Properties

Label 4029.2.a.l
Level 4029
Weight 2
Character orbit 4029.a
Self dual Yes
Analytic conductor 32.172
Analytic rank 0
Dimension 32
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: \(32\)
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.

\(\operatorname{Tr}(f)(q) = \) \(32q \) \(\mathstrut -\mathstrut q^{2} \) \(\mathstrut -\mathstrut 32q^{3} \) \(\mathstrut +\mathstrut 41q^{4} \) \(\mathstrut -\mathstrut q^{5} \) \(\mathstrut +\mathstrut q^{6} \) \(\mathstrut +\mathstrut 4q^{7} \) \(\mathstrut -\mathstrut 3q^{8} \) \(\mathstrut +\mathstrut 32q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \(32q \) \(\mathstrut -\mathstrut q^{2} \) \(\mathstrut -\mathstrut 32q^{3} \) \(\mathstrut +\mathstrut 41q^{4} \) \(\mathstrut -\mathstrut q^{5} \) \(\mathstrut +\mathstrut q^{6} \) \(\mathstrut +\mathstrut 4q^{7} \) \(\mathstrut -\mathstrut 3q^{8} \) \(\mathstrut +\mathstrut 32q^{9} \) \(\mathstrut +\mathstrut 17q^{10} \) \(\mathstrut +\mathstrut 8q^{11} \) \(\mathstrut -\mathstrut 41q^{12} \) \(\mathstrut +\mathstrut 17q^{13} \) \(\mathstrut +\mathstrut q^{14} \) \(\mathstrut +\mathstrut q^{15} \) \(\mathstrut +\mathstrut 55q^{16} \) \(\mathstrut -\mathstrut 32q^{17} \) \(\mathstrut -\mathstrut q^{18} \) \(\mathstrut +\mathstrut 48q^{19} \) \(\mathstrut -\mathstrut 7q^{20} \) \(\mathstrut -\mathstrut 4q^{21} \) \(\mathstrut -\mathstrut 4q^{22} \) \(\mathstrut -\mathstrut 19q^{23} \) \(\mathstrut +\mathstrut 3q^{24} \) \(\mathstrut +\mathstrut 63q^{25} \) \(\mathstrut +\mathstrut 27q^{26} \) \(\mathstrut -\mathstrut 32q^{27} \) \(\mathstrut +\mathstrut 17q^{28} \) \(\mathstrut -\mathstrut 15q^{29} \) \(\mathstrut -\mathstrut 17q^{30} \) \(\mathstrut +\mathstrut 20q^{31} \) \(\mathstrut +\mathstrut 13q^{32} \) \(\mathstrut -\mathstrut 8q^{33} \) \(\mathstrut +\mathstrut q^{34} \) \(\mathstrut +\mathstrut 22q^{35} \) \(\mathstrut +\mathstrut 41q^{36} \) \(\mathstrut +\mathstrut 6q^{37} \) \(\mathstrut +\mathstrut 11q^{38} \) \(\mathstrut -\mathstrut 17q^{39} \) \(\mathstrut +\mathstrut 47q^{40} \) \(\mathstrut +\mathstrut q^{41} \) \(\mathstrut -\mathstrut q^{42} \) \(\mathstrut +\mathstrut 40q^{43} \) \(\mathstrut +\mathstrut 22q^{44} \) \(\mathstrut -\mathstrut q^{45} \) \(\mathstrut +\mathstrut 5q^{46} \) \(\mathstrut -\mathstrut 5q^{47} \) \(\mathstrut -\mathstrut 55q^{48} \) \(\mathstrut +\mathstrut 88q^{49} \) \(\mathstrut +\mathstrut 17q^{50} \) \(\mathstrut +\mathstrut 32q^{51} \) \(\mathstrut +\mathstrut 23q^{52} \) \(\mathstrut -\mathstrut 34q^{53} \) \(\mathstrut +\mathstrut q^{54} \) \(\mathstrut +\mathstrut 48q^{55} \) \(\mathstrut -\mathstrut 48q^{57} \) \(\mathstrut -\mathstrut 9q^{58} \) \(\mathstrut +\mathstrut 41q^{59} \) \(\mathstrut +\mathstrut 7q^{60} \) \(\mathstrut +\mathstrut 20q^{61} \) \(\mathstrut +\mathstrut 15q^{62} \) \(\mathstrut +\mathstrut 4q^{63} \) \(\mathstrut +\mathstrut 93q^{64} \) \(\mathstrut -\mathstrut 58q^{65} \) \(\mathstrut +\mathstrut 4q^{66} \) \(\mathstrut +\mathstrut 52q^{67} \) \(\mathstrut -\mathstrut 41q^{68} \) \(\mathstrut +\mathstrut 19q^{69} \) \(\mathstrut +\mathstrut 25q^{70} \) \(\mathstrut +\mathstrut q^{71} \) \(\mathstrut -\mathstrut 3q^{72} \) \(\mathstrut +\mathstrut 19q^{73} \) \(\mathstrut +\mathstrut 12q^{74} \) \(\mathstrut -\mathstrut 63q^{75} \) \(\mathstrut +\mathstrut 128q^{76} \) \(\mathstrut -\mathstrut 20q^{77} \) \(\mathstrut -\mathstrut 27q^{78} \) \(\mathstrut +\mathstrut 32q^{79} \) \(\mathstrut -\mathstrut 16q^{80} \) \(\mathstrut +\mathstrut 32q^{81} \) \(\mathstrut -\mathstrut 5q^{82} \) \(\mathstrut +\mathstrut 31q^{83} \) \(\mathstrut -\mathstrut 17q^{84} \) \(\mathstrut +\mathstrut q^{85} \) \(\mathstrut -\mathstrut 62q^{86} \) \(\mathstrut +\mathstrut 15q^{87} \) \(\mathstrut +\mathstrut 35q^{88} \) \(\mathstrut +\mathstrut 18q^{89} \) \(\mathstrut +\mathstrut 17q^{90} \) \(\mathstrut +\mathstrut 48q^{91} \) \(\mathstrut -\mathstrut 75q^{92} \) \(\mathstrut -\mathstrut 20q^{93} \) \(\mathstrut +\mathstrut 29q^{94} \) \(\mathstrut +\mathstrut 5q^{95} \) \(\mathstrut -\mathstrut 13q^{96} \) \(\mathstrut +\mathstrut 17q^{97} \) \(\mathstrut +\mathstrut 30q^{98} \) \(\mathstrut +\mathstrut 8q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 −2.77670 −1.00000 5.71004 −0.322981 2.77670 −2.70395 −10.3017 1.00000 0.896820
1.2 −2.65510 −1.00000 5.04957 −3.36488 2.65510 2.92058 −8.09693 1.00000 8.93412
1.3 −2.57711 −1.00000 4.64151 2.80201 2.57711 −2.75409 −6.80748 1.00000 −7.22109
1.4 −2.50856 −1.00000 4.29286 −2.69434 2.50856 3.74400 −5.75176 1.00000 6.75889
1.5 −2.27866 −1.00000 3.19228 −3.13196 2.27866 −0.0802156 −2.71679 1.00000 7.13667
1.6 −2.16757 −1.00000 2.69838 2.47527 2.16757 5.12027 −1.51379 1.00000 −5.36532
1.7 −2.03180 −1.00000 2.12821 1.66964 2.03180 −1.52463 −0.260503 1.00000 −3.39237
1.8 −1.67650 −1.00000 0.810659 −3.83953 1.67650 −4.72769 1.99393 1.00000 6.43697
1.9 −1.61915 −1.00000 0.621643 1.62143 1.61915 3.15810 2.23177 1.00000 −2.62534
1.10 −1.60231 −1.00000 0.567397 −0.489899 1.60231 −0.574101 2.29547 1.00000 0.784971
1.11 −1.34067 −1.00000 −0.202611 1.16053 1.34067 −4.05917 2.95297 1.00000 −1.55588
1.12 −1.17408 −1.00000 −0.621542 3.86856 1.17408 3.06255 3.07789 1.00000 −4.54199
1.13 −0.857766 −1.00000 −1.26424 −4.41756 0.857766 0.00991750 2.79995 1.00000 3.78923
1.14 −0.510062 −1.00000 −1.73984 −1.60726 0.510062 −0.772958 1.90755 1.00000 0.819801
1.15 −0.249798 −1.00000 −1.93760 0.601573 0.249798 −2.69175 0.983604 1.00000 −0.150272
1.16 −0.0772262 −1.00000 −1.99404 3.97384 0.0772262 0.969209 0.308444 1.00000 −0.306884
1.17 −0.0717307 −1.00000 −1.99485 −1.92367 0.0717307 3.89464 0.286554 1.00000 0.137987
1.18 0.403182 −1.00000 −1.83744 2.23661 −0.403182 −0.778796 −1.54719 1.00000 0.901761
1.19 0.437930 −1.00000 −1.80822 −1.50297 −0.437930 −4.33772 −1.66773 1.00000 −0.658196
1.20 0.937640 −1.00000 −1.12083 0.347083 −0.937640 4.09662 −2.92622 1.00000 0.325439
See all 32 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.32
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 \(S_{2}^{\mathrm{new}}(\Gamma_0(4029))\):

\(T_{2}^{32} + \cdots\)
\(T_{5}^{32} + \cdots\)