Properties

Label 182.2.a.d
Level $182$
Weight $2$
Character orbit 182.a
Self dual yes
Analytic conductor $1.453$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

Related objects

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Newspace parameters

Level: \( N \) \(=\) \( 182 = 2 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 182.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(1.45327731679\)
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

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

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

Atkin-Lehner signs

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

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 182.2.a.d 1
3.b odd 2 1 1638.2.a.f 1
4.b odd 2 1 1456.2.a.d 1
5.b even 2 1 4550.2.a.c 1
7.b odd 2 1 1274.2.a.j 1
7.c even 3 2 1274.2.f.d 2
7.d odd 6 2 1274.2.f.i 2
8.b even 2 1 5824.2.a.k 1
8.d odd 2 1 5824.2.a.x 1
13.b even 2 1 2366.2.a.e 1
13.d odd 4 2 2366.2.d.e 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
182.2.a.d 1 1.a even 1 1 trivial
1274.2.a.j 1 7.b odd 2 1
1274.2.f.d 2 7.c even 3 2
1274.2.f.i 2 7.d odd 6 2
1456.2.a.d 1 4.b odd 2 1
1638.2.a.f 1 3.b odd 2 1
2366.2.a.e 1 13.b even 2 1
2366.2.d.e 2 13.d odd 4 2
4550.2.a.c 1 5.b even 2 1
5824.2.a.k 1 8.b even 2 1
5824.2.a.x 1 8.d odd 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(182))\):

\( T_{3} - 1 \)
\( T_{5} \)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( -1 + T \)
$3$ \( -1 + T \)
$5$ \( T \)
$7$ \( -1 + T \)
$11$ \( 3 + T \)
$13$ \( -1 + T \)
$17$ \( T \)
$19$ \( -2 + T \)
$23$ \( 3 + T \)
$29$ \( T \)
$31$ \( -5 + T \)
$37$ \( 7 + T \)
$41$ \( -3 + T \)
$43$ \( -8 + T \)
$47$ \( 3 + T \)
$53$ \( 12 + T \)
$59$ \( -6 + T \)
$61$ \( 1 + T \)
$67$ \( -5 + T \)
$71$ \( -12 + T \)
$73$ \( -11 + T \)
$79$ \( 1 + T \)
$83$ \( -12 + T \)
$89$ \( 18 + T \)
$97$ \( -17 + T \)
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