Properties

Label 4029.2.a.i
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.

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

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 −2.74441 −1.00000 5.53180 1.03743 2.74441 3.45867 −9.69270 1.00000 −2.84714
1.2 −2.73699 −1.00000 5.49111 −3.81698 2.73699 −1.31322 −9.55513 1.00000 10.4470
1.3 −2.33071 −1.00000 3.43222 −2.50795 2.33071 −3.36649 −3.33810 1.00000 5.84531
1.4 −2.24485 −1.00000 3.03936 −1.59596 2.24485 3.55304 −2.33321 1.00000 3.58269
1.5 −1.94224 −1.00000 1.77230 1.77354 1.94224 −4.05542 0.442253 1.00000 −3.44464
1.6 −1.76780 −1.00000 1.12513 2.69545 1.76780 −0.714180 1.54660 1.00000 −4.76502
1.7 −1.65426 −1.00000 0.736566 1.27876 1.65426 3.55385 2.09004 1.00000 −2.11539
1.8 −1.40882 −1.00000 −0.0152236 −1.73169 1.40882 −3.56707 2.83909 1.00000 2.43964
1.9 −1.11147 −1.00000 −0.764631 −3.15121 1.11147 3.42561 3.07281 1.00000 3.50248
1.10 −0.756348 −1.00000 −1.42794 1.91333 0.756348 −1.89190 2.59271 1.00000 −1.44714
1.11 −0.693247 −1.00000 −1.51941 3.35677 0.693247 3.59459 2.43982 1.00000 −2.32707
1.12 −0.495377 −1.00000 −1.75460 −3.92669 0.495377 0.792012 1.85994 1.00000 1.94519
1.13 −0.141417 −1.00000 −1.98000 0.465802 0.141417 −1.58651 0.562841 1.00000 −0.0658725
1.14 −0.0249015 −1.00000 −1.99938 −2.90996 0.0249015 1.03650 0.0995904 1.00000 0.0724622
1.15 0.309286 −1.00000 −1.90434 −1.20431 −0.309286 2.27357 −1.20756 1.00000 −0.372476
1.16 0.454785 −1.00000 −1.79317 2.38795 −0.454785 0.109769 −1.72508 1.00000 1.08600
1.17 0.813229 −1.00000 −1.33866 1.02037 −0.813229 −1.92081 −2.71509 1.00000 0.829792
1.18 1.57851 −1.00000 0.491696 3.59209 −1.57851 3.03695 −2.38087 1.00000 5.67016
1.19 1.57938 −1.00000 0.494430 −1.92798 −1.57938 −2.95110 −2.37786 1.00000 −3.04500
1.20 1.74670 −1.00000 1.05095 −2.47902 −1.74670 4.46118 −1.65770 1.00000 −4.33009
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.i 25
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
4029.2.a.i 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