Properties

Label 273.2.a.a
Level $273$
Weight $2$
Character orbit 273.a
Self dual yes
Analytic conductor $2.180$
Analytic rank $1$
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: \(1\)
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

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

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

$p$ $F_p(T)$
$2$ \( 2 + T \)
$3$ \( 1 + T \)
$5$ \( 1 + T \)
$7$ \( -1 + T \)
$11$ \( 2 + T \)
$13$ \( -1 + T \)
$17$ \( 4 + T \)
$19$ \( -3 + T \)
$23$ \( 9 + T \)
$29$ \( 1 + T \)
$31$ \( 5 + T \)
$37$ \( 8 + T \)
$41$ \( -6 + T \)
$43$ \( 9 + T \)
$47$ \( 3 + T \)
$53$ \( -3 + T \)
$59$ \( T \)
$61$ \( -10 + T \)
$67$ \( 2 + T \)
$71$ \( -12 + T \)
$73$ \( -5 + T \)
$79$ \( 13 + T \)
$83$ \( 11 + T \)
$89$ \( -1 + T \)
$97$ \( -1 + T \)
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