Properties

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

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [182,2,Mod(1,182)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(182, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("182.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 182 = 2 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 182.a (trivial)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
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

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \( q - q^{2} + 3 q^{3} + q^{4} - 3 q^{6} + q^{7} - q^{8} + 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( q - q^{2} + 3 q^{3} + q^{4} - 3 q^{6} + q^{7} - q^{8} + 6 q^{9} - 5 q^{11} + 3 q^{12} - q^{13} - q^{14} + q^{16} - 4 q^{17} - 6 q^{18} + 2 q^{19} + 3 q^{21} + 5 q^{22} + 5 q^{23} - 3 q^{24} - 5 q^{25} + q^{26} + 9 q^{27} + q^{28} + 4 q^{29} + q^{31} - q^{32} - 15 q^{33} + 4 q^{34} + 6 q^{36} + 7 q^{37} - 2 q^{38} - 3 q^{39} - 9 q^{41} - 3 q^{42} - 12 q^{43} - 5 q^{44} - 5 q^{46} - 7 q^{47} + 3 q^{48} + q^{49} + 5 q^{50} - 12 q^{51} - q^{52} - 4 q^{53} - 9 q^{54} - q^{56} + 6 q^{57} - 4 q^{58} - 6 q^{59} + 13 q^{61} - q^{62} + 6 q^{63} + q^{64} + 15 q^{66} + 11 q^{67} - 4 q^{68} + 15 q^{69} - 6 q^{72} + 7 q^{73} - 7 q^{74} - 15 q^{75} + 2 q^{76} - 5 q^{77} + 3 q^{78} - 17 q^{79} + 9 q^{81} + 9 q^{82} + 4 q^{83} + 3 q^{84} + 12 q^{86} + 12 q^{87} + 5 q^{88} + 14 q^{89} - q^{91} + 5 q^{92} + 3 q^{93} + 7 q^{94} - 3 q^{96} + 5 q^{97} - q^{98} - 30 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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.

comment: embeddings in the coefficient field
 
gp: mfembed(f)
 
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 3.00000 1.00000 0 −3.00000 1.00000 −1.00000 6.00000 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.b 1
3.b odd 2 1 1638.2.a.q 1
4.b odd 2 1 1456.2.a.b 1
5.b even 2 1 4550.2.a.o 1
7.b odd 2 1 1274.2.a.a 1
7.c even 3 2 1274.2.f.m 2
7.d odd 6 2 1274.2.f.u 2
8.b even 2 1 5824.2.a.a 1
8.d odd 2 1 5824.2.a.be 1
13.b even 2 1 2366.2.a.o 1
13.d odd 4 2 2366.2.d.i 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
182.2.a.b 1 1.a even 1 1 trivial
1274.2.a.a 1 7.b odd 2 1
1274.2.f.m 2 7.c even 3 2
1274.2.f.u 2 7.d odd 6 2
1456.2.a.b 1 4.b odd 2 1
1638.2.a.q 1 3.b odd 2 1
2366.2.a.o 1 13.b even 2 1
2366.2.d.i 2 13.d odd 4 2
4550.2.a.o 1 5.b even 2 1
5824.2.a.a 1 8.b even 2 1
5824.2.a.be 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(182))\):

\( T_{3} - 3 \) Copy content Toggle raw display
\( T_{5} \) Copy content Toggle raw display

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T + 1 \) Copy content Toggle raw display
$3$ \( T - 3 \) Copy content Toggle raw display
$5$ \( T \) Copy content Toggle raw display
$7$ \( T - 1 \) Copy content Toggle raw display
$11$ \( T + 5 \) Copy content Toggle raw display
$13$ \( T + 1 \) Copy content Toggle raw display
$17$ \( T + 4 \) Copy content Toggle raw display
$19$ \( T - 2 \) Copy content Toggle raw display
$23$ \( T - 5 \) Copy content Toggle raw display
$29$ \( T - 4 \) Copy content Toggle raw display
$31$ \( T - 1 \) Copy content Toggle raw display
$37$ \( T - 7 \) Copy content Toggle raw display
$41$ \( T + 9 \) Copy content Toggle raw display
$43$ \( T + 12 \) Copy content Toggle raw display
$47$ \( T + 7 \) Copy content Toggle raw display
$53$ \( T + 4 \) Copy content Toggle raw display
$59$ \( T + 6 \) Copy content Toggle raw display
$61$ \( T - 13 \) Copy content Toggle raw display
$67$ \( T - 11 \) Copy content Toggle raw display
$71$ \( T \) Copy content Toggle raw display
$73$ \( T - 7 \) Copy content Toggle raw display
$79$ \( T + 17 \) Copy content Toggle raw display
$83$ \( T - 4 \) Copy content Toggle raw display
$89$ \( T - 14 \) Copy content Toggle raw display
$97$ \( T - 5 \) Copy content Toggle raw display
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