Properties

Label 4029.2.a.k
Level 4029
Weight 2
Character orbit 4029.a
Self dual Yes
Analytic conductor 32.172
Analytic rank 0
Dimension 31
CM No

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Newspace parameters

Level: \( N \) = \( 4029 = 3 \cdot 17 \cdot 79 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4029.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.1717269744\)
Analytic rank: \(0\)
Dimension: \(31\)
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.

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

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 −2.61491 1.00000 4.83775 −2.62328 −2.61491 −4.80522 −7.42046 1.00000 6.85964
1.2 −2.56879 1.00000 4.59868 3.14567 −2.56879 −0.137684 −6.67546 1.00000 −8.08058
1.3 −2.41826 1.00000 3.84800 1.43707 −2.41826 3.74160 −4.46895 1.00000 −3.47522
1.4 −2.28064 1.00000 3.20133 2.67486 −2.28064 −3.60745 −2.73981 1.00000 −6.10039
1.5 −2.22001 1.00000 2.92842 −1.63428 −2.22001 −1.90265 −2.06110 1.00000 3.62811
1.6 −1.88694 1.00000 1.56054 −0.846288 −1.88694 3.01609 0.829236 1.00000 1.59689
1.7 −1.73268 1.00000 1.00217 2.89501 −1.73268 3.30216 1.72891 1.00000 −5.01613
1.8 −1.49453 1.00000 0.233609 −1.69557 −1.49453 0.268778 2.63992 1.00000 2.53407
1.9 −1.27443 1.00000 −0.375837 −3.50336 −1.27443 −0.192219 3.02783 1.00000 4.46478
1.10 −1.26690 1.00000 −0.394972 3.60603 −1.26690 −2.46109 3.03418 1.00000 −4.56847
1.11 −0.719826 1.00000 −1.48185 1.82945 −0.719826 0.414755 2.50633 1.00000 −1.31688
1.12 −0.639237 1.00000 −1.59138 −1.53158 −0.639237 −2.74819 2.29574 1.00000 0.979040
1.13 −0.626356 1.00000 −1.60768 −1.73582 −0.626356 −3.52892 2.25969 1.00000 1.08724
1.14 −0.103363 1.00000 −1.98932 −2.25663 −0.103363 4.11147 0.412347 1.00000 0.233252
1.15 0.0488355 1.00000 −1.99762 −0.188126 0.0488355 3.46836 −0.195225 1.00000 −0.00918720
1.16 0.0509119 1.00000 −1.99741 3.95784 0.0509119 1.89285 −0.203515 1.00000 0.201501
1.17 0.308270 1.00000 −1.90497 2.48291 0.308270 3.17570 −1.20379 1.00000 0.765408
1.18 0.617959 1.00000 −1.61813 3.16624 0.617959 −0.196167 −2.23585 1.00000 1.95660
1.19 0.680303 1.00000 −1.53719 −1.16933 0.680303 −3.22223 −2.40636 1.00000 −0.795496
1.20 0.959467 1.00000 −1.07942 −3.93035 0.959467 −0.0159719 −2.95460 1.00000 −3.77104
See all 31 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.31
Significant digits:
Format:

Inner twists

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

Atkin-Lehner signs

\( p \) Sign
\(3\) \(-1\)
\(17\) \(-1\)
\(79\) \(-1\)

Hecke kernels

This newform can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(4029))\):

\(T_{2}^{31} - \cdots\)
\(T_{5}^{31} - \cdots\)