Properties

Label 8018.2.a.k
Level 8018
Weight 2
Character orbit 8018.a
Self dual Yes
Analytic conductor 64.024
Analytic rank 0
Dimension 49
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: \(0\)
Dimension: \(49\)
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.

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

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 −3.18331 1.00000 4.19262 −3.18331 −3.25533 1.00000 7.13346 4.19262
1.2 1.00000 −3.16496 1.00000 −1.03983 −3.16496 −1.27872 1.00000 7.01700 −1.03983
1.3 1.00000 −3.03631 1.00000 −0.470191 −3.03631 3.61227 1.00000 6.21915 −0.470191
1.4 1.00000 −3.03421 1.00000 −2.36281 −3.03421 −0.910676 1.00000 6.20641 −2.36281
1.5 1.00000 −2.78216 1.00000 3.32795 −2.78216 4.62132 1.00000 4.74040 3.32795
1.6 1.00000 −2.76297 1.00000 0.238506 −2.76297 2.08661 1.00000 4.63399 0.238506
1.7 1.00000 −2.47584 1.00000 1.97954 −2.47584 −2.02339 1.00000 3.12981 1.97954
1.8 1.00000 −2.35762 1.00000 −3.55313 −2.35762 −1.02341 1.00000 2.55835 −3.55313
1.9 1.00000 −2.16417 1.00000 3.75376 −2.16417 4.09027 1.00000 1.68362 3.75376
1.10 1.00000 −2.15958 1.00000 −0.594727 −2.15958 4.60099 1.00000 1.66376 −0.594727
1.11 1.00000 −1.57817 1.00000 −2.42122 −1.57817 −1.17267 1.00000 −0.509368 −2.42122
1.12 1.00000 −1.45260 1.00000 2.56447 −1.45260 −3.76816 1.00000 −0.889956 2.56447
1.13 1.00000 −1.41679 1.00000 −3.74277 −1.41679 3.98944 1.00000 −0.992702 −3.74277
1.14 1.00000 −1.33535 1.00000 0.425182 −1.33535 −2.10915 1.00000 −1.21683 0.425182
1.15 1.00000 −1.22925 1.00000 −2.52525 −1.22925 3.13859 1.00000 −1.48895 −2.52525
1.16 1.00000 −1.06684 1.00000 3.41038 −1.06684 −0.896941 1.00000 −1.86186 3.41038
1.17 1.00000 −0.823102 1.00000 1.30158 −0.823102 0.990463 1.00000 −2.32250 1.30158
1.18 1.00000 −0.655875 1.00000 3.82378 −0.655875 −1.10690 1.00000 −2.56983 3.82378
1.19 1.00000 −0.460040 1.00000 −0.746209 −0.460040 −4.50236 1.00000 −2.78836 −0.746209
1.20 1.00000 −0.411559 1.00000 −1.49400 −0.411559 −1.21130 1.00000 −2.83062 −1.49400
See all 49 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.49
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 \(T_{3}^{49} - \cdots\) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(8018))\).