Properties

Label 4034.2.a.b
Level 4034
Weight 2
Character orbit 4034.a
Self dual yes
Analytic conductor 32.212
Analytic rank 1
Dimension 35
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4034 = 2 \cdot 2017 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4034.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(32.2116521754\)
Analytic rank: \(1\)
Dimension: \(35\)
Coefficient ring index: multiple of None
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.

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

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 −3.27997 1.00000 2.11941 3.27997 −0.124927 −1.00000 7.75819 −2.11941
1.2 −1.00000 −3.25702 1.00000 −1.18968 3.25702 1.65832 −1.00000 7.60820 1.18968
1.3 −1.00000 −2.93683 1.00000 0.0231797 2.93683 −4.16598 −1.00000 5.62497 −0.0231797
1.4 −1.00000 −2.83579 1.00000 4.39396 2.83579 −1.33504 −1.00000 5.04172 −4.39396
1.5 −1.00000 −2.39986 1.00000 −1.11547 2.39986 2.17590 −1.00000 2.75933 1.11547
1.6 −1.00000 −2.23091 1.00000 1.94904 2.23091 1.55699 −1.00000 1.97697 −1.94904
1.7 −1.00000 −2.01951 1.00000 3.52220 2.01951 −0.0194784 −1.00000 1.07840 −3.52220
1.8 −1.00000 −1.96432 1.00000 −0.678471 1.96432 4.37365 −1.00000 0.858567 0.678471
1.9 −1.00000 −1.95232 1.00000 −1.60299 1.95232 −2.46247 −1.00000 0.811553 1.60299
1.10 −1.00000 −1.90524 1.00000 −3.49980 1.90524 −2.88392 −1.00000 0.629935 3.49980
1.11 −1.00000 −1.74374 1.00000 −3.34943 1.74374 0.122108 −1.00000 0.0406325 3.34943
1.12 −1.00000 −1.52925 1.00000 3.51675 1.52925 −1.62140 −1.00000 −0.661396 −3.51675
1.13 −1.00000 −1.35256 1.00000 −0.395568 1.35256 1.50560 −1.00000 −1.17057 0.395568
1.14 −1.00000 −1.19422 1.00000 1.77357 1.19422 2.63831 −1.00000 −1.57384 −1.77357
1.15 −1.00000 −0.841269 1.00000 −1.88225 0.841269 −4.21612 −1.00000 −2.29227 1.88225
1.16 −1.00000 −0.715791 1.00000 2.28149 0.715791 −4.66835 −1.00000 −2.48764 −2.28149
1.17 −1.00000 −0.237603 1.00000 3.33211 0.237603 4.34322 −1.00000 −2.94355 −3.33211
1.18 −1.00000 0.00791248 1.00000 −2.05271 −0.00791248 −2.16347 −1.00000 −2.99994 2.05271
1.19 −1.00000 0.0555653 1.00000 0.675723 −0.0555653 −0.0958620 −1.00000 −2.99691 −0.675723
1.20 −1.00000 0.280261 1.00000 0.751535 −0.280261 1.30988 −1.00000 −2.92145 −0.751535
See all 35 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.35
Significant digits:
Format:

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 4034.2.a.b 35
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
4034.2.a.b 35 1.a even 1 1 trivial

Atkin-Lehner signs

\( p \) Sign
\(2\) \(1\)
\(2017\) \(1\)