Properties

Label 8018.2.a.g
Level 8018
Weight 2
Character orbit 8018.a
Self dual Yes
Analytic conductor 64.024
Analytic rank 1
Dimension 34
CM No

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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: \(34\)
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.

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

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 −3.32805 1.00000 2.33043 3.32805 −1.71896 −1.00000 8.07595 −2.33043
1.2 −1.00000 −3.23421 1.00000 −1.01489 3.23421 2.27890 −1.00000 7.46011 1.01489
1.3 −1.00000 −3.00067 1.00000 −2.58515 3.00067 −5.14244 −1.00000 6.00401 2.58515
1.4 −1.00000 −2.69123 1.00000 2.65985 2.69123 −4.28568 −1.00000 4.24273 −2.65985
1.5 −1.00000 −2.58591 1.00000 −1.96812 2.58591 −0.600261 −1.00000 3.68694 1.96812
1.6 −1.00000 −2.57203 1.00000 3.90529 2.57203 −2.74849 −1.00000 3.61534 −3.90529
1.7 −1.00000 −2.37210 1.00000 −2.30761 2.37210 0.129234 −1.00000 2.62686 2.30761
1.8 −1.00000 −2.35248 1.00000 0.260869 2.35248 1.92119 −1.00000 2.53416 −0.260869
1.9 −1.00000 −1.88003 1.00000 1.30460 1.88003 −0.890859 −1.00000 0.534497 −1.30460
1.10 −1.00000 −1.50410 1.00000 0.693241 1.50410 2.70952 −1.00000 −0.737675 −0.693241
1.11 −1.00000 −1.36628 1.00000 2.24574 1.36628 3.44497 −1.00000 −1.13329 −2.24574
1.12 −1.00000 −1.32663 1.00000 −0.835058 1.32663 −1.21991 −1.00000 −1.24006 0.835058
1.13 −1.00000 −1.30982 1.00000 1.77709 1.30982 −3.58679 −1.00000 −1.28436 −1.77709
1.14 −1.00000 −1.00694 1.00000 −1.74347 1.00694 −4.04026 −1.00000 −1.98607 1.74347
1.15 −1.00000 −0.597156 1.00000 −2.37023 0.597156 1.41575 −1.00000 −2.64341 2.37023
1.16 −1.00000 −0.562142 1.00000 1.56640 0.562142 3.17308 −1.00000 −2.68400 −1.56640
1.17 −1.00000 −0.129854 1.00000 1.90646 0.129854 −0.0260326 −1.00000 −2.98314 −1.90646
1.18 −1.00000 0.0912120 1.00000 −2.07635 −0.0912120 −4.23935 −1.00000 −2.99168 2.07635
1.19 −1.00000 0.129131 1.00000 −3.52572 −0.129131 −2.82586 −1.00000 −2.98333 3.52572
1.20 −1.00000 0.234828 1.00000 −3.98534 −0.234828 1.98646 −1.00000 −2.94486 3.98534
See all 34 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.34
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 \(T_{3}^{34} + \cdots\) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(8018))\).