Properties

Label 483.2.a.a
Level $483$
Weight $2$
Character orbit 483.a
Self dual yes
Analytic conductor $3.857$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 483 = 3 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 483.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(3.85677441763\)
Analytic rank: \(0\)
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

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

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 1.00000 0 1.00000 0
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(3\) \(-1\)
\(7\) \(-1\)
\(23\) \(-1\)

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 483.2.a.a 1
3.b odd 2 1 1449.2.a.c 1
4.b odd 2 1 7728.2.a.e 1
7.b odd 2 1 3381.2.a.m 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
483.2.a.a 1 1.a even 1 1 trivial
1449.2.a.c 1 3.b odd 2 1
3381.2.a.m 1 7.b odd 2 1
7728.2.a.e 1 4.b odd 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(483))\):

\( T_{2} - 2 \)
\( T_{5} \)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( -2 + T \)
$3$ \( -1 + T \)
$5$ \( T \)
$7$ \( -1 + T \)
$11$ \( -1 + T \)
$13$ \( -2 + T \)
$17$ \( -4 + T \)
$19$ \( 3 + T \)
$23$ \( -1 + T \)
$29$ \( 6 + T \)
$31$ \( 2 + T \)
$37$ \( 2 + T \)
$41$ \( -1 + T \)
$43$ \( 8 + T \)
$47$ \( 5 + T \)
$53$ \( -3 + T \)
$59$ \( -5 + T \)
$61$ \( -13 + T \)
$67$ \( T \)
$71$ \( T \)
$73$ \( 16 + T \)
$79$ \( 2 + T \)
$83$ \( -6 + T \)
$89$ \( -6 + T \)
$97$ \( -10 + T \)
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