Properties

Label 6027.2.a.h
Level 6027
Weight 2
Character orbit 6027.a
Self dual yes
Analytic conductor 48.126
Analytic rank 0
Dimension 1
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) \(=\) \( 6027 = 3 \cdot 7^{2} \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6027.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(48.1258372982\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 861)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q + 2q^{2} + q^{3} + 2q^{4} + 2q^{6} + q^{9} + O(q^{10}) \) \( q + 2q^{2} + q^{3} + 2q^{4} + 2q^{6} + q^{9} + 4q^{11} + 2q^{12} - q^{13} - 4q^{16} + 4q^{17} + 2q^{18} + 7q^{19} + 8q^{22} + 6q^{23} - 5q^{25} - 2q^{26} + q^{27} - 8q^{29} + q^{31} - 8q^{32} + 4q^{33} + 8q^{34} + 2q^{36} + 7q^{37} + 14q^{38} - q^{39} - q^{41} - 7q^{43} + 8q^{44} + 12q^{46} - 4q^{48} - 10q^{50} + 4q^{51} - 2q^{52} + 4q^{53} + 2q^{54} + 7q^{57} - 16q^{58} + 8q^{59} + 2q^{61} + 2q^{62} - 8q^{64} + 8q^{66} + 13q^{67} + 8q^{68} + 6q^{69} - 6q^{71} + q^{73} + 14q^{74} - 5q^{75} + 14q^{76} - 2q^{78} - 7q^{79} + q^{81} - 2q^{82} + 8q^{83} - 14q^{86} - 8q^{87} + 14q^{89} + 12q^{92} + q^{93} - 8q^{96} - 2q^{97} + 4q^{99} + O(q^{100}) \)

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
2.00000 1.00000 2.00000 0 2.00000 0 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 6027.2.a.h 1
7.b odd 2 1 6027.2.a.g 1
7.c even 3 2 861.2.i.a 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
861.2.i.a 2 7.c even 3 2
6027.2.a.g 1 7.b odd 2 1
6027.2.a.h 1 1.a even 1 1 trivial

Atkin-Lehner signs

\( p \) Sign
\(3\) \(-1\)
\(7\) \(1\)
\(41\) \(1\)

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(6027))\):

\( T_{2} - 2 \)
\( T_{5} \)
\( T_{13} + 1 \)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( 1 - 2 T + 2 T^{2} \)
$3$ \( 1 - T \)
$5$ \( 1 + 5 T^{2} \)
$7$ 1
$11$ \( 1 - 4 T + 11 T^{2} \)
$13$ \( 1 + T + 13 T^{2} \)
$17$ \( 1 - 4 T + 17 T^{2} \)
$19$ \( 1 - 7 T + 19 T^{2} \)
$23$ \( 1 - 6 T + 23 T^{2} \)
$29$ \( 1 + 8 T + 29 T^{2} \)
$31$ \( 1 - T + 31 T^{2} \)
$37$ \( 1 - 7 T + 37 T^{2} \)
$41$ \( 1 + T \)
$43$ \( 1 + 7 T + 43 T^{2} \)
$47$ \( 1 + 47 T^{2} \)
$53$ \( 1 - 4 T + 53 T^{2} \)
$59$ \( 1 - 8 T + 59 T^{2} \)
$61$ \( 1 - 2 T + 61 T^{2} \)
$67$ \( 1 - 13 T + 67 T^{2} \)
$71$ \( 1 + 6 T + 71 T^{2} \)
$73$ \( 1 - T + 73 T^{2} \)
$79$ \( 1 + 7 T + 79 T^{2} \)
$83$ \( 1 - 8 T + 83 T^{2} \)
$89$ \( 1 - 14 T + 89 T^{2} \)
$97$ \( 1 + 2 T + 97 T^{2} \)
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