathstrut 12q^{7} \) \(\mathstrut +\mathstrut 30q^{8} \) \(\mathstrut +\mathstrut 154q^{9} \) \(\mathstrut +\mathstrut 5q^{10} \) \(\mathstrut +\mathstrut 53q^{11} \) \(\mathstrut -\mathstrut 6q^{12} \) \(\mathstrut -\mathstrut 123q^{13} \) \(\mathstrut +\mathstrut 21q^{14} \) \(\mathstrut +\mathstrut 29q^{15} \) \(\mathstrut +\mathstrut 166q^{16} \) \(\mathstrut -\mathstrut 35q^{17} \) \(\mathstrut +\mathstrut 28q^{18} \) \(\mathstrut +\mathstrut 23q^{19} \) \(\mathstrut +\mathstrut 93q^{20} \) \(\mathstrut +\mathstrut 72q^{21} \) \(\mathstrut +\mathstrut 8q^{22} \) \(\mathstrut +\mathstrut 42q^{23} \) \(\mathstrut +\mathstrut 55q^{24} \) \(\mathstrut +\mathstrut 153q^{25} \) \(\mathstrut -\mathstrut 10q^{26} \) \(\mathstrut +\mathstrut 7q^{27} \) \(\mathstrut +\mathstrut 39q^{28} \) \(\mathstrut +\mathstrut 86q^{29} \) \(\mathstrut +\mathstrut 44q^{30} \) \(\mathstrut +\mathstrut 16q^{31} \) \(\mathstrut +\mathstrut 70q^{32} \) \(\mathstrut +\mathstrut 40q^{33} \) \(\mathstrut +\mathstrut 10q^{34} \) \(\mathstrut +\mathstrut 6q^{35} \) \(\mathstrut +\mathstrut 222q^{36} \) \(\mathstrut +\mathstrut 52q^{37} \) \(\mathstrut +\mathstrut 12q^{38} \) \(\mathstrut -\mathstrut q^{39} \) \(\mathstrut +\mathstrut 14q^{40} \) \(\mathstrut +\mathstrut 80q^{41} \) \(\mathstrut +\mathstrut 29q^{42} \) \(\mathstrut +\mathstrut 2q^{43} \) \(\mathstrut +\mathstrut 143q^{44} \) \(\mathstrut +\mathstrut 137q^{45} \) \(\mathstrut +\mathstrut 39q^{46} \) \(\mathstrut +\mathstrut 45q^{47} \) \(\mathstrut -\mathstrut 27q^{48} \) \(\mathstrut +\mathstrut 163q^{49} \) \(\mathstrut +\mathstrut 102q^{50} \) \(\mathstrut +\mathstrut 48q^{51} \) \(\mathstrut -\mathstrut 136q^{52} \) \(\mathstrut +\mathstrut 117q^{53} \) \(\mathstrut +\mathstrut 75q^{54} \) \(\mathstrut +\mathstrut 20q^{55} \) \(\mathstrut +\mathstrut 88q^{56} \) \(\mathstrut +\mathstrut 67q^{57} \) \(\mathstrut +\mathstrut 56q^{58} \) \(\mathstrut +\mathstrut 88q^{59} \) \(\mathstrut +\mathstrut 96q^{60} \) \(\mathstrut +\mathstrut 57q^{61} \) \(\mathstrut -\mathstrut 13q^{62} \) \(\mathstrut +\mathstrut 48q^{63} \) \(\mathstrut +\mathstrut 228q^{64} \) \(\mathstrut -\mathstrut 46q^{65} \) \(\mathstrut +\mathstrut 28q^{66} \) \(\mathstrut +\mathstrut 43q^{67} \) \(\mathstrut -\mathstrut 56q^{68} \) \(\mathstrut +\mathstrut 92q^{69} \) \(\mathstrut +\mathstrut 14q^{70} \) \(\mathstrut +\mathstrut 90q^{71} \) \(\mathstrut +\mathstrut 98q^{72} \) \(\mathstrut +\mathstrut 25q^{73} \) \(\mathstrut +\mathstrut 80q^{74} \) \(\mathstrut +\mathstrut 21q^{75} \) \(\mathstrut +\mathstrut 75q^{76} \) \(\mathstrut +\mathstrut 112q^{77} \) \(\mathstrut -\mathstrut 16q^{78} \) \(\mathstrut +\mathstrut 36q^{79} \) \(\mathstrut +\mathstrut 208q^{80} \) \(\mathstrut +\mathstrut 231q^{81} \) \(\mathstrut -\mathstrut 27q^{82} \) \(\mathstrut +\mathstrut 93q^{83} \) \(\mathstrut +\mathstrut 175q^{84} \) \(\mathstrut +\mathstrut 77q^{85} \) \(\mathstrut +\mathstrut 199q^{86} \) \(\mathstrut +\mathstrut 15q^{87} \) \(\mathstrut +\mathstrut 43q^{88} \) \(\mathstrut +\mathstrut 140q^{89} \) \(\mathstrut +\mathstrut 11q^{90} \) \(\mathstrut -\mathstrut 12q^{91} \) \(\mathstrut +\mathstrut 93q^{92} \) \(\mathstrut +\mathstrut 140q^{93} \) \(\mathstrut +\mathstrut 4q^{94} \) \(\mathstrut +\mathstrut 23q^{95} \) \(\mathstrut +\mathstrut 105q^{96} \) \(\mathstrut +\mathstrut 43q^{97} \) \(\mathstrut +\mathstrut 67q^{98} \) \(\mathstrut +\mathstrut 140q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 −2.75439 −0.861643 5.58668 3.86069 2.37330 2.91861 −9.87912 −2.25757 −10.6339
1.2 −2.74057 −2.54852 5.51070 −0.432732 6.98439 3.36424 −9.62130 3.49496 1.18593
1.3 −2.71192 −2.81974 5.35451 4.11778 7.64691 −3.85646 −9.09715 4.95095 −11.1671
1.4 −2.69112 1.73469 5.24211 2.53592 −4.66825 −4.16450 −8.72491 0.00913932 −6.82446
1.5 −2.68053 2.57455 5.18522 0.534092 −6.90114 −0.399106 −8.53805 3.62830 −1.43165
1.6 −2.65517 −0.380089 5.04992 1.30385 1.00920 0.922271 −8.09806 −2.85553 −3.46193
1.7 −2.60439 −3.42443 4.78284 −1.92258 8.91854 −3.26289 −7.24759 8.72671 5.00714
1.8 −2.52129 0.498790 4.35689 −0.537697 −1.25759 −2.34122 −5.94240 −2.75121 1.35569
1.9 −2.52093 1.18363 4.35509 −0.839879 −2.98385 2.35424 −5.93701 −1.59902 2.11728
1.10 −2.49040 −2.13188 4.20211 −1.49942 5.30925 −0.951507 −5.48415 1.54493 3.73417
1.11 −2.47080 2.36731 4.10488 −1.23232 −5.84916 4.18566 −5.20074 2.60415 3.04483
1.12 −2.26767 −1.90418 3.14232 −3.16055 4.31804 −3.88251 −2.59040 0.625886 7.16707
1.13 −2.26442 2.63903 3.12758 3.87429 −5.97587 0.802453 −2.55330 3.96450 −8.77301
1.14 −2.25898 −0.131578 3.10301 3.21477 0.297232 0.192917 −2.49169 −2.98269 −7.26212
1.15 −2.22237 3.41646 2.93895 1.79804 −7.59266 3.28634 −2.08670 8.67221 −3.99592
1.16 −2.19076 0.906147 2.79943 −2.56920 −1.98515 −1.27799 −1.75137 −2.17890 5.62849
1.17 −2.17075 −1.42264 2.71217 −2.44924 3.08820 1.96298 −1.54596 −0.976102 5.31670
1.18 −2.16481 1.72504 2.68638 −0.175994 −3.73438 −2.81780 −1.48588 −0.0242310 0.380992
1.19 −2.14591 −1.26575 2.60492 3.62169 2.71619 0.00950737 −1.29811 −1.39787 −7.77182
1.20 −2.11210 −0.313775 2.46095 −4.01398 0.662722 2.82593 −0.973578 −2.90155 8.47792
See next 80 embeddings (of 123 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.123
Significant digits:
Format:

Inner twists

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

Atkin-Lehner signs

\( p \) Sign
\(13\) \(1\)
\(463\) \(-1\)

Hecke kernels

This newform can be constructed as the kernel of the linear operator \(T_{2}^{123} - \cdots\) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(6019))\).