Properties

Label 273.2.a.b
Level $273$
Weight $2$
Character orbit 273.a
Self dual yes
Analytic conductor $2.180$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 273 = 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 273.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(2.17991597518\)
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

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

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 1.00000 2.00000 −1.00000 0 1.00000 2.00000
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

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

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 273.2.a.b 1
3.b odd 2 1 819.2.a.a 1
4.b odd 2 1 4368.2.a.i 1
5.b even 2 1 6825.2.a.a 1
7.b odd 2 1 1911.2.a.g 1
13.b even 2 1 3549.2.a.b 1
21.c even 2 1 5733.2.a.a 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
273.2.a.b 1 1.a even 1 1 trivial
819.2.a.a 1 3.b odd 2 1
1911.2.a.g 1 7.b odd 2 1
3549.2.a.b 1 13.b even 2 1
4368.2.a.i 1 4.b odd 2 1
5733.2.a.a 1 21.c even 2 1
6825.2.a.a 1 5.b even 2 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2} - 2 \) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(273))\).

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( -2 + T \)
$3$ \( -1 + T \)
$5$ \( -1 + T \)
$7$ \( 1 + T \)
$11$ \( 2 + T \)
$13$ \( 1 + T \)
$17$ \( T \)
$19$ \( -1 + T \)
$23$ \( -3 + T \)
$29$ \( 5 + T \)
$31$ \( -9 + T \)
$37$ \( T \)
$41$ \( -2 + T \)
$43$ \( 1 + T \)
$47$ \( -3 + T \)
$53$ \( 9 + T \)
$59$ \( T \)
$61$ \( 2 + T \)
$67$ \( -10 + T \)
$71$ \( 12 + T \)
$73$ \( -15 + T \)
$79$ \( -11 + T \)
$83$ \( -3 + T \)
$89$ \( 17 + T \)
$97$ \( -3 + T \)
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