Properties

Label 546.2.a.a
Level $546$
Weight $2$
Character orbit 546.a
Self dual yes
Analytic conductor $4.360$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 546.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(4.35983195036\)
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

\(f(q)\) \(=\) \( q - q^{2} - q^{3} + q^{4} - q^{5} + q^{6} - q^{7} - q^{8} + q^{9} + O(q^{10}) \) \( q - q^{2} - q^{3} + q^{4} - q^{5} + q^{6} - q^{7} - q^{8} + q^{9} + q^{10} - q^{11} - q^{12} + q^{13} + q^{14} + q^{15} + q^{16} - q^{17} - q^{18} + 7q^{19} - q^{20} + q^{21} + q^{22} + 3q^{23} + q^{24} - 4q^{25} - q^{26} - q^{27} - q^{28} - 3q^{29} - q^{30} + 8q^{31} - q^{32} + q^{33} + q^{34} + q^{35} + q^{36} + 7q^{37} - 7q^{38} - q^{39} + q^{40} + 8q^{41} - q^{42} + 7q^{43} - q^{44} - q^{45} - 3q^{46} + 8q^{47} - q^{48} + q^{49} + 4q^{50} + q^{51} + q^{52} - 10q^{53} + q^{54} + q^{55} + q^{56} - 7q^{57} + 3q^{58} + 4q^{59} + q^{60} + 7q^{61} - 8q^{62} - q^{63} + q^{64} - q^{65} - q^{66} + 2q^{67} - q^{68} - 3q^{69} - q^{70} + 4q^{71} - q^{72} - q^{73} - 7q^{74} + 4q^{75} + 7q^{76} + q^{77} + q^{78} + 2q^{79} - q^{80} + q^{81} - 8q^{82} - 6q^{83} + q^{84} + q^{85} - 7q^{86} + 3q^{87} + q^{88} + 14q^{89} + q^{90} - q^{91} + 3q^{92} - 8q^{93} - 8q^{94} - 7q^{95} + q^{96} - 14q^{97} - q^{98} - q^{99} + O(q^{100}) \)

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

Atkin-Lehner signs

\( p \) Sign
\(2\) \(1\)
\(3\) \(1\)
\(7\) \(1\)
\(13\) \(-1\)

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 546.2.a.a 1
3.b odd 2 1 1638.2.a.r 1
4.b odd 2 1 4368.2.a.s 1
7.b odd 2 1 3822.2.a.n 1
13.b even 2 1 7098.2.a.t 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
546.2.a.a 1 1.a even 1 1 trivial
1638.2.a.r 1 3.b odd 2 1
3822.2.a.n 1 7.b odd 2 1
4368.2.a.s 1 4.b odd 2 1
7098.2.a.t 1 13.b even 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(546))\):

\( T_{5} + 1 \)
\( T_{11} + 1 \)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( 1 + T \)
$3$ \( 1 + T \)
$5$ \( 1 + T \)
$7$ \( 1 + T \)
$11$ \( 1 + T \)
$13$ \( -1 + T \)
$17$ \( 1 + T \)
$19$ \( -7 + T \)
$23$ \( -3 + T \)
$29$ \( 3 + T \)
$31$ \( -8 + T \)
$37$ \( -7 + T \)
$41$ \( -8 + T \)
$43$ \( -7 + T \)
$47$ \( -8 + T \)
$53$ \( 10 + T \)
$59$ \( -4 + T \)
$61$ \( -7 + T \)
$67$ \( -2 + T \)
$71$ \( -4 + T \)
$73$ \( 1 + T \)
$79$ \( -2 + T \)
$83$ \( 6 + T \)
$89$ \( -14 + T \)
$97$ \( 14 + T \)
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