Properties

Label 8018.2.a.i
Level 8018
Weight 2
Character orbit 8018.a
Self dual Yes
Analytic conductor 64.024
Analytic rank 0
Dimension 43
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: \(0\)
Dimension: \(43\)
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.

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

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 −3.34431 1.00000 −3.91124 3.34431 0.821669 −1.00000 8.18441 3.91124
1.2 −1.00000 −3.24783 1.00000 2.20422 3.24783 3.82287 −1.00000 7.54837 −2.20422
1.3 −1.00000 −2.91293 1.00000 2.71400 2.91293 1.04550 −1.00000 5.48515 −2.71400
1.4 −1.00000 −2.88859 1.00000 −0.162345 2.88859 −3.68356 −1.00000 5.34393 0.162345
1.5 −1.00000 −2.71486 1.00000 −0.740916 2.71486 4.34624 −1.00000 4.37046 0.740916
1.6 −1.00000 −2.54429 1.00000 −4.40933 2.54429 −2.39004 −1.00000 3.47339 4.40933
1.7 −1.00000 −2.53282 1.00000 2.86896 2.53282 3.12244 −1.00000 3.41520 −2.86896
1.8 −1.00000 −2.22097 1.00000 0.529365 2.22097 −2.58907 −1.00000 1.93269 −0.529365
1.9 −1.00000 −2.12309 1.00000 0.333090 2.12309 −1.76432 −1.00000 1.50753 −0.333090
1.10 −1.00000 −2.06580 1.00000 4.42069 2.06580 −2.80943 −1.00000 1.26754 −4.42069
1.11 −1.00000 −1.98111 1.00000 −2.70035 1.98111 2.97081 −1.00000 0.924794 2.70035
1.12 −1.00000 −1.78337 1.00000 −3.15111 1.78337 −2.13059 −1.00000 0.180410 3.15111
1.13 −1.00000 −1.49345 1.00000 1.29948 1.49345 −1.68221 −1.00000 −0.769617 −1.29948
1.14 −1.00000 −1.36513 1.00000 0.286730 1.36513 −1.35155 −1.00000 −1.13641 −0.286730
1.15 −1.00000 −1.12203 1.00000 −3.99522 1.12203 0.851275 −1.00000 −1.74104 3.99522
1.16 −1.00000 −1.11378 1.00000 4.02830 1.11378 1.02145 −1.00000 −1.75949 −4.02830
1.17 −1.00000 −1.00471 1.00000 −1.06211 1.00471 0.645369 −1.00000 −1.99055 1.06211
1.18 −1.00000 −0.978925 1.00000 −2.13476 0.978925 5.08930 −1.00000 −2.04171 2.13476
1.19 −1.00000 −0.765202 1.00000 −1.80247 0.765202 4.51708 −1.00000 −2.41447 1.80247
1.20 −1.00000 −0.649534 1.00000 3.59840 0.649534 4.54706 −1.00000 −2.57811 −3.59840
See all 43 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.43
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 \(T_{3}^{43} - \cdots\) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(8018))\).