Properties

Label 546.2.a.g
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

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

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 2.00000 1.00000 1.00000 1.00000 1.00000 2.00000
\(n\): 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.g 1
3.b odd 2 1 1638.2.a.d 1
4.b odd 2 1 4368.2.a.k 1
7.b odd 2 1 3822.2.a.t 1
13.b even 2 1 7098.2.a.j 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
546.2.a.g 1 1.a even 1 1 trivial
1638.2.a.d 1 3.b odd 2 1
3822.2.a.t 1 7.b odd 2 1
4368.2.a.k 1 4.b odd 2 1
7098.2.a.j 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(546))\):

\( T_{5} - 2 \) Copy content Toggle raw display
\( T_{11} + 4 \) Copy content Toggle raw display

Hecke characteristic polynomials

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