Properties

Label 6034.2.a.c
Level 6034
Weight 2
Character orbit 6034.a
Self dual yes
Analytic conductor 48.182
Analytic rank 1
Dimension 1
CM no
Inner twists 1

Related objects

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Newspace parameters

Level: \( N \) = \( 6034 = 2 \cdot 7 \cdot 431 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6034.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(48.1817325796\)
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

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

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
−1.00000 −2.00000 1.00000 −4.00000 2.00000 −1.00000 −1.00000 1.00000 4.00000
\(n\): 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 6034.2.a.c 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
6034.2.a.c 1 1.a even 1 1 trivial

Atkin-Lehner signs

\( p \) Sign
\(2\) \(1\)
\(7\) \(1\)
\(431\) \(1\)

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(6034))\):

\( T_{3} + 2 \)
\( T_{5} + 4 \)
\( T_{11} + 4 \)

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ \( 1 + T \)
$3$ \( 1 + 2 T + 3 T^{2} \)
$5$ \( 1 + 4 T + 5 T^{2} \)
$7$ \( 1 + T \)
$11$ \( 1 + 4 T + 11 T^{2} \)
$13$ \( 1 + 6 T + 13 T^{2} \)
$17$ \( 1 + 2 T + 17 T^{2} \)
$19$ \( 1 + 2 T + 19 T^{2} \)
$23$ \( 1 + 23 T^{2} \)
$29$ \( 1 - 6 T + 29 T^{2} \)
$31$ \( 1 + 8 T + 31 T^{2} \)
$37$ \( 1 - 8 T + 37 T^{2} \)
$41$ \( 1 + 10 T + 41 T^{2} \)
$43$ \( 1 + 6 T + 43 T^{2} \)
$47$ \( 1 + 47 T^{2} \)
$53$ \( 1 - 6 T + 53 T^{2} \)
$59$ \( 1 - 6 T + 59 T^{2} \)
$61$ \( 1 - 8 T + 61 T^{2} \)
$67$ \( 1 - 10 T + 67 T^{2} \)
$71$ \( 1 + 71 T^{2} \)
$73$ \( 1 + 2 T + 73 T^{2} \)
$79$ \( 1 + 79 T^{2} \)
$83$ \( 1 - 4 T + 83 T^{2} \)
$89$ \( 1 + 18 T + 89 T^{2} \)
$97$ \( 1 - 6 T + 97 T^{2} \)
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