Properties

Label 546.4.a.e
Level $546$
Weight $4$
Character orbit 546.a
Self dual yes
Analytic conductor $32.215$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 546.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(32.2150428631\)
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

\(f(q)\) \(=\) \( q + 2q^{2} + 3q^{3} + 4q^{4} + 9q^{5} + 6q^{6} - 7q^{7} + 8q^{8} + 9q^{9} + O(q^{10}) \) \( q + 2q^{2} + 3q^{3} + 4q^{4} + 9q^{5} + 6q^{6} - 7q^{7} + 8q^{8} + 9q^{9} + 18q^{10} + 62q^{11} + 12q^{12} - 13q^{13} - 14q^{14} + 27q^{15} + 16q^{16} - 16q^{17} + 18q^{18} + 79q^{19} + 36q^{20} - 21q^{21} + 124q^{22} - 155q^{23} + 24q^{24} - 44q^{25} - 26q^{26} + 27q^{27} - 28q^{28} + 51q^{29} + 54q^{30} + 243q^{31} + 32q^{32} + 186q^{33} - 32q^{34} - 63q^{35} + 36q^{36} + 412q^{37} + 158q^{38} - 39q^{39} + 72q^{40} - 406q^{41} - 42q^{42} - 103q^{43} + 248q^{44} + 81q^{45} - 310q^{46} + 429q^{47} + 48q^{48} + 49q^{49} - 88q^{50} - 48q^{51} - 52q^{52} - 169q^{53} + 54q^{54} + 558q^{55} - 56q^{56} + 237q^{57} + 102q^{58} + 320q^{59} + 108q^{60} - 614q^{61} + 486q^{62} - 63q^{63} + 64q^{64} - 117q^{65} + 372q^{66} + 258q^{67} - 64q^{68} - 465q^{69} - 126q^{70} - 264q^{71} + 72q^{72} - 121q^{73} + 824q^{74} - 132q^{75} + 316q^{76} - 434q^{77} - 78q^{78} - 967q^{79} + 144q^{80} + 81q^{81} - 812q^{82} - 679q^{83} - 84q^{84} - 144q^{85} - 206q^{86} + 153q^{87} + 496q^{88} + 1059q^{89} + 162q^{90} + 91q^{91} - 620q^{92} + 729q^{93} + 858q^{94} + 711q^{95} + 96q^{96} - 21q^{97} + 98q^{98} + 558q^{99} + O(q^{100}) \)

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 3.00000 4.00000 9.00000 6.00000 −7.00000 8.00000 9.00000 18.0000
\(n\): 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 546.4.a.e 1
3.b odd 2 1 1638.4.a.b 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
546.4.a.e 1 1.a even 1 1 trivial
1638.4.a.b 1 3.b odd 2 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{5} - 9 \) acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(546))\).

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( -2 + T \)
$3$ \( -3 + T \)
$5$ \( -9 + T \)
$7$ \( 7 + T \)
$11$ \( -62 + T \)
$13$ \( 13 + T \)
$17$ \( 16 + T \)
$19$ \( -79 + T \)
$23$ \( 155 + T \)
$29$ \( -51 + T \)
$31$ \( -243 + T \)
$37$ \( -412 + T \)
$41$ \( 406 + T \)
$43$ \( 103 + T \)
$47$ \( -429 + T \)
$53$ \( 169 + T \)
$59$ \( -320 + T \)
$61$ \( 614 + T \)
$67$ \( -258 + T \)
$71$ \( 264 + T \)
$73$ \( 121 + T \)
$79$ \( 967 + T \)
$83$ \( 679 + T \)
$89$ \( -1059 + T \)
$97$ \( 21 + T \)
show more
show less