Properties

Label 4029.2.a.f
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.

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

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 −2.46822 −1.00000 4.09210 0.833166 2.46822 −0.715489 −5.16375 1.00000 −2.05644
1.2 −2.41406 −1.00000 3.82770 1.38907 2.41406 −5.15713 −4.41218 1.00000 −3.35331
1.3 −2.30059 −1.00000 3.29272 −0.193972 2.30059 1.10356 −2.97403 1.00000 0.446250
1.4 −1.97908 −1.00000 1.91674 3.55725 1.97908 2.67617 0.164776 1.00000 −7.04007
1.5 −1.55293 −1.00000 0.411606 −3.25042 1.55293 1.50369 2.46667 1.00000 5.04769
1.6 −1.21952 −1.00000 −0.512778 −1.58706 1.21952 −3.41478 3.06438 1.00000 1.93545
1.7 −1.18480 −1.00000 −0.596253 −2.40127 1.18480 −0.655760 3.07604 1.00000 2.84502
1.8 −0.922410 −1.00000 −1.14916 −0.0437394 0.922410 4.58186 2.90482 1.00000 0.0403457
1.9 −0.891747 −1.00000 −1.20479 2.60961 0.891747 −3.10366 2.85786 1.00000 −2.32711
1.10 −0.821645 −1.00000 −1.32490 1.58661 0.821645 1.25319 2.73189 1.00000 −1.30363
1.11 −0.236594 −1.00000 −1.94402 3.94072 0.236594 −1.91925 0.933134 1.00000 −0.932353
1.12 0.220817 −1.00000 −1.95124 −3.79014 −0.220817 −3.98824 −0.872503 1.00000 −0.836928
1.13 0.736590 −1.00000 −1.45743 −2.90793 −0.736590 −3.09183 −2.54671 1.00000 −2.14196
1.14 0.795328 −1.00000 −1.36745 2.82245 −0.795328 −3.74228 −2.67823 1.00000 2.24477
1.15 0.799151 −1.00000 −1.36136 0.403932 −0.799151 1.36573 −2.68623 1.00000 0.322802
1.16 0.843162 −1.00000 −1.28908 −2.14706 −0.843162 4.16350 −2.77323 1.00000 −1.81032
1.17 1.73045 −1.00000 0.994457 2.73352 −1.73045 −2.97598 −1.74004 1.00000 4.73022
1.18 1.95682 −1.00000 1.82914 0.334746 −1.95682 4.67011 −0.334351 1.00000 0.655037
1.19 2.12169 −1.00000 2.50157 3.09428 −2.12169 −1.64576 1.06418 1.00000 6.56509
1.20 2.37194 −1.00000 3.62611 −0.369639 −2.37194 −3.46859 3.85703 1.00000 −0.876762
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.f 22
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
4029.2.a.f 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