Properties

Label 8018.2.a.h
Level 8018
Weight 2
Character orbit 8018.a
Self dual Yes
Analytic conductor 64.024
Analytic rank 0
Dimension 41
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: \(41\)
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.

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

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 −3.10704 1.00000 −3.25849 3.10704 4.58720 −1.00000 6.65369 3.25849
1.2 −1.00000 −2.99911 1.00000 0.291646 2.99911 −2.03701 −1.00000 5.99467 −0.291646
1.3 −1.00000 −2.94121 1.00000 −2.18985 2.94121 −0.696753 −1.00000 5.65074 2.18985
1.4 −1.00000 −2.61753 1.00000 0.199936 2.61753 0.481093 −1.00000 3.85148 −0.199936
1.5 −1.00000 −2.52494 1.00000 2.43918 2.52494 0.521147 −1.00000 3.37531 −2.43918
1.6 −1.00000 −2.15334 1.00000 −3.70592 2.15334 −3.79982 −1.00000 1.63688 3.70592
1.7 −1.00000 −2.09909 1.00000 1.36520 2.09909 4.01442 −1.00000 1.40618 −1.36520
1.8 −1.00000 −1.96501 1.00000 −1.27031 1.96501 1.60889 −1.00000 0.861269 1.27031
1.9 −1.00000 −1.82110 1.00000 −3.54712 1.82110 −2.30184 −1.00000 0.316404 3.54712
1.10 −1.00000 −1.75523 1.00000 −0.0353436 1.75523 −4.74271 −1.00000 0.0808489 0.0353436
1.11 −1.00000 −1.66216 1.00000 −4.08852 1.66216 3.79799 −1.00000 −0.237209 4.08852
1.12 −1.00000 −1.48981 1.00000 2.56048 1.48981 1.18596 −1.00000 −0.780452 −2.56048
1.13 −1.00000 −1.39030 1.00000 4.04446 1.39030 −1.52895 −1.00000 −1.06708 −4.04446
1.14 −1.00000 −1.20998 1.00000 0.0448427 1.20998 −2.73874 −1.00000 −1.53595 −0.0448427
1.15 −1.00000 −0.949118 1.00000 −3.26613 0.949118 3.22650 −1.00000 −2.09917 3.26613
1.16 −1.00000 −0.776259 1.00000 2.71672 0.776259 2.01306 −1.00000 −2.39742 −2.71672
1.17 −1.00000 −0.438243 1.00000 −0.442957 0.438243 2.11643 −1.00000 −2.80794 0.442957
1.18 −1.00000 0.0343445 1.00000 −1.14164 −0.0343445 −1.82320 −1.00000 −2.99882 1.14164
1.19 −1.00000 0.100035 1.00000 −0.345424 −0.100035 2.97223 −1.00000 −2.98999 0.345424
1.20 −1.00000 0.237080 1.00000 0.796437 −0.237080 2.80350 −1.00000 −2.94379 −0.796437
See all 41 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.41
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 \(T_{3}^{41} - \cdots\) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(8018))\).