Properties

Label 4034.2.a.a
Level 4034
Weight 2
Character orbit 4034.a
Self dual Yes
Analytic conductor 32.212
Analytic rank 1
Dimension 33
CM No

Related objects

Downloads

Learn more about

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: \(33\)
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.

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

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 −3.41599 1.00000 1.09379 −3.41599 4.04655 1.00000 8.66901 1.09379
1.2 1.00000 −3.31212 1.00000 −3.97668 −3.31212 0.855437 1.00000 7.97011 −3.97668
1.3 1.00000 −2.82298 1.00000 0.779916 −2.82298 −3.19115 1.00000 4.96923 0.779916
1.4 1.00000 −2.73960 1.00000 −3.73363 −2.73960 −3.98248 1.00000 4.50543 −3.73363
1.5 1.00000 −2.69679 1.00000 −2.92996 −2.69679 3.32033 1.00000 4.27265 −2.92996
1.6 1.00000 −2.68746 1.00000 1.22075 −2.68746 −1.79428 1.00000 4.22244 1.22075
1.7 1.00000 −2.63161 1.00000 1.62454 −2.63161 2.40683 1.00000 3.92538 1.62454
1.8 1.00000 −2.03082 1.00000 −0.733478 −2.03082 −1.85114 1.00000 1.12424 −0.733478
1.9 1.00000 −1.80963 1.00000 0.856694 −1.80963 0.353536 1.00000 0.274766 0.856694
1.10 1.00000 −1.73259 1.00000 3.77683 −1.73259 0.621551 1.00000 0.00185264 3.77683
1.11 1.00000 −1.72838 1.00000 −2.88558 −1.72838 −0.799535 1.00000 −0.0126910 −2.88558
1.12 1.00000 −1.65119 1.00000 −2.90851 −1.65119 0.175106 1.00000 −0.273565 −2.90851
1.13 1.00000 −1.42842 1.00000 2.01766 −1.42842 0.289927 1.00000 −0.959611 2.01766
1.14 1.00000 −0.945997 1.00000 −2.44770 −0.945997 2.03235 1.00000 −2.10509 −2.44770
1.15 1.00000 −0.523973 1.00000 1.37573 −0.523973 −3.92552 1.00000 −2.72545 1.37573
1.16 1.00000 −0.423572 1.00000 −0.487122 −0.423572 2.40385 1.00000 −2.82059 −0.487122
1.17 1.00000 −0.366256 1.00000 0.145528 −0.366256 3.13381 1.00000 −2.86586 0.145528
1.18 1.00000 −0.289410 1.00000 −3.81688 −0.289410 −2.88122 1.00000 −2.91624 −3.81688
1.19 1.00000 −0.264302 1.00000 2.82441 −0.264302 −2.96778 1.00000 −2.93014 2.82441
1.20 1.00000 −0.138152 1.00000 −3.80380 −0.138152 3.68849 1.00000 −2.98091 −3.80380
See all 33 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.33
Significant digits:
Format:

Inner twists

This newform does not have CM; other inner twists have not been computed.

Atkin-Lehner signs

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