Properties

Label 6017.2.a.f
Level 6017
Weight 2
Character orbit 6017.a
Self dual Yes
Analytic conductor 48.046
Analytic rank 0
Dimension 121
CM No

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Newspace parameters

Level: \( N \) = \( 6017 = 11 \cdot 547 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6017.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.0459868962\)
Analytic rank: \(0\)
Dimension: \(121\)
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.

\(\operatorname{Tr}(f)(q) = \) \(121q \) \(\mathstrut +\mathstrut 2q^{2} \) \(\mathstrut +\mathstrut 18q^{3} \) \(\mathstrut +\mathstrut 138q^{4} \) \(\mathstrut +\mathstrut 13q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut +\mathstrut 56q^{7} \) \(\mathstrut +\mathstrut 12q^{8} \) \(\mathstrut +\mathstrut 143q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \(121q \) \(\mathstrut +\mathstrut 2q^{2} \) \(\mathstrut +\mathstrut 18q^{3} \) \(\mathstrut +\mathstrut 138q^{4} \) \(\mathstrut +\mathstrut 13q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut +\mathstrut 56q^{7} \) \(\mathstrut +\mathstrut 12q^{8} \) \(\mathstrut +\mathstrut 143q^{9} \) \(\mathstrut +\mathstrut 20q^{10} \) \(\mathstrut -\mathstrut 121q^{11} \) \(\mathstrut +\mathstrut 40q^{12} \) \(\mathstrut +\mathstrut 31q^{13} \) \(\mathstrut +\mathstrut 7q^{14} \) \(\mathstrut +\mathstrut 53q^{15} \) \(\mathstrut +\mathstrut 164q^{16} \) \(\mathstrut -\mathstrut 23q^{17} \) \(\mathstrut +\mathstrut 14q^{18} \) \(\mathstrut +\mathstrut 62q^{19} \) \(\mathstrut +\mathstrut 53q^{20} \) \(\mathstrut +\mathstrut 19q^{21} \) \(\mathstrut -\mathstrut 2q^{22} \) \(\mathstrut +\mathstrut 34q^{23} \) \(\mathstrut +\mathstrut 34q^{24} \) \(\mathstrut +\mathstrut 172q^{25} \) \(\mathstrut +\mathstrut 34q^{26} \) \(\mathstrut +\mathstrut 87q^{27} \) \(\mathstrut +\mathstrut 91q^{28} \) \(\mathstrut -\mathstrut 30q^{29} \) \(\mathstrut +\mathstrut 2q^{30} \) \(\mathstrut +\mathstrut 102q^{31} \) \(\mathstrut +\mathstrut 31q^{32} \) \(\mathstrut -\mathstrut 18q^{33} \) \(\mathstrut +\mathstrut 30q^{34} \) \(\mathstrut +\mathstrut 20q^{35} \) \(\mathstrut +\mathstrut 164q^{36} \) \(\mathstrut +\mathstrut 58q^{37} \) \(\mathstrut +\mathstrut 35q^{38} \) \(\mathstrut +\mathstrut 42q^{39} \) \(\mathstrut +\mathstrut 52q^{40} \) \(\mathstrut -\mathstrut 12q^{41} \) \(\mathstrut +\mathstrut 56q^{42} \) \(\mathstrut +\mathstrut 96q^{43} \) \(\mathstrut -\mathstrut 138q^{44} \) \(\mathstrut +\mathstrut 72q^{45} \) \(\mathstrut +\mathstrut 48q^{46} \) \(\mathstrut +\mathstrut 136q^{47} \) \(\mathstrut +\mathstrut 99q^{48} \) \(\mathstrut +\mathstrut 199q^{49} \) \(\mathstrut -\mathstrut 7q^{50} \) \(\mathstrut +\mathstrut 22q^{51} \) \(\mathstrut +\mathstrut 81q^{52} \) \(\mathstrut +\mathstrut 24q^{53} \) \(\mathstrut +\mathstrut 37q^{54} \) \(\mathstrut -\mathstrut 13q^{55} \) \(\mathstrut +\mathstrut 28q^{56} \) \(\mathstrut +\mathstrut 25q^{57} \) \(\mathstrut +\mathstrut 76q^{58} \) \(\mathstrut +\mathstrut 58q^{59} \) \(\mathstrut +\mathstrut 81q^{60} \) \(\mathstrut +\mathstrut 14q^{61} \) \(\mathstrut -\mathstrut 2q^{62} \) \(\mathstrut +\mathstrut 152q^{63} \) \(\mathstrut +\mathstrut 236q^{64} \) \(\mathstrut -\mathstrut 29q^{65} \) \(\mathstrut -\mathstrut 10q^{66} \) \(\mathstrut +\mathstrut 112q^{67} \) \(\mathstrut -\mathstrut 61q^{68} \) \(\mathstrut +\mathstrut 41q^{69} \) \(\mathstrut +\mathstrut 105q^{70} \) \(\mathstrut +\mathstrut 56q^{71} \) \(\mathstrut +\mathstrut 71q^{72} \) \(\mathstrut +\mathstrut 113q^{73} \) \(\mathstrut -\mathstrut 23q^{74} \) \(\mathstrut +\mathstrut 111q^{75} \) \(\mathstrut +\mathstrut 144q^{76} \) \(\mathstrut -\mathstrut 56q^{77} \) \(\mathstrut +\mathstrut 59q^{78} \) \(\mathstrut +\mathstrut 80q^{79} \) \(\mathstrut +\mathstrut 100q^{80} \) \(\mathstrut +\mathstrut 177q^{81} \) \(\mathstrut +\mathstrut 123q^{82} \) \(\mathstrut +\mathstrut 6q^{83} \) \(\mathstrut +\mathstrut 79q^{84} \) \(\mathstrut +\mathstrut 26q^{85} \) \(\mathstrut +\mathstrut 14q^{86} \) \(\mathstrut +\mathstrut 180q^{87} \) \(\mathstrut -\mathstrut 12q^{88} \) \(\mathstrut +\mathstrut 26q^{89} \) \(\mathstrut +\mathstrut 75q^{90} \) \(\mathstrut +\mathstrut 72q^{91} \) \(\mathstrut +\mathstrut 58q^{92} \) \(\mathstrut +\mathstrut 139q^{93} \) \(\mathstrut +\mathstrut 37q^{94} \) \(\mathstrut +\mathstrut 39q^{95} \) \(\mathstrut +\mathstrut 66q^{96} \) \(\mathstrut +\mathstrut 136q^{97} \) \(\mathstrut +\mathstrut 7q^{98} \) \(\mathstrut -\mathstrut 143q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 −2.76609 1.72204 5.65124 1.59310 −4.76331 4.82706 −10.0996 −0.0345853 −4.40666
1.2 −2.74533 −1.76027 5.53683 −2.91942 4.83253 1.39362 −9.70977 0.0985659 8.01478
1.3 −2.73908 1.22981 5.50258 −1.73351 −3.36855 −3.95971 −9.59385 −1.48757 4.74824
1.4 −2.69280 3.13292 5.25118 0.629801 −8.43634 −1.84618 −8.75479 6.81521 −1.69593
1.5 −2.68922 1.49908 5.23192 −2.86648 −4.03136 3.78429 −8.69136 −0.752759 7.70861
1.6 −2.66480 −1.17356 5.10118 4.42559 3.12731 1.20677 −8.26404 −1.62275 −11.7933
1.7 −2.61029 −0.993650 4.81359 −3.58363 2.59371 2.54427 −7.34428 −2.01266 9.35430
1.8 −2.58820 0.659368 4.69880 0.894285 −1.70658 −1.01597 −6.98504 −2.56523 −2.31459
1.9 −2.57735 −3.20978 4.64274 2.33292 8.27272 1.38140 −6.81126 7.30267 −6.01276
1.10 −2.54623 −1.76925 4.48328 −0.663879 4.50492 −3.59601 −6.32301 0.130248 1.69039
1.11 −2.47328 −1.34586 4.11710 2.94670 3.32869 −2.85130 −5.23618 −1.18866 −7.28801
1.12 −2.37440 −0.379878 3.63775 −1.52566 0.901981 2.31296 −3.88867 −2.85569 3.62251
1.13 −2.32206 0.535084 3.39196 −0.511363 −1.24250 3.83500 −3.23221 −2.71368 1.18742
1.14 −2.30378 2.53807 3.30742 3.98214 −5.84717 −4.26603 −3.01201 3.44182 −9.17400
1.15 −2.29477 3.40179 3.26597 3.88142 −7.80633 2.49357 −2.90510 8.57220 −8.90697
1.16 −2.27604 3.24984 3.18035 −3.77187 −7.39676 3.04189 −2.68652 7.56146 8.58492
1.17 −2.26471 2.40007 3.12892 2.90605 −5.43547 2.22739 −2.55669 2.76034 −6.58136
1.18 −2.25579 −2.77556 3.08857 0.288075 6.26106 1.78637 −2.45557 4.70373 −0.649836
1.19 −2.22670 0.200688 2.95817 3.39958 −0.446870 −0.867591 −2.13356 −2.95972 −7.56983
1.20 −2.10704 −1.55624 2.43961 −0.464512 3.27907 −0.781558 −0.926282 −0.578102 0.978744
See next 80 embeddings (of 121 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.121
Significant digits:
Format:

Inner twists

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

Atkin-Lehner signs

\( p \) Sign
\(11\) \(1\)
\(547\) \(-1\)

Hecke kernels

This newform can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(6017))\):

\(T_{2}^{121} - \cdots\)
\(T_{3}^{121} - \cdots\)