Properties

Label 6017.2.a.d
Level 6017
Weight 2
Character orbit 6017.a
Self dual Yes
Analytic conductor 48.046
Analytic rank 1
Dimension 107
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: \(1\)
Dimension: \(107\)
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.

\(\operatorname{Tr}(f)(q) = \) \(107q \) \(\mathstrut -\mathstrut 3q^{2} \) \(\mathstrut -\mathstrut 18q^{3} \) \(\mathstrut +\mathstrut 91q^{4} \) \(\mathstrut -\mathstrut 15q^{5} \) \(\mathstrut -\mathstrut 54q^{7} \) \(\mathstrut -\mathstrut 3q^{8} \) \(\mathstrut +\mathstrut 95q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \(107q \) \(\mathstrut -\mathstrut 3q^{2} \) \(\mathstrut -\mathstrut 18q^{3} \) \(\mathstrut +\mathstrut 91q^{4} \) \(\mathstrut -\mathstrut 15q^{5} \) \(\mathstrut -\mathstrut 54q^{7} \) \(\mathstrut -\mathstrut 3q^{8} \) \(\mathstrut +\mathstrut 95q^{9} \) \(\mathstrut -\mathstrut 14q^{10} \) \(\mathstrut -\mathstrut 107q^{11} \) \(\mathstrut -\mathstrut 50q^{12} \) \(\mathstrut -\mathstrut 24q^{13} \) \(\mathstrut -\mathstrut 17q^{14} \) \(\mathstrut -\mathstrut 47q^{15} \) \(\mathstrut +\mathstrut 63q^{16} \) \(\mathstrut +\mathstrut 25q^{17} \) \(\mathstrut -\mathstrut 37q^{18} \) \(\mathstrut -\mathstrut 55q^{19} \) \(\mathstrut -\mathstrut 31q^{20} \) \(\mathstrut +\mathstrut 15q^{21} \) \(\mathstrut +\mathstrut 3q^{22} \) \(\mathstrut -\mathstrut 38q^{23} \) \(\mathstrut +\mathstrut 4q^{24} \) \(\mathstrut +\mathstrut 62q^{25} \) \(\mathstrut -\mathstrut 16q^{26} \) \(\mathstrut -\mathstrut 57q^{27} \) \(\mathstrut -\mathstrut 101q^{28} \) \(\mathstrut +\mathstrut 27q^{29} \) \(\mathstrut -\mathstrut 14q^{30} \) \(\mathstrut -\mathstrut 112q^{31} \) \(\mathstrut -\mathstrut 4q^{32} \) \(\mathstrut +\mathstrut 18q^{33} \) \(\mathstrut -\mathstrut 66q^{34} \) \(\mathstrut +\mathstrut 8q^{35} \) \(\mathstrut +\mathstrut 35q^{36} \) \(\mathstrut -\mathstrut 60q^{37} \) \(\mathstrut -\mathstrut 45q^{38} \) \(\mathstrut -\mathstrut 58q^{39} \) \(\mathstrut -\mathstrut 50q^{40} \) \(\mathstrut -\mathstrut 14q^{41} \) \(\mathstrut -\mathstrut 36q^{42} \) \(\mathstrut -\mathstrut 78q^{43} \) \(\mathstrut -\mathstrut 91q^{44} \) \(\mathstrut -\mathstrut 68q^{45} \) \(\mathstrut -\mathstrut 18q^{46} \) \(\mathstrut -\mathstrut 109q^{47} \) \(\mathstrut -\mathstrut 99q^{48} \) \(\mathstrut +\mathstrut 61q^{49} \) \(\mathstrut -\mathstrut 32q^{50} \) \(\mathstrut -\mathstrut 10q^{51} \) \(\mathstrut -\mathstrut 111q^{52} \) \(\mathstrut -\mathstrut 30q^{53} \) \(\mathstrut -\mathstrut 3q^{54} \) \(\mathstrut +\mathstrut 15q^{55} \) \(\mathstrut -\mathstrut 44q^{56} \) \(\mathstrut +\mathstrut q^{57} \) \(\mathstrut -\mathstrut 98q^{58} \) \(\mathstrut -\mathstrut 48q^{59} \) \(\mathstrut -\mathstrut 119q^{60} \) \(\mathstrut -\mathstrut 30q^{61} \) \(\mathstrut +\mathstrut 32q^{62} \) \(\mathstrut -\mathstrut 126q^{63} \) \(\mathstrut +\mathstrut 3q^{64} \) \(\mathstrut +\mathstrut 43q^{65} \) \(\mathstrut -\mathstrut 77q^{67} \) \(\mathstrut +\mathstrut 53q^{68} \) \(\mathstrut -\mathstrut 51q^{69} \) \(\mathstrut -\mathstrut 87q^{70} \) \(\mathstrut -\mathstrut 40q^{71} \) \(\mathstrut -\mathstrut 82q^{72} \) \(\mathstrut -\mathstrut 83q^{73} \) \(\mathstrut +\mathstrut 11q^{74} \) \(\mathstrut -\mathstrut 69q^{75} \) \(\mathstrut -\mathstrut 108q^{76} \) \(\mathstrut +\mathstrut 54q^{77} \) \(\mathstrut -\mathstrut 53q^{78} \) \(\mathstrut -\mathstrut 66q^{79} \) \(\mathstrut -\mathstrut 96q^{80} \) \(\mathstrut +\mathstrut 51q^{81} \) \(\mathstrut -\mathstrut 133q^{82} \) \(\mathstrut -\mathstrut 32q^{83} \) \(\mathstrut +\mathstrut 27q^{84} \) \(\mathstrut -\mathstrut 66q^{85} \) \(\mathstrut -\mathstrut 46q^{86} \) \(\mathstrut -\mathstrut 136q^{87} \) \(\mathstrut +\mathstrut 3q^{88} \) \(\mathstrut -\mathstrut 56q^{89} \) \(\mathstrut +\mathstrut 9q^{90} \) \(\mathstrut -\mathstrut 86q^{91} \) \(\mathstrut -\mathstrut 94q^{92} \) \(\mathstrut -\mathstrut 33q^{93} \) \(\mathstrut -\mathstrut 93q^{94} \) \(\mathstrut -\mathstrut 25q^{95} \) \(\mathstrut -\mathstrut 4q^{96} \) \(\mathstrut -\mathstrut 109q^{97} \) \(\mathstrut -\mathstrut 38q^{98} \) \(\mathstrut -\mathstrut 95q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 −2.75999 −3.06184 5.61754 −2.40388 8.45065 −3.94507 −9.98436 6.37487 6.63467
1.2 −2.74218 −0.127111 5.51953 0.930528 0.348561 −1.52234 −9.65117 −2.98384 −2.55167
1.3 −2.62131 1.98857 4.87127 −3.39892 −5.21266 −2.62575 −7.52650 0.954412 8.90963
1.4 −2.60586 −1.61281 4.79053 1.44359 4.20277 4.40298 −7.27174 −0.398838 −3.76179
1.5 −2.59133 1.08669 4.71497 2.54775 −2.81596 −0.206322 −7.03537 −1.81911 −6.60204
1.6 −2.52748 −3.01490 4.38814 1.64213 7.62008 3.19622 −6.03597 6.08959 −4.15044
1.7 −2.41913 2.57679 3.85218 −1.00520 −6.23359 1.76420 −4.48067 3.63986 2.43171
1.8 −2.41316 −1.13111 3.82334 3.33661 2.72954 −4.21510 −4.40000 −1.72060 −8.05177
1.9 −2.40409 −1.43849 3.77967 −1.50400 3.45826 0.877876 −4.27850 −0.930757 3.61576
1.10 −2.38163 −3.08400 3.67215 2.12353 7.34495 −4.46240 −3.98245 6.51107 −5.05746
1.11 −2.34564 1.00441 3.50205 3.21165 −2.35600 2.32596 −3.52327 −1.99115 −7.53339
1.12 −2.29221 −1.10986 3.25421 −2.25000 2.54402 −3.87042 −2.87492 −1.76822 5.15746
1.13 −2.27956 2.53160 3.19638 −2.07837 −5.77093 −1.61665 −2.72721 3.40901 4.73776
1.14 −2.25361 −2.32484 3.07875 −3.74526 5.23928 −1.13542 −2.43109 2.40489 8.44036
1.15 −2.23665 0.286457 3.00262 −1.07868 −0.640706 −2.04238 −2.24251 −2.91794 2.41263
1.16 −2.18792 2.65305 2.78699 0.440982 −5.80465 2.17034 −1.72186 4.03866 −0.964832
1.17 −2.16456 1.81828 2.68531 1.50320 −3.93577 −2.76616 −1.48340 0.306139 −3.25377
1.18 −2.10238 0.723159 2.42000 −4.03444 −1.52035 0.772372 −0.882990 −2.47704 8.48191
1.19 −2.03276 −2.20432 2.13212 2.54068 4.48086 2.78766 −0.268560 1.85904 −5.16459
1.20 −1.94021 −0.488619 1.76440 −3.27450 0.948022 −5.11134 0.457109 −2.76125 6.35321
See next 80 embeddings (of 107 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.107
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 \(S_{2}^{\mathrm{new}}(\Gamma_0(6017))\):

\(T_{2}^{107} + \cdots\)
\(T_{3}^{107} + \cdots\)