Properties

Label 4034.2.a.c
Level 4034
Weight 2
Character orbit 4034.a
Self dual Yes
Analytic conductor 32.212
Analytic rank 0
Dimension 49
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: \(0\)
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.

\(\operatorname{Tr}(f)(q) = \) \(49q \) \(\mathstrut -\mathstrut 49q^{2} \) \(\mathstrut +\mathstrut 8q^{3} \) \(\mathstrut +\mathstrut 49q^{4} \) \(\mathstrut -\mathstrut 8q^{5} \) \(\mathstrut -\mathstrut 8q^{6} \) \(\mathstrut +\mathstrut 18q^{7} \) \(\mathstrut -\mathstrut 49q^{8} \) \(\mathstrut +\mathstrut 59q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \(49q \) \(\mathstrut -\mathstrut 49q^{2} \) \(\mathstrut +\mathstrut 8q^{3} \) \(\mathstrut +\mathstrut 49q^{4} \) \(\mathstrut -\mathstrut 8q^{5} \) \(\mathstrut -\mathstrut 8q^{6} \) \(\mathstrut +\mathstrut 18q^{7} \) \(\mathstrut -\mathstrut 49q^{8} \) \(\mathstrut +\mathstrut 59q^{9} \) \(\mathstrut +\mathstrut 8q^{10} \) \(\mathstrut +\mathstrut q^{11} \) \(\mathstrut +\mathstrut 8q^{12} \) \(\mathstrut +\mathstrut 9q^{13} \) \(\mathstrut -\mathstrut 18q^{14} \) \(\mathstrut +\mathstrut 15q^{15} \) \(\mathstrut +\mathstrut 49q^{16} \) \(\mathstrut -\mathstrut 27q^{17} \) \(\mathstrut -\mathstrut 59q^{18} \) \(\mathstrut +\mathstrut 27q^{19} \) \(\mathstrut -\mathstrut 8q^{20} \) \(\mathstrut +\mathstrut 13q^{21} \) \(\mathstrut -\mathstrut q^{22} \) \(\mathstrut +\mathstrut 16q^{23} \) \(\mathstrut -\mathstrut 8q^{24} \) \(\mathstrut +\mathstrut 71q^{25} \) \(\mathstrut -\mathstrut 9q^{26} \) \(\mathstrut +\mathstrut 29q^{27} \) \(\mathstrut +\mathstrut 18q^{28} \) \(\mathstrut -\mathstrut 7q^{29} \) \(\mathstrut -\mathstrut 15q^{30} \) \(\mathstrut +\mathstrut 75q^{31} \) \(\mathstrut -\mathstrut 49q^{32} \) \(\mathstrut -\mathstrut 3q^{33} \) \(\mathstrut +\mathstrut 27q^{34} \) \(\mathstrut -\mathstrut 16q^{35} \) \(\mathstrut +\mathstrut 59q^{36} \) \(\mathstrut +\mathstrut 36q^{37} \) \(\mathstrut -\mathstrut 27q^{38} \) \(\mathstrut +\mathstrut 24q^{39} \) \(\mathstrut +\mathstrut 8q^{40} \) \(\mathstrut -\mathstrut 12q^{41} \) \(\mathstrut -\mathstrut 13q^{42} \) \(\mathstrut +\mathstrut 22q^{43} \) \(\mathstrut +\mathstrut q^{44} \) \(\mathstrut +\mathstrut 5q^{45} \) \(\mathstrut -\mathstrut 16q^{46} \) \(\mathstrut +\mathstrut 26q^{47} \) \(\mathstrut +\mathstrut 8q^{48} \) \(\mathstrut +\mathstrut 107q^{49} \) \(\mathstrut -\mathstrut 71q^{50} \) \(\mathstrut +\mathstrut 35q^{51} \) \(\mathstrut +\mathstrut 9q^{52} \) \(\mathstrut -\mathstrut 10q^{53} \) \(\mathstrut -\mathstrut 29q^{54} \) \(\mathstrut +\mathstrut 76q^{55} \) \(\mathstrut -\mathstrut 18q^{56} \) \(\mathstrut -\mathstrut 10q^{57} \) \(\mathstrut +\mathstrut 7q^{58} \) \(\mathstrut +\mathstrut 9q^{59} \) \(\mathstrut +\mathstrut 15q^{60} \) \(\mathstrut +\mathstrut 87q^{61} \) \(\mathstrut -\mathstrut 75q^{62} \) \(\mathstrut +\mathstrut 68q^{63} \) \(\mathstrut +\mathstrut 49q^{64} \) \(\mathstrut -\mathstrut 6q^{65} \) \(\mathstrut +\mathstrut 3q^{66} \) \(\mathstrut +\mathstrut 46q^{67} \) \(\mathstrut -\mathstrut 27q^{68} \) \(\mathstrut +\mathstrut 70q^{69} \) \(\mathstrut +\mathstrut 16q^{70} \) \(\mathstrut +\mathstrut 40q^{71} \) \(\mathstrut -\mathstrut 59q^{72} \) \(\mathstrut +\mathstrut 6q^{73} \) \(\mathstrut -\mathstrut 36q^{74} \) \(\mathstrut +\mathstrut 69q^{75} \) \(\mathstrut +\mathstrut 27q^{76} \) \(\mathstrut -\mathstrut 12q^{77} \) \(\mathstrut -\mathstrut 24q^{78} \) \(\mathstrut +\mathstrut 76q^{79} \) \(\mathstrut -\mathstrut 8q^{80} \) \(\mathstrut +\mathstrut 77q^{81} \) \(\mathstrut +\mathstrut 12q^{82} \) \(\mathstrut -\mathstrut 32q^{83} \) \(\mathstrut +\mathstrut 13q^{84} \) \(\mathstrut +\mathstrut 19q^{85} \) \(\mathstrut -\mathstrut 22q^{86} \) \(\mathstrut +\mathstrut 36q^{87} \) \(\mathstrut -\mathstrut q^{88} \) \(\mathstrut +\mathstrut 34q^{89} \) \(\mathstrut -\mathstrut 5q^{90} \) \(\mathstrut +\mathstrut 119q^{91} \) \(\mathstrut +\mathstrut 16q^{92} \) \(\mathstrut -\mathstrut 5q^{93} \) \(\mathstrut -\mathstrut 26q^{94} \) \(\mathstrut -\mathstrut 2q^{95} \) \(\mathstrut -\mathstrut 8q^{96} \) \(\mathstrut +\mathstrut 52q^{97} \) \(\mathstrut -\mathstrut 107q^{98} \) \(\mathstrut +\mathstrut 26q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 −3.15201 1.00000 −2.19549 3.15201 −1.72689 −1.00000 6.93518 2.19549
1.2 −1.00000 −3.09927 1.00000 −2.61970 3.09927 −2.12795 −1.00000 6.60550 2.61970
1.3 −1.00000 −2.82194 1.00000 −1.46398 2.82194 3.02991 −1.00000 4.96334 1.46398
1.4 −1.00000 −2.80221 1.00000 1.91358 2.80221 −1.55673 −1.00000 4.85238 −1.91358
1.5 −1.00000 −2.75660 1.00000 3.24124 2.75660 3.57367 −1.00000 4.59882 −3.24124
1.6 −1.00000 −2.73587 1.00000 −3.97663 2.73587 4.88134 −1.00000 4.48496 3.97663
1.7 −1.00000 −2.70268 1.00000 1.64140 2.70268 4.14098 −1.00000 4.30446 −1.64140
1.8 −1.00000 −2.62176 1.00000 1.44534 2.62176 −4.09354 −1.00000 3.87363 −1.44534
1.9 −1.00000 −2.38186 1.00000 1.49052 2.38186 −1.41584 −1.00000 2.67326 −1.49052
1.10 −1.00000 −1.96102 1.00000 1.55397 1.96102 −2.12307 −1.00000 0.845608 −1.55397
1.11 −1.00000 −1.82471 1.00000 −3.41474 1.82471 −0.804060 −1.00000 0.329557 3.41474
1.12 −1.00000 −1.80649 1.00000 0.991336 1.80649 3.46798 −1.00000 0.263400 −0.991336
1.13 −1.00000 −1.65034 1.00000 −3.69499 1.65034 0.484734 −1.00000 −0.276387 3.69499
1.14 −1.00000 −1.64240 1.00000 −1.67247 1.64240 −0.216059 −1.00000 −0.302515 1.67247
1.15 −1.00000 −1.33333 1.00000 2.98893 1.33333 1.91777 −1.00000 −1.22223 −2.98893
1.16 −1.00000 −1.09618 1.00000 −0.358556 1.09618 −2.93033 −1.00000 −1.79840 0.358556
1.17 −1.00000 −0.796272 1.00000 −4.15767 0.796272 2.72658 −1.00000 −2.36595 4.15767
1.18 −1.00000 −0.604236 1.00000 −1.43680 0.604236 3.64541 −1.00000 −2.63490 1.43680
1.19 −1.00000 −0.600384 1.00000 0.151444 0.600384 −2.68719 −1.00000 −2.63954 −0.151444
1.20 −1.00000 −0.372757 1.00000 0.124605 0.372757 −2.88406 −1.00000 −2.86105 −0.124605
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
\(2\) \(1\)
\(2017\) \(-1\)