Properties

Label 8018.2.a.e
Level 8018
Weight 2
Character orbit 8018.a
Self dual Yes
Analytic conductor 64.024
Analytic rank 1
Dimension 32
CM No

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 8018 = 2 \cdot 19 \cdot 211 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8018.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0240523407\)
Analytic rank: \(1\)
Dimension: \(32\)
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.

\(\operatorname{Tr}(f)(q) = \) \(32q \) \(\mathstrut +\mathstrut 32q^{2} \) \(\mathstrut -\mathstrut 7q^{3} \) \(\mathstrut +\mathstrut 32q^{4} \) \(\mathstrut -\mathstrut 6q^{5} \) \(\mathstrut -\mathstrut 7q^{6} \) \(\mathstrut -\mathstrut 5q^{7} \) \(\mathstrut +\mathstrut 32q^{8} \) \(\mathstrut +\mathstrut 15q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \(32q \) \(\mathstrut +\mathstrut 32q^{2} \) \(\mathstrut -\mathstrut 7q^{3} \) \(\mathstrut +\mathstrut 32q^{4} \) \(\mathstrut -\mathstrut 6q^{5} \) \(\mathstrut -\mathstrut 7q^{6} \) \(\mathstrut -\mathstrut 5q^{7} \) \(\mathstrut +\mathstrut 32q^{8} \) \(\mathstrut +\mathstrut 15q^{9} \) \(\mathstrut -\mathstrut 6q^{10} \) \(\mathstrut -\mathstrut 21q^{11} \) \(\mathstrut -\mathstrut 7q^{12} \) \(\mathstrut -\mathstrut 19q^{13} \) \(\mathstrut -\mathstrut 5q^{14} \) \(\mathstrut -\mathstrut 14q^{15} \) \(\mathstrut +\mathstrut 32q^{16} \) \(\mathstrut -\mathstrut 14q^{17} \) \(\mathstrut +\mathstrut 15q^{18} \) \(\mathstrut -\mathstrut 32q^{19} \) \(\mathstrut -\mathstrut 6q^{20} \) \(\mathstrut -\mathstrut 26q^{21} \) \(\mathstrut -\mathstrut 21q^{22} \) \(\mathstrut -\mathstrut 13q^{23} \) \(\mathstrut -\mathstrut 7q^{24} \) \(\mathstrut -\mathstrut 10q^{25} \) \(\mathstrut -\mathstrut 19q^{26} \) \(\mathstrut -\mathstrut 25q^{27} \) \(\mathstrut -\mathstrut 5q^{28} \) \(\mathstrut -\mathstrut 42q^{29} \) \(\mathstrut -\mathstrut 14q^{30} \) \(\mathstrut -\mathstrut 15q^{31} \) \(\mathstrut +\mathstrut 32q^{32} \) \(\mathstrut -\mathstrut 32q^{33} \) \(\mathstrut -\mathstrut 14q^{34} \) \(\mathstrut -\mathstrut 22q^{35} \) \(\mathstrut +\mathstrut 15q^{36} \) \(\mathstrut -\mathstrut 54q^{37} \) \(\mathstrut -\mathstrut 32q^{38} \) \(\mathstrut -\mathstrut 32q^{39} \) \(\mathstrut -\mathstrut 6q^{40} \) \(\mathstrut -\mathstrut 16q^{41} \) \(\mathstrut -\mathstrut 26q^{42} \) \(\mathstrut -\mathstrut 37q^{43} \) \(\mathstrut -\mathstrut 21q^{44} \) \(\mathstrut -\mathstrut 46q^{45} \) \(\mathstrut -\mathstrut 13q^{46} \) \(\mathstrut -\mathstrut 9q^{47} \) \(\mathstrut -\mathstrut 7q^{48} \) \(\mathstrut -\mathstrut 7q^{49} \) \(\mathstrut -\mathstrut 10q^{50} \) \(\mathstrut -\mathstrut 32q^{51} \) \(\mathstrut -\mathstrut 19q^{52} \) \(\mathstrut -\mathstrut 53q^{53} \) \(\mathstrut -\mathstrut 25q^{54} \) \(\mathstrut -\mathstrut 17q^{55} \) \(\mathstrut -\mathstrut 5q^{56} \) \(\mathstrut +\mathstrut 7q^{57} \) \(\mathstrut -\mathstrut 42q^{58} \) \(\mathstrut -\mathstrut 34q^{59} \) \(\mathstrut -\mathstrut 14q^{60} \) \(\mathstrut -\mathstrut 33q^{61} \) \(\mathstrut -\mathstrut 15q^{62} \) \(\mathstrut +\mathstrut 18q^{63} \) \(\mathstrut +\mathstrut 32q^{64} \) \(\mathstrut -\mathstrut 50q^{65} \) \(\mathstrut -\mathstrut 32q^{66} \) \(\mathstrut -\mathstrut 53q^{67} \) \(\mathstrut -\mathstrut 14q^{68} \) \(\mathstrut -\mathstrut 40q^{69} \) \(\mathstrut -\mathstrut 22q^{70} \) \(\mathstrut -\mathstrut 27q^{71} \) \(\mathstrut +\mathstrut 15q^{72} \) \(\mathstrut -\mathstrut 43q^{73} \) \(\mathstrut -\mathstrut 54q^{74} \) \(\mathstrut +\mathstrut 5q^{75} \) \(\mathstrut -\mathstrut 32q^{76} \) \(\mathstrut -\mathstrut 56q^{77} \) \(\mathstrut -\mathstrut 32q^{78} \) \(\mathstrut -\mathstrut 11q^{79} \) \(\mathstrut -\mathstrut 6q^{80} \) \(\mathstrut -\mathstrut 8q^{81} \) \(\mathstrut -\mathstrut 16q^{82} \) \(\mathstrut -\mathstrut 17q^{83} \) \(\mathstrut -\mathstrut 26q^{84} \) \(\mathstrut -\mathstrut 30q^{85} \) \(\mathstrut -\mathstrut 37q^{86} \) \(\mathstrut +\mathstrut 3q^{87} \) \(\mathstrut -\mathstrut 21q^{88} \) \(\mathstrut -\mathstrut 21q^{89} \) \(\mathstrut -\mathstrut 46q^{90} \) \(\mathstrut -\mathstrut 67q^{91} \) \(\mathstrut -\mathstrut 13q^{92} \) \(\mathstrut -\mathstrut 31q^{93} \) \(\mathstrut -\mathstrut 9q^{94} \) \(\mathstrut +\mathstrut 6q^{95} \) \(\mathstrut -\mathstrut 7q^{96} \) \(\mathstrut -\mathstrut 51q^{97} \) \(\mathstrut -\mathstrut 7q^{98} \) \(\mathstrut -\mathstrut 32q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 1.00000 −3.42265 1.00000 −0.619065 −3.42265 1.32007 1.00000 8.71451 −0.619065
1.2 1.00000 −2.94867 1.00000 2.45411 −2.94867 1.73401 1.00000 5.69467 2.45411
1.3 1.00000 −2.87951 1.00000 −0.727191 −2.87951 −4.06984 1.00000 5.29156 −0.727191
1.4 1.00000 −2.65255 1.00000 −0.493279 −2.65255 4.58344 1.00000 4.03601 −0.493279
1.5 1.00000 −2.56478 1.00000 −2.25248 −2.56478 1.14049 1.00000 3.57812 −2.25248
1.6 1.00000 −2.29667 1.00000 −2.85656 −2.29667 3.49764 1.00000 2.27470 −2.85656
1.7 1.00000 −1.99099 1.00000 3.02780 −1.99099 −1.37345 1.00000 0.964042 3.02780
1.8 1.00000 −1.92818 1.00000 −0.990094 −1.92818 2.57830 1.00000 0.717864 −0.990094
1.9 1.00000 −1.89970 1.00000 0.525736 −1.89970 −0.379709 1.00000 0.608871 0.525736
1.10 1.00000 −1.64186 1.00000 2.36809 −1.64186 −2.99072 1.00000 −0.304289 2.36809
1.11 1.00000 −1.43969 1.00000 −3.67207 −1.43969 −3.77033 1.00000 −0.927290 −3.67207
1.12 1.00000 −1.26197 1.00000 2.06188 −1.26197 −2.59785 1.00000 −1.40744 2.06188
1.13 1.00000 −0.617240 1.00000 −3.87436 −0.617240 −1.63807 1.00000 −2.61901 −3.87436
1.14 1.00000 −0.547499 1.00000 −0.949125 −0.547499 0.838427 1.00000 −2.70024 −0.949125
1.15 1.00000 −0.474859 1.00000 1.84074 −0.474859 4.63773 1.00000 −2.77451 1.84074
1.16 1.00000 −0.175124 1.00000 3.03871 −0.175124 −1.35318 1.00000 −2.96933 3.03871
1.17 1.00000 −0.0920586 1.00000 2.87697 −0.0920586 2.64672 1.00000 −2.99153 2.87697
1.18 1.00000 0.124655 1.00000 −2.23561 0.124655 3.94220 1.00000 −2.98446 −2.23561
1.19 1.00000 0.137782 1.00000 −1.40913 0.137782 −4.42829 1.00000 −2.98102 −1.40913
1.20 1.00000 0.281409 1.00000 0.922067 0.281409 −0.498686 1.00000 −2.92081 0.922067
See all 32 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.32
Significant digits:
Format:

Inner twists

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

Atkin-Lehner signs

\( p \) Sign
\(2\) \(-1\)
\(19\) \(1\)
\(211\) \(-1\)

Hecke kernels

This newform can be constructed as the kernel of the linear operator \(T_{3}^{32} + \cdots\) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(8018))\).