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

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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: \(35\)
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.

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

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 −3.27997 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 have CM; other inner twists have not been computed.

Atkin-Lehner signs

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