Properties

Label 6019.2.a.b
Level 6019
Weight 2
Character orbit 6019.a
Self dual Yes
Analytic conductor 48.062
Analytic rank 1
Dimension 101
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: \(1\)
Dimension: \(101\)
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.

\(\operatorname{Tr}(f)(q) = \) \(101q \) \(\mathstrut -\mathstrut 8q^{2} \) \(\mathstrut -\mathstrut 13q^{3} \) \(\mathstrut +\mathstrut 86q^{4} \) \(\mathstrut -\mathstrut 43q^{5} \) \(\mathstrut -\mathstrut 10q^{6} \) \(\mathstrut -\mathstrut q^{7} \) \(\mathstrut -\mathstrut 24q^{8} \) \(\mathstrut +\mathstrut 52q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \(101q \) \(\mathstrut -\mathstrut 8q^{2} \) \(\mathstrut -\mathstrut 13q^{3} \) \(\mathstrut +\mathstrut 86q^{4} \) \(\mathstrut -\mathstrut 43q^{5} \) \(\mathstrut -\mathstrut 10q^{6} \) \(\mathstrut -\mathstrut q^{7} \) \(\mathstrut -\mathstrut 24q^{8} \) \(\mathstrut +\mathstrut 52q^{9} \) \(\mathstrut -\mathstrut 19q^{10} \) \(\mathstrut -\mathstrut 42q^{11} \) \(\mathstrut -\mathstrut 28q^{12} \) \(\mathstrut +\mathstrut 101q^{13} \) \(\mathstrut -\mathstrut 45q^{14} \) \(\mathstrut -\mathstrut 15q^{15} \) \(\mathstrut +\mathstrut 48q^{16} \) \(\mathstrut -\mathstrut 83q^{17} \) \(\mathstrut -\mathstrut 4q^{18} \) \(\mathstrut -\mathstrut 18q^{19} \) \(\mathstrut -\mathstrut 51q^{20} \) \(\mathstrut -\mathstrut 50q^{21} \) \(\mathstrut -\mathstrut 20q^{22} \) \(\mathstrut -\mathstrut 64q^{23} \) \(\mathstrut -\mathstrut 23q^{24} \) \(\mathstrut +\mathstrut 46q^{25} \) \(\mathstrut -\mathstrut 8q^{26} \) \(\mathstrut -\mathstrut 37q^{27} \) \(\mathstrut -\mathstrut 11q^{28} \) \(\mathstrut -\mathstrut 117q^{29} \) \(\mathstrut -\mathstrut 28q^{30} \) \(\mathstrut -\mathstrut 10q^{31} \) \(\mathstrut -\mathstrut 36q^{32} \) \(\mathstrut -\mathstrut 20q^{33} \) \(\mathstrut -\mathstrut 10q^{34} \) \(\mathstrut -\mathstrut 53q^{35} \) \(\mathstrut -\mathstrut 16q^{36} \) \(\mathstrut -\mathstrut 27q^{37} \) \(\mathstrut -\mathstrut 68q^{38} \) \(\mathstrut -\mathstrut 13q^{39} \) \(\mathstrut -\mathstrut 42q^{40} \) \(\mathstrut -\mathstrut 60q^{41} \) \(\mathstrut -\mathstrut 31q^{42} \) \(\mathstrut -\mathstrut 16q^{43} \) \(\mathstrut -\mathstrut 89q^{44} \) \(\mathstrut -\mathstrut 56q^{45} \) \(\mathstrut +\mathstrut 5q^{46} \) \(\mathstrut -\mathstrut 23q^{47} \) \(\mathstrut -\mathstrut 37q^{48} \) \(\mathstrut +\mathstrut 48q^{49} \) \(\mathstrut -\mathstrut 30q^{50} \) \(\mathstrut -\mathstrut 68q^{51} \) \(\mathstrut +\mathstrut 86q^{52} \) \(\mathstrut -\mathstrut 189q^{53} \) \(\mathstrut -\mathstrut 23q^{54} \) \(\mathstrut +\mathstrut 3q^{55} \) \(\mathstrut -\mathstrut 106q^{56} \) \(\mathstrut -\mathstrut 25q^{57} \) \(\mathstrut -\mathstrut 82q^{59} \) \(\mathstrut +\mathstrut 6q^{60} \) \(\mathstrut -\mathstrut 68q^{61} \) \(\mathstrut -\mathstrut 57q^{62} \) \(\mathstrut +\mathstrut 3q^{63} \) \(\mathstrut -\mathstrut 2q^{64} \) \(\mathstrut -\mathstrut 43q^{65} \) \(\mathstrut -\mathstrut 40q^{66} \) \(\mathstrut -\mathstrut 13q^{67} \) \(\mathstrut -\mathstrut 138q^{68} \) \(\mathstrut -\mathstrut 92q^{69} \) \(\mathstrut +\mathstrut 18q^{70} \) \(\mathstrut -\mathstrut 39q^{71} \) \(\mathstrut -\mathstrut 20q^{72} \) \(\mathstrut +\mathstrut 19q^{73} \) \(\mathstrut -\mathstrut 88q^{74} \) \(\mathstrut -\mathstrut 21q^{75} \) \(\mathstrut -\mathstrut 53q^{76} \) \(\mathstrut -\mathstrut 147q^{77} \) \(\mathstrut -\mathstrut 10q^{78} \) \(\mathstrut -\mathstrut 19q^{79} \) \(\mathstrut -\mathstrut 104q^{80} \) \(\mathstrut -\mathstrut 55q^{81} \) \(\mathstrut +\mathstrut 27q^{82} \) \(\mathstrut -\mathstrut 49q^{83} \) \(\mathstrut -\mathstrut 59q^{84} \) \(\mathstrut -\mathstrut 27q^{85} \) \(\mathstrut -\mathstrut 99q^{86} \) \(\mathstrut -\mathstrut 33q^{87} \) \(\mathstrut -\mathstrut 41q^{88} \) \(\mathstrut -\mathstrut 70q^{89} \) \(\mathstrut -\mathstrut 49q^{90} \) \(\mathstrut -\mathstrut q^{91} \) \(\mathstrut -\mathstrut 111q^{92} \) \(\mathstrut -\mathstrut 84q^{93} \) \(\mathstrut +\mathstrut 4q^{94} \) \(\mathstrut -\mathstrut 82q^{95} \) \(\mathstrut -\mathstrut 7q^{96} \) \(\mathstrut +\mathstrut 25q^{97} \) \(\mathstrut -\mathstrut 37q^{98} \) \(\mathstrut -\mathstrut 41q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 −2.77092 −0.383319 5.67797 −1.00861 1.06214 0.495501 −10.1914 −2.85307 2.79476
1.2 −2.75200 0.205353 5.57349 −1.15382 −0.565131 4.79173 −9.83422 −2.95783 3.17530
1.3 −2.66557 −0.463578 5.10529 3.99027 1.23570 −1.40213 −8.27737 −2.78510 −10.6364
1.4 −2.61088 −2.81902 4.81671 −3.25148 7.36014 3.68170 −7.35411 4.94689 8.48923
1.5 −2.59744 2.60815 4.74669 −0.0717768 −6.77450 0.808846 −7.13437 3.80242 0.186436
1.6 −2.53156 1.58470 4.40878 2.52136 −4.01175 −1.30202 −6.09798 −0.488741 −6.38296
1.7 −2.51903 1.84872 4.34553 −3.50196 −4.65699 1.30916 −5.90847 0.417768 8.82155
1.8 −2.47893 −2.41040 4.14507 2.56792 5.97521 2.73390 −5.31747 2.81004 −6.36569
1.9 −2.44907 −1.63543 3.99796 −2.35876 4.00528 1.29431 −4.89316 −0.325384 5.77678
1.10 −2.35123 −2.62167 3.52828 −1.32904 6.16416 −2.62369 −3.59334 3.87318 3.12489
1.11 −2.33786 −0.380371 3.46560 −3.85216 0.889254 −3.60381 −3.42637 −2.85532 9.00581
1.12 −2.32242 2.86947 3.39365 0.571930 −6.66413 −0.979167 −3.23665 5.23387 −1.32826
1.13 −2.31630 0.457851 3.36526 2.03378 −1.06052 1.32033 −3.16236 −2.79037 −4.71086
1.14 −2.22409 −1.49293 2.94657 −0.404702 3.32042 −4.24821 −2.10525 −0.771146 0.900094
1.15 −2.18475 1.46102 2.77312 −4.12132 −3.19197 2.89283 −1.68907 −0.865408 9.00405
1.16 −2.11661 2.26026 2.48003 −0.342197 −4.78408 3.30081 −1.01604 2.10876 0.724298
1.17 −2.06993 −2.73222 2.28462 1.87227 5.65552 −2.93607 −0.589152 4.46505 −3.87547
1.18 −2.04146 1.76541 2.16756 −1.03624 −3.60401 −3.97509 −0.342069 0.116656 2.11544
1.19 −2.03639 −1.20777 2.14690 3.16451 2.45949 3.67207 −0.299141 −1.54130 −6.44419
1.20 −1.88082 −1.45946 1.53747 1.38464 2.74498 −0.844871 0.869931 −0.869978 −2.60424
See next 80 embeddings (of 101 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.101
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 \(T_{2}^{101} + \cdots\) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(6019))\).