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
Inner twists 1

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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: \(34\)
Twist minimal: yes
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.

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

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:

Atkin-Lehner signs

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

Inner twists

This newform does not admit any (nontrivial) inner twists.

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 8018.2.a.g 34
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
8018.2.a.g 34 1.a even 1 1 trivial

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \(T_{3}^{34} + \cdots\) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(8018))\).

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database