Properties

Label 4029.2.a.j
Level 4029
Weight 2
Character orbit 4029.a
Self dual yes
Analytic conductor 32.172
Analytic rank 0
Dimension 25
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: \(0\)
Dimension: \(25\)
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.

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

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 −2.64938 1.00000 5.01922 0.160966 −2.64938 −0.166444 −7.99906 1.00000 −0.426461
1.2 −2.33976 1.00000 3.47445 −0.253256 −2.33976 −1.85897 −3.44986 1.00000 0.592558
1.3 −2.01628 1.00000 2.06539 1.36022 −2.01628 −1.99574 −0.131838 1.00000 −2.74259
1.4 −1.89235 1.00000 1.58099 −3.51419 −1.89235 −2.76756 0.792916 1.00000 6.65008
1.5 −1.73737 1.00000 1.01844 3.91288 −1.73737 2.21072 1.70533 1.00000 −6.79810
1.6 −1.71946 1.00000 0.956548 −0.401705 −1.71946 3.91285 1.79418 1.00000 0.690716
1.7 −1.19187 1.00000 −0.579444 −1.97485 −1.19187 1.20760 3.07436 1.00000 2.35376
1.8 −0.991328 1.00000 −1.01727 3.49390 −0.991328 −2.79439 2.99110 1.00000 −3.46360
1.9 −0.960337 1.00000 −1.07775 −2.82407 −0.960337 −0.386767 2.95568 1.00000 2.71206
1.10 −0.645538 1.00000 −1.58328 2.70107 −0.645538 4.18986 2.31314 1.00000 −1.74364
1.11 −0.517388 1.00000 −1.73231 −0.162302 −0.517388 −5.01323 1.93105 1.00000 0.0839730
1.12 0.367511 1.00000 −1.86494 −0.382809 0.367511 2.18053 −1.42041 1.00000 −0.140687
1.13 0.375442 1.00000 −1.85904 −2.43598 0.375442 3.04964 −1.44885 1.00000 −0.914570
1.14 0.777638 1.00000 −1.39528 1.77745 0.777638 0.717944 −2.64030 1.00000 1.38222
1.15 0.782307 1.00000 −1.38800 −1.22158 0.782307 −4.37722 −2.65045 1.00000 −0.955651
1.16 1.12130 1.00000 −0.742675 3.71073 1.12130 4.45947 −3.07538 1.00000 4.16086
1.17 1.24074 1.00000 −0.460556 −3.76050 1.24074 −4.20824 −3.05292 1.00000 −4.66581
1.18 1.54939 1.00000 0.400614 −2.39535 1.54939 1.82690 −2.47808 1.00000 −3.71134
1.19 1.88836 1.00000 1.56590 −1.95166 1.88836 −1.51083 −0.819741 1.00000 −3.68543
1.20 2.09012 1.00000 2.36860 3.44470 2.09012 0.589185 0.770426 1.00000 7.19983
See all 25 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.25
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.j 25
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
4029.2.a.j 25 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(4029))\):

\(T_{2}^{25} - \cdots\)
\(T_{5}^{25} - \cdots\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database