Properties

Label 46.2.a.a
Level $46$
Weight $2$
Character orbit 46.a
Self dual yes
Analytic conductor $0.367$
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] = [46,2,Mod(1,46)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(46, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("46.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 46 = 2 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 46.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: \(0.367311849298\)
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)
 
\(f(q)\) \(=\) \( q - q^{2} + q^{4} + 4 q^{5} - 4 q^{7} - q^{8} - 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( q - q^{2} + q^{4} + 4 q^{5} - 4 q^{7} - q^{8} - 3 q^{9} - 4 q^{10} + 2 q^{11} - 2 q^{13} + 4 q^{14} + q^{16} - 2 q^{17} + 3 q^{18} - 2 q^{19} + 4 q^{20} - 2 q^{22} + q^{23} + 11 q^{25} + 2 q^{26} - 4 q^{28} + 2 q^{29} - q^{32} + 2 q^{34} - 16 q^{35} - 3 q^{36} - 4 q^{37} + 2 q^{38} - 4 q^{40} + 6 q^{41} + 10 q^{43} + 2 q^{44} - 12 q^{45} - q^{46} + 9 q^{49} - 11 q^{50} - 2 q^{52} - 4 q^{53} + 8 q^{55} + 4 q^{56} - 2 q^{58} + 12 q^{59} - 8 q^{61} + 12 q^{63} + q^{64} - 8 q^{65} - 10 q^{67} - 2 q^{68} + 16 q^{70} + 3 q^{72} + 6 q^{73} + 4 q^{74} - 2 q^{76} - 8 q^{77} - 12 q^{79} + 4 q^{80} + 9 q^{81} - 6 q^{82} + 14 q^{83} - 8 q^{85} - 10 q^{86} - 2 q^{88} - 6 q^{89} + 12 q^{90} + 8 q^{91} + q^{92} - 8 q^{95} + 6 q^{97} - 9 q^{98} - 6 q^{99}+O(q^{100}) \) 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 0 1.00000 4.00000 0 −4.00000 −1.00000 −3.00000 −4.00000
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(2\) \(1\)
\(23\) \(-1\)

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 46.2.a.a 1
3.b odd 2 1 414.2.a.b 1
4.b odd 2 1 368.2.a.d 1
5.b even 2 1 1150.2.a.h 1
5.c odd 4 2 1150.2.b.d 2
7.b odd 2 1 2254.2.a.c 1
8.b even 2 1 1472.2.a.f 1
8.d odd 2 1 1472.2.a.g 1
11.b odd 2 1 5566.2.a.h 1
12.b even 2 1 3312.2.a.b 1
13.b even 2 1 7774.2.a.d 1
20.d odd 2 1 9200.2.a.p 1
23.b odd 2 1 1058.2.a.c 1
69.c even 2 1 9522.2.a.p 1
92.b even 2 1 8464.2.a.g 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
46.2.a.a 1 1.a even 1 1 trivial
368.2.a.d 1 4.b odd 2 1
414.2.a.b 1 3.b odd 2 1
1058.2.a.c 1 23.b odd 2 1
1150.2.a.h 1 5.b even 2 1
1150.2.b.d 2 5.c odd 4 2
1472.2.a.f 1 8.b even 2 1
1472.2.a.g 1 8.d odd 2 1
2254.2.a.c 1 7.b odd 2 1
3312.2.a.b 1 12.b even 2 1
5566.2.a.h 1 11.b odd 2 1
7774.2.a.d 1 13.b even 2 1
8464.2.a.g 1 92.b even 2 1
9200.2.a.p 1 20.d odd 2 1
9522.2.a.p 1 69.c even 2 1

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(\Gamma_0(46))\).

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T + 1 \) Copy content Toggle raw display
$3$ \( T \) Copy content Toggle raw display
$5$ \( T - 4 \) Copy content Toggle raw display
$7$ \( T + 4 \) Copy content Toggle raw display
$11$ \( T - 2 \) Copy content Toggle raw display
$13$ \( T + 2 \) Copy content Toggle raw display
$17$ \( T + 2 \) Copy content Toggle raw display
$19$ \( T + 2 \) Copy content Toggle raw display
$23$ \( T - 1 \) Copy content Toggle raw display
$29$ \( T - 2 \) Copy content Toggle raw display
$31$ \( T \) Copy content Toggle raw display
$37$ \( T + 4 \) Copy content Toggle raw display
$41$ \( T - 6 \) Copy content Toggle raw display
$43$ \( T - 10 \) Copy content Toggle raw display
$47$ \( T \) Copy content Toggle raw display
$53$ \( T + 4 \) Copy content Toggle raw display
$59$ \( T - 12 \) Copy content Toggle raw display
$61$ \( T + 8 \) Copy content Toggle raw display
$67$ \( T + 10 \) Copy content Toggle raw display
$71$ \( T \) Copy content Toggle raw display
$73$ \( T - 6 \) Copy content Toggle raw display
$79$ \( T + 12 \) Copy content Toggle raw display
$83$ \( T - 14 \) Copy content Toggle raw display
$89$ \( T + 6 \) Copy content Toggle raw display
$97$ \( T - 6 \) Copy content Toggle raw display
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