Properties

Label 4017.2.a.j
Level 4017
Weight 2
Character orbit 4017.a
Self dual Yes
Analytic conductor 32.076
Analytic rank 0
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: \(0\)
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.

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

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 −2.65319 −1.00000 5.03939 3.62608 2.65319 −1.69720 −8.06407 1.00000 −9.62067
1.2 −2.36961 −1.00000 3.61506 −2.39998 2.36961 −0.116274 −3.82707 1.00000 5.68703
1.3 −2.18299 −1.00000 2.76546 2.14752 2.18299 0.603238 −1.67100 1.00000 −4.68803
1.4 −1.97968 −1.00000 1.91913 2.16016 1.97968 5.12656 0.160099 1.00000 −4.27642
1.5 −1.79927 −1.00000 1.23739 1.64720 1.79927 1.60963 1.37215 1.00000 −2.96376
1.6 −1.55573 −1.00000 0.420296 −1.90089 1.55573 0.0358686 2.45759 1.00000 2.95727
1.7 −1.27578 −1.00000 −0.372378 −0.506188 1.27578 −3.05259 3.02664 1.00000 0.645786
1.8 −0.925244 −1.00000 −1.14392 3.08995 0.925244 −0.0396192 2.90890 1.00000 −2.85895
1.9 −0.858580 −1.00000 −1.26284 −4.02605 0.858580 1.69085 2.80141 1.00000 3.45668
1.10 −0.491539 −1.00000 −1.75839 −1.95668 0.491539 −2.76715 1.84740 1.00000 0.961784
1.11 −0.254687 −1.00000 −1.93513 −0.644426 0.254687 3.73934 1.00223 1.00000 0.164127
1.12 −0.0371239 −1.00000 −1.99862 2.55043 0.0371239 1.94695 0.148445 1.00000 −0.0946818
1.13 0.0202075 −1.00000 −1.99959 −1.35659 −0.0202075 −0.669195 −0.0808216 1.00000 −0.0274131
1.14 0.506527 −1.00000 −1.74343 4.00697 −0.506527 4.25155 −1.89615 1.00000 2.02964
1.15 0.940078 −1.00000 −1.11625 −1.95082 −0.940078 −0.363346 −2.92952 1.00000 −1.83392
1.16 1.30548 −1.00000 −0.295718 2.71388 −1.30548 2.93494 −2.99702 1.00000 3.54292
1.17 1.39323 −1.00000 −0.0589163 0.623512 −1.39323 −3.51013 −2.86854 1.00000 0.868695
1.18 1.59660 −1.00000 0.549133 −3.22334 −1.59660 2.57812 −2.31645 1.00000 −5.14639
1.19 1.86177 −1.00000 1.46619 −1.56946 −1.86177 2.25881 −0.993826 1.00000 −2.92198
1.20 2.02058 −1.00000 2.08276 4.24376 −2.02058 −1.21618 0.167219 1.00000 8.57486
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 \(S_{2}^{\mathrm{new}}(\Gamma_0(4017))\):

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