Properties

Label 4029.2.a.g
Level 4029
Weight 2
Character orbit 4029.a
Self dual yes
Analytic conductor 32.172
Analytic rank 1
Dimension 22
CM no
Inner twists 1

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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: \(1\)
Dimension: \(22\)
Coefficient ring index: multiple of None
Twist minimal: yes
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.

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

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 −2.65075 −1.00000 5.02646 2.28366 2.65075 3.33771 −8.02237 1.00000 −6.05341
1.2 −2.17605 −1.00000 2.73521 1.58006 2.17605 −0.969003 −1.59985 1.00000 −3.43828
1.3 −2.12762 −1.00000 2.52678 −3.72932 2.12762 −2.25712 −1.12080 1.00000 7.93460
1.4 −1.99316 −1.00000 1.97270 −1.27823 1.99316 0.558075 0.0544076 1.00000 2.54772
1.5 −1.52080 −1.00000 0.312840 4.21021 1.52080 −4.25725 2.56584 1.00000 −6.40289
1.6 −1.32697 −1.00000 −0.239163 −0.116261 1.32697 0.614865 2.97129 1.00000 0.154274
1.7 −1.06401 −1.00000 −0.867885 2.98305 1.06401 −1.35946 3.05146 1.00000 −3.17400
1.8 −1.04848 −1.00000 −0.900691 −0.0290827 1.04848 2.65326 3.04131 1.00000 0.0304926
1.9 −0.770110 −1.00000 −1.40693 −2.32965 0.770110 −2.53396 2.62371 1.00000 1.79409
1.10 −0.193122 −1.00000 −1.96270 0.930576 0.193122 3.24035 0.765286 1.00000 −0.179715
1.11 −0.0913921 −1.00000 −1.99165 −1.96751 0.0913921 −3.33061 0.364805 1.00000 0.179815
1.12 0.241023 −1.00000 −1.94191 −3.77754 −0.241023 3.81286 −0.950090 1.00000 −0.910473
1.13 0.321205 −1.00000 −1.89683 2.50638 −0.321205 1.79876 −1.25168 1.00000 0.805062
1.14 0.977627 −1.00000 −1.04425 4.02352 −0.977627 0.138355 −2.97614 1.00000 3.93350
1.15 1.13663 −1.00000 −0.708075 0.214323 −1.13663 −3.67011 −3.07808 1.00000 0.243606
1.16 1.23345 −1.00000 −0.478591 1.09712 −1.23345 2.41639 −3.05723 1.00000 1.35325
1.17 1.71068 −1.00000 0.926413 −0.235086 −1.71068 −1.75585 −1.83656 1.00000 −0.402156
1.18 2.05356 −1.00000 2.21711 2.39106 −2.05356 −1.51026 0.445844 1.00000 4.91018
1.19 2.08589 −1.00000 2.35095 0.140268 −2.08589 1.76887 0.732041 1.00000 0.292585
1.20 2.23779 −1.00000 3.00772 −1.81110 −2.23779 1.95143 2.25507 1.00000 −4.05288
See all 22 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.22
Significant digits:
Format:

Inner twists

This newform does not admit any (nontrivial) inner twists.

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 4029.2.a.g 22
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
4029.2.a.g 22 1.a even 1 1 trivial

Atkin-Lehner signs

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

Hecke kernels

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

\(T_{2}^{22} - \cdots\)
\(T_{5}^{22} - \cdots\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database