Properties

Label 182.4.a.b
Level $182$
Weight $4$
Character orbit 182.a
Self dual yes
Analytic conductor $10.738$
Analytic rank $1$
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] = [182,4,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, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("182.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 182 = 2 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 4 \)
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: \(10.7383476210\)
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

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \( q + 2 q^{2} - 8 q^{3} + 4 q^{4} + 3 q^{5} - 16 q^{6} + 7 q^{7} + 8 q^{8} + 37 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( q + 2 q^{2} - 8 q^{3} + 4 q^{4} + 3 q^{5} - 16 q^{6} + 7 q^{7} + 8 q^{8} + 37 q^{9} + 6 q^{10} - 54 q^{11} - 32 q^{12} + 13 q^{13} + 14 q^{14} - 24 q^{15} + 16 q^{16} - 96 q^{17} + 74 q^{18} - 151 q^{19} + 12 q^{20} - 56 q^{21} - 108 q^{22} + 33 q^{23} - 64 q^{24} - 116 q^{25} + 26 q^{26} - 80 q^{27} + 28 q^{28} + 183 q^{29} - 48 q^{30} - 331 q^{31} + 32 q^{32} + 432 q^{33} - 192 q^{34} + 21 q^{35} + 148 q^{36} - 88 q^{37} - 302 q^{38} - 104 q^{39} + 24 q^{40} - 42 q^{41} - 112 q^{42} + 353 q^{43} - 216 q^{44} + 111 q^{45} + 66 q^{46} - 465 q^{47} - 128 q^{48} + 49 q^{49} - 232 q^{50} + 768 q^{51} + 52 q^{52} + 195 q^{53} - 160 q^{54} - 162 q^{55} + 56 q^{56} + 1208 q^{57} + 366 q^{58} + 552 q^{59} - 96 q^{60} + 470 q^{61} - 662 q^{62} + 259 q^{63} + 64 q^{64} + 39 q^{65} + 864 q^{66} + 254 q^{67} - 384 q^{68} - 264 q^{69} + 42 q^{70} + 132 q^{71} + 296 q^{72} - 943 q^{73} - 176 q^{74} + 928 q^{75} - 604 q^{76} - 378 q^{77} - 208 q^{78} - 727 q^{79} + 48 q^{80} - 359 q^{81} - 84 q^{82} - 1197 q^{83} - 224 q^{84} - 288 q^{85} + 706 q^{86} - 1464 q^{87} - 432 q^{88} + 753 q^{89} + 222 q^{90} + 91 q^{91} + 132 q^{92} + 2648 q^{93} - 930 q^{94} - 453 q^{95} - 256 q^{96} + 1037 q^{97} + 98 q^{98} - 1998 q^{99}+O(q^{100}) \) 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
2.00000 −8.00000 4.00000 3.00000 −16.0000 7.00000 8.00000 37.0000 6.00000
\(n\): 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 182.4.a.b 1
3.b odd 2 1 1638.4.a.d 1
4.b odd 2 1 1456.4.a.g 1
7.b odd 2 1 1274.4.a.i 1
13.b even 2 1 2366.4.a.a 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
182.4.a.b 1 1.a even 1 1 trivial
1274.4.a.i 1 7.b odd 2 1
1456.4.a.g 1 4.b odd 2 1
1638.4.a.d 1 3.b odd 2 1
2366.4.a.a 1 13.b even 2 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{3} + 8 \) acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(182))\). Copy content Toggle raw display

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T - 2 \) Copy content Toggle raw display
$3$ \( T + 8 \) Copy content Toggle raw display
$5$ \( T - 3 \) Copy content Toggle raw display
$7$ \( T - 7 \) Copy content Toggle raw display
$11$ \( T + 54 \) Copy content Toggle raw display
$13$ \( T - 13 \) Copy content Toggle raw display
$17$ \( T + 96 \) Copy content Toggle raw display
$19$ \( T + 151 \) Copy content Toggle raw display
$23$ \( T - 33 \) Copy content Toggle raw display
$29$ \( T - 183 \) Copy content Toggle raw display
$31$ \( T + 331 \) Copy content Toggle raw display
$37$ \( T + 88 \) Copy content Toggle raw display
$41$ \( T + 42 \) Copy content Toggle raw display
$43$ \( T - 353 \) Copy content Toggle raw display
$47$ \( T + 465 \) Copy content Toggle raw display
$53$ \( T - 195 \) Copy content Toggle raw display
$59$ \( T - 552 \) Copy content Toggle raw display
$61$ \( T - 470 \) Copy content Toggle raw display
$67$ \( T - 254 \) Copy content Toggle raw display
$71$ \( T - 132 \) Copy content Toggle raw display
$73$ \( T + 943 \) Copy content Toggle raw display
$79$ \( T + 727 \) Copy content Toggle raw display
$83$ \( T + 1197 \) Copy content Toggle raw display
$89$ \( T - 753 \) Copy content Toggle raw display
$97$ \( T - 1037 \) Copy content Toggle raw display
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