Properties

Label 4017.2.a.i
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.

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

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 −2.74549 −1.00000 5.53773 0.596155 2.74549 −1.94658 −9.71281 1.00000 −1.63674
1.2 −2.66982 −1.00000 5.12792 −3.00815 2.66982 2.19544 −8.35096 1.00000 8.03119
1.3 −2.38645 −1.00000 3.69513 2.94139 2.38645 −4.88857 −4.04533 1.00000 −7.01947
1.4 −2.31427 −1.00000 3.35587 3.52277 2.31427 3.16201 −3.13785 1.00000 −8.15265
1.5 −2.25716 −1.00000 3.09477 −2.92277 2.25716 −0.587921 −2.47106 1.00000 6.59715
1.6 −2.08104 −1.00000 2.33074 1.74075 2.08104 −0.124046 −0.688276 1.00000 −3.62257
1.7 −1.54007 −1.00000 0.371810 −0.217078 1.54007 2.62202 2.50752 1.00000 0.334314
1.8 −1.47736 −1.00000 0.182601 −3.64531 1.47736 −4.01724 2.68496 1.00000 5.38545
1.9 −1.46195 −1.00000 0.137285 −2.88545 1.46195 1.16184 2.72319 1.00000 4.21838
1.10 −0.726163 −1.00000 −1.47269 0.449507 0.726163 4.04793 2.52174 1.00000 −0.326416
1.11 −0.590079 −1.00000 −1.65181 0.503953 0.590079 −2.98562 2.15486 1.00000 −0.297372
1.12 −0.307676 −1.00000 −1.90534 −1.88076 0.307676 −3.18485 1.20158 1.00000 0.578664
1.13 −0.150477 −1.00000 −1.97736 2.78105 0.150477 2.48525 0.598501 1.00000 −0.418485
1.14 0.444143 −1.00000 −1.80274 0.495430 −0.444143 2.63750 −1.68896 1.00000 0.220041
1.15 0.823398 −1.00000 −1.32202 −3.52626 −0.823398 −0.677842 −2.73534 1.00000 −2.90351
1.16 0.831544 −1.00000 −1.30853 −3.33918 −0.831544 −4.05766 −2.75119 1.00000 −2.77667
1.17 0.883592 −1.00000 −1.21927 3.49819 −0.883592 −3.21070 −2.84452 1.00000 3.09097
1.18 1.25624 −1.00000 −0.421872 0.726022 −1.25624 0.867951 −3.04244 1.00000 0.912055
1.19 1.44489 −1.00000 0.0877157 4.08746 −1.44489 −1.49545 −2.76305 1.00000 5.90594
1.20 1.46693 −1.00000 0.151895 0.636277 −1.46693 −0.403322 −2.71105 1.00000 0.933377
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 \(S_{2}^{\mathrm{new}}(\Gamma_0(4017))\):

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