Properties

Label 6014.2.a.e
Level 6014
Weight 2
Character orbit 6014.a
Self dual Yes
Analytic conductor 48.022
Analytic rank 1
Dimension 21
CM No

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Newspace parameters

Level: \( N \) = \( 6014 = 2 \cdot 31 \cdot 97 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6014.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.0220317756\)
Analytic rank: \(1\)
Dimension: \(21\)
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.

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

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 1.00000 −3.14785 1.00000 1.07577 −3.14785 −0.384133 1.00000 6.90896 1.07577
1.2 1.00000 −3.05317 1.00000 0.104652 −3.05317 −2.07086 1.00000 6.32187 0.104652
1.3 1.00000 −2.57113 1.00000 3.16346 −2.57113 −4.41426 1.00000 3.61072 3.16346
1.4 1.00000 −2.42118 1.00000 −1.30859 −2.42118 3.90591 1.00000 2.86213 −1.30859
1.5 1.00000 −2.40239 1.00000 −4.08857 −2.40239 0.438180 1.00000 2.77149 −4.08857
1.6 1.00000 −1.86116 1.00000 −3.25735 −1.86116 −2.35478 1.00000 0.463919 −3.25735
1.7 1.00000 −1.32252 1.00000 −0.257676 −1.32252 −2.07296 1.00000 −1.25095 −0.257676
1.8 1.00000 −1.27481 1.00000 1.77282 −1.27481 1.20773 1.00000 −1.37487 1.77282
1.9 1.00000 −1.26246 1.00000 2.97735 −1.26246 1.38275 1.00000 −1.40619 2.97735
1.10 1.00000 −1.09484 1.00000 −2.95477 −1.09484 4.52432 1.00000 −1.80131 −2.95477
1.11 1.00000 −1.07052 1.00000 −1.71120 −1.07052 −0.903944 1.00000 −1.85399 −1.71120
1.12 1.00000 −0.343301 1.00000 1.80151 −0.343301 0.627271 1.00000 −2.88214 1.80151
1.13 1.00000 −0.333415 1.00000 −2.81042 −0.333415 −3.40902 1.00000 −2.88883 −2.81042
1.14 1.00000 0.436625 1.00000 −0.0518544 0.436625 0.167384 1.00000 −2.80936 −0.0518544
1.15 1.00000 0.761502 1.00000 −0.855697 0.761502 0.402181 1.00000 −2.42012 −0.855697
1.16 1.00000 1.37186 1.00000 −2.00517 1.37186 2.66469 1.00000 −1.11799 −2.00517
1.17 1.00000 1.56192 1.00000 −3.75184 1.56192 −2.39374 1.00000 −0.560398 −3.75184
1.18 1.00000 1.71445 1.00000 2.08645 1.71445 −3.84728 1.00000 −0.0606696 2.08645
1.19 1.00000 1.74046 1.00000 0.258024 1.74046 −2.13023 1.00000 0.0291912 0.258024
1.20 1.00000 2.22590 1.00000 1.86093 2.22590 −2.90456 1.00000 1.95462 1.86093
See all 21 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.21
Significant digits:
Format:

Inner twists

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

Atkin-Lehner signs

\( p \) Sign
\(2\) \(-1\)
\(31\) \(-1\)
\(97\) \(1\)

Hecke kernels

This newform can be constructed as the kernel of the linear operator \(T_{3}^{21} + \cdots\) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(6014))\).