Properties

Label 4029.2.a.h
Level 4029
Weight 2
Character orbit 4029.a
Self dual yes
Analytic conductor 32.172
Analytic rank 1
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: \(1\)
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.

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

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 −2.72160 1.00000 5.40711 −2.75991 −2.72160 0.631996 −9.27279 1.00000 7.51137
1.2 −2.56536 1.00000 4.58108 2.03955 −2.56536 3.97532 −6.62141 1.00000 −5.23220
1.3 −2.38168 1.00000 3.67240 4.36966 −2.38168 −4.18483 −3.98313 1.00000 −10.4071
1.4 −2.32685 1.00000 3.41424 −3.48051 −2.32685 3.88205 −3.29073 1.00000 8.09862
1.5 −2.14934 1.00000 2.61967 −2.01369 −2.14934 −1.06654 −1.33187 1.00000 4.32810
1.6 −2.03763 1.00000 2.15194 1.97362 −2.03763 1.01571 −0.309598 1.00000 −4.02151
1.7 −2.01259 1.00000 2.05052 −0.898800 −2.01259 −4.86016 −0.101684 1.00000 1.80892
1.8 −1.64354 1.00000 0.701226 −1.87389 −1.64354 4.02619 2.13459 1.00000 3.07982
1.9 −1.29135 1.00000 −0.332415 2.00535 −1.29135 −2.01131 3.01196 1.00000 −2.58960
1.10 −1.16862 1.00000 −0.634325 −0.405562 −1.16862 −1.60950 3.07853 1.00000 0.473948
1.11 −0.743888 1.00000 −1.44663 0.602376 −0.743888 4.42261 2.56391 1.00000 −0.448100
1.12 −0.691575 1.00000 −1.52172 1.10999 −0.691575 −0.538181 2.43554 1.00000 −0.767639
1.13 −0.319374 1.00000 −1.89800 −2.81066 −0.319374 −2.62902 1.24492 1.00000 0.897652
1.14 −0.107521 1.00000 −1.98844 −4.11054 −0.107521 −2.41834 0.428841 1.00000 0.441969
1.15 0.0993996 1.00000 −1.99012 1.12985 0.0993996 0.411227 −0.396616 1.00000 0.112306
1.16 0.384561 1.00000 −1.85211 −1.18123 0.384561 2.30830 −1.48137 1.00000 −0.454254
1.17 0.785597 1.00000 −1.38284 −0.680986 0.785597 0.961909 −2.65755 1.00000 −0.534981
1.18 1.22160 1.00000 −0.507691 −3.76998 1.22160 4.22641 −3.06340 1.00000 −4.60542
1.19 1.36573 1.00000 −0.134771 0.714593 1.36573 −2.88499 −2.91553 1.00000 0.975944
1.20 1.40291 1.00000 −0.0318502 3.36351 1.40291 −1.96099 −2.85050 1.00000 4.71869
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.h 25
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
4029.2.a.h 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