Properties

Label 4017.2.a.g
Level 4017
Weight 2
Character orbit 4017.a
Self dual Yes
Analytic conductor 32.076
Analytic rank 0
Dimension 24
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: \(24\)
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.

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

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 −2.64656 −1.00000 5.00429 2.13528 2.64656 3.46294 −7.95105 1.00000 −5.65115
1.2 −2.42509 −1.00000 3.88107 −0.736887 2.42509 −2.40625 −4.56178 1.00000 1.78702
1.3 −2.29414 −1.00000 3.26307 −3.12687 2.29414 −2.80124 −2.89765 1.00000 7.17346
1.4 −2.16909 −1.00000 2.70494 0.657691 2.16909 −0.817989 −1.52908 1.00000 −1.42659
1.5 −1.94312 −1.00000 1.77572 −0.275874 1.94312 3.15290 0.435811 1.00000 0.536057
1.6 −1.52294 −1.00000 0.319360 3.31668 1.52294 −2.60872 2.55952 1.00000 −5.05112
1.7 −1.32626 −1.00000 −0.241032 −0.192408 1.32626 3.16535 2.97219 1.00000 0.255184
1.8 −1.17908 −1.00000 −0.609765 4.22706 1.17908 3.50133 3.07713 1.00000 −4.98405
1.9 −0.607674 −1.00000 −1.63073 −3.70104 0.607674 0.175250 2.20630 1.00000 2.24902
1.10 −0.574597 −1.00000 −1.66984 −2.72483 0.574597 0.829930 2.10868 1.00000 1.56568
1.11 −0.389331 −1.00000 −1.84842 0.642702 0.389331 −1.35418 1.49831 1.00000 −0.250224
1.12 0.0298243 −1.00000 −1.99911 3.06004 −0.0298243 −1.69214 −0.119271 1.00000 0.0912635
1.13 0.543206 −1.00000 −1.70493 2.45290 −0.543206 0.874109 −2.01254 1.00000 1.33243
1.14 0.671722 −1.00000 −1.54879 −1.67775 −0.671722 5.02977 −2.38380 1.00000 −1.12698
1.15 0.794802 −1.00000 −1.36829 −2.06654 −0.794802 −0.419104 −2.67712 1.00000 −1.64249
1.16 1.05828 −1.00000 −0.880046 −0.912505 −1.05828 −3.63309 −3.04789 1.00000 −0.965685
1.17 1.57828 −1.00000 0.490964 −1.83430 −1.57828 4.32058 −2.38168 1.00000 −2.89504
1.18 1.68466 −1.00000 0.838074 0.142092 −1.68466 −0.0282508 −1.95745 1.00000 0.239376
1.19 1.73242 −1.00000 1.00128 0.756937 −1.73242 −4.14115 −1.73020 1.00000 1.31133
1.20 1.86289 −1.00000 1.47035 4.02931 −1.86289 3.22519 −0.986675 1.00000 7.50616
See all 24 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.24
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 \(S_{2}^{\mathrm{new}}(\Gamma_0(4017))\):

\(T_{2}^{24} - \cdots\)
\(T_{23}^{24} - \cdots\)