Properties

Label 4017.2.a.h
Level 4017
Weight 2
Character orbit 4017.a
Self dual Yes
Analytic conductor 32.076
Analytic rank 1
Dimension 25
CM No

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Newspace parameters

Level: \( N \) = \( 4017 = 3 \cdot 13 \cdot 103 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4017.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.0759064919\)
Analytic rank: \(1\)
Dimension: \(25\)
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.

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

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 −2.74671 −1.00000 5.54443 −3.14409 2.74671 −4.71348 −9.73553 1.00000 8.63591
1.2 −2.70695 −1.00000 5.32758 2.36895 2.70695 2.88217 −9.00759 1.00000 −6.41264
1.3 −2.67819 −1.00000 5.17269 −0.816148 2.67819 2.66447 −8.49705 1.00000 2.18580
1.4 −2.21324 −1.00000 2.89842 2.02862 2.21324 −4.79566 −1.98841 1.00000 −4.48982
1.5 −2.06452 −1.00000 2.26226 −0.587747 2.06452 −1.74034 −0.541432 1.00000 1.21342
1.6 −1.82913 −1.00000 1.34571 4.14175 1.82913 −1.02190 1.19679 1.00000 −7.57579
1.7 −1.77190 −1.00000 1.13963 −2.58005 1.77190 2.67810 1.52449 1.00000 4.57158
1.8 −1.38482 −1.00000 −0.0822870 −0.467175 1.38482 −3.78384 2.88358 1.00000 0.646950
1.9 −1.29020 −1.00000 −0.335394 1.27850 1.29020 0.146656 3.01312 1.00000 −1.64951
1.10 −0.985882 −1.00000 −1.02804 −3.07225 0.985882 1.70297 2.98529 1.00000 3.02888
1.11 −0.856339 −1.00000 −1.26668 1.28941 0.856339 1.75524 2.79739 1.00000 −1.10417
1.12 −0.633751 −1.00000 −1.59836 3.72594 0.633751 −0.819859 2.28046 1.00000 −2.36132
1.13 −0.451110 −1.00000 −1.79650 −1.20422 0.451110 5.19076 1.71264 1.00000 0.543237
1.14 −0.0180837 −1.00000 −1.99967 −4.11271 0.0180837 −4.60383 0.0723287 1.00000 0.0743729
1.15 0.343002 −1.00000 −1.88235 1.20148 −0.343002 −3.15145 −1.33165 1.00000 0.412112
1.16 0.563268 −1.00000 −1.68273 2.43057 −0.563268 2.01416 −2.07436 1.00000 1.36906
1.17 0.626060 −1.00000 −1.60805 −4.21209 −0.626060 2.03004 −2.25885 1.00000 −2.63702
1.18 1.34842 −1.00000 −0.181762 −1.77320 −1.34842 1.31404 −2.94193 1.00000 −2.39102
1.19 1.62615 −1.00000 0.644365 0.607200 −1.62615 4.96474 −2.20447 1.00000 0.987398
1.20 1.81336 −1.00000 1.28829 3.11371 −1.81336 −0.776263 −1.29059 1.00000 5.64629
See all 25 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.25
Significant digits:
Format:

Inner twists

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

Atkin-Lehner signs

\( p \) Sign
\(3\) \(1\)
\(13\) \(-1\)
\(103\) \(-1\)

Hecke kernels

This newform can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(4017))\):

\(T_{2}^{25} + \cdots\)
\(T_{23}^{25} + \cdots\)