Properties

Label 182.2.a.c
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

Downloads

Learn more about

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

\(f(q)\) \(=\) \( q + q^{2} + q^{4} + 2q^{5} - q^{7} + q^{8} - 3q^{9} + O(q^{10}) \) \( q + q^{2} + q^{4} + 2q^{5} - q^{7} + q^{8} - 3q^{9} + 2q^{10} + 4q^{11} - q^{13} - q^{14} + q^{16} - 6q^{17} - 3q^{18} + 2q^{20} + 4q^{22} + 8q^{23} - q^{25} - q^{26} - q^{28} - 10q^{29} - 8q^{31} + q^{32} - 6q^{34} - 2q^{35} - 3q^{36} + 6q^{37} + 2q^{40} - 6q^{41} + 4q^{43} + 4q^{44} - 6q^{45} + 8q^{46} - 8q^{47} + q^{49} - q^{50} - q^{52} + 6q^{53} + 8q^{55} - q^{56} - 10q^{58} + 8q^{59} + 10q^{61} - 8q^{62} + 3q^{63} + q^{64} - 2q^{65} + 4q^{67} - 6q^{68} - 2q^{70} - 8q^{71} - 3q^{72} + 2q^{73} + 6q^{74} - 4q^{77} + 8q^{79} + 2q^{80} + 9q^{81} - 6q^{82} - 12q^{85} + 4q^{86} + 4q^{88} + 18q^{89} - 6q^{90} + q^{91} + 8q^{92} - 8q^{94} + 2q^{97} + q^{98} - 12q^{99} + O(q^{100}) \)

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 0 1.00000 2.00000 0 −1.00000 1.00000 −3.00000 2.00000
\(n\): 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.c 1
3.b odd 2 1 1638.2.a.c 1
4.b odd 2 1 1456.2.a.i 1
5.b even 2 1 4550.2.a.g 1
7.b odd 2 1 1274.2.a.l 1
7.c even 3 2 1274.2.f.f 2
7.d odd 6 2 1274.2.f.g 2
8.b even 2 1 5824.2.a.l 1
8.d odd 2 1 5824.2.a.m 1
13.b even 2 1 2366.2.a.d 1
13.d odd 4 2 2366.2.d.d 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
182.2.a.c 1 1.a even 1 1 trivial
1274.2.a.l 1 7.b odd 2 1
1274.2.f.f 2 7.c even 3 2
1274.2.f.g 2 7.d odd 6 2
1456.2.a.i 1 4.b odd 2 1
1638.2.a.c 1 3.b odd 2 1
2366.2.a.d 1 13.b even 2 1
2366.2.d.d 2 13.d odd 4 2
4550.2.a.g 1 5.b even 2 1
5824.2.a.l 1 8.b even 2 1
5824.2.a.m 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(182))\):

\( T_{3} \)
\( T_{5} - 2 \)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( -1 + T \)
$3$ \( T \)
$5$ \( -2 + T \)
$7$ \( 1 + T \)
$11$ \( -4 + T \)
$13$ \( 1 + T \)
$17$ \( 6 + T \)
$19$ \( T \)
$23$ \( -8 + T \)
$29$ \( 10 + T \)
$31$ \( 8 + T \)
$37$ \( -6 + T \)
$41$ \( 6 + T \)
$43$ \( -4 + T \)
$47$ \( 8 + T \)
$53$ \( -6 + T \)
$59$ \( -8 + T \)
$61$ \( -10 + T \)
$67$ \( -4 + T \)
$71$ \( 8 + T \)
$73$ \( -2 + T \)
$79$ \( -8 + T \)
$83$ \( T \)
$89$ \( -18 + T \)
$97$ \( -2 + T \)
show more
show less