Properties

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

Related objects

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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: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q + q^{3} - 2q^{4} - 3q^{5} + q^{7} + q^{9} + O(q^{10}) \) \( q + q^{3} - 2q^{4} - 3q^{5} + q^{7} + q^{9} - 4q^{11} - 2q^{12} + 2q^{13} - 3q^{15} + 4q^{16} + q^{17} + 5q^{19} + 6q^{20} + q^{21} - 7q^{23} + 4q^{25} + q^{27} - 2q^{28} + 10q^{29} + 4q^{31} - 4q^{33} - 3q^{35} - 2q^{36} - 5q^{37} + 2q^{39} - 6q^{41} + 6q^{43} + 8q^{44} - 3q^{45} - 3q^{47} + 4q^{48} - 6q^{49} + q^{51} - 4q^{52} + 3q^{53} + 12q^{55} + 5q^{57} - 9q^{59} + 6q^{60} + 9q^{61} + q^{63} - 8q^{64} - 6q^{65} + 12q^{67} - 2q^{68} - 7q^{69} - 6q^{71} - 4q^{73} + 4q^{75} - 10q^{76} - 4q^{77} - q^{79} - 12q^{80} + q^{81} - 16q^{83} - 2q^{84} - 3q^{85} + 10q^{87} + 12q^{89} + 2q^{91} + 14q^{92} + 4q^{93} - 15q^{95} + 2q^{97} - 4q^{99} + O(q^{100}) \)

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 \(\iota_m(\nu)\) \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1.1
0
0 1.00000 −2.00000 −3.00000 0 1.00000 0 1.00000 0
\(n\): e.g. 2-40 or 990-1000
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.a 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
4029.2.a.a 1 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(4029))\):

\( T_{2} \)
\( T_{5} + 3 \)

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ \( 1 + 2 T^{2} \)
$3$ \( 1 - T \)
$5$ \( 1 + 3 T + 5 T^{2} \)
$7$ \( 1 - T + 7 T^{2} \)
$11$ \( 1 + 4 T + 11 T^{2} \)
$13$ \( 1 - 2 T + 13 T^{2} \)
$17$ \( 1 - T \)
$19$ \( 1 - 5 T + 19 T^{2} \)
$23$ \( 1 + 7 T + 23 T^{2} \)
$29$ \( 1 - 10 T + 29 T^{2} \)
$31$ \( 1 - 4 T + 31 T^{2} \)
$37$ \( 1 + 5 T + 37 T^{2} \)
$41$ \( 1 + 6 T + 41 T^{2} \)
$43$ \( 1 - 6 T + 43 T^{2} \)
$47$ \( 1 + 3 T + 47 T^{2} \)
$53$ \( 1 - 3 T + 53 T^{2} \)
$59$ \( 1 + 9 T + 59 T^{2} \)
$61$ \( 1 - 9 T + 61 T^{2} \)
$67$ \( 1 - 12 T + 67 T^{2} \)
$71$ \( 1 + 6 T + 71 T^{2} \)
$73$ \( 1 + 4 T + 73 T^{2} \)
$79$ \( 1 + T \)
$83$ \( 1 + 16 T + 83 T^{2} \)
$89$ \( 1 - 12 T + 89 T^{2} \)
$97$ \( 1 - 2 T + 97 T^{2} \)
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