Properties

Label 1452.4.a.c
Level $1452$
Weight $4$
Character orbit 1452.a
Self dual yes
Analytic conductor $85.671$
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] = [1452,4,Mod(1,1452)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1452, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 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("1452.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1452 = 2^{2} \cdot 3 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1452.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: \(85.6707733283\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 132)
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)
 
\(f(q)\) \(=\) \( q - 3 q^{3} + 22 q^{5} + 20 q^{7} + 9 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( q - 3 q^{3} + 22 q^{5} + 20 q^{7} + 9 q^{9} - 22 q^{13} - 66 q^{15} - 110 q^{17} - 48 q^{19} - 60 q^{21} + 72 q^{23} + 359 q^{25} - 27 q^{27} + 142 q^{29} + 184 q^{31} + 440 q^{35} - 194 q^{37} + 66 q^{39} + 482 q^{41} + 80 q^{43} + 198 q^{45} + 392 q^{47} + 57 q^{49} + 330 q^{51} - 34 q^{53} + 144 q^{57} - 108 q^{59} - 382 q^{61} + 180 q^{63} - 484 q^{65} + 84 q^{67} - 216 q^{69} - 1040 q^{71} + 606 q^{73} - 1077 q^{75} + 1292 q^{79} + 81 q^{81} - 356 q^{83} - 2420 q^{85} - 426 q^{87} - 406 q^{89} - 440 q^{91} - 552 q^{93} - 1056 q^{95} + 1090 q^{97}+O(q^{100}) \) 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
0 −3.00000 0 22.0000 0 20.0000 0 9.00000 0
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(2\) \( -1 \)
\(3\) \( +1 \)
\(11\) \( -1 \)

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 1452.4.a.c 1
11.b odd 2 1 132.4.a.c 1
33.d even 2 1 396.4.a.a 1
44.c even 2 1 528.4.a.l 1
88.b odd 2 1 2112.4.a.n 1
88.g even 2 1 2112.4.a.a 1
132.d odd 2 1 1584.4.a.a 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
132.4.a.c 1 11.b odd 2 1
396.4.a.a 1 33.d even 2 1
528.4.a.l 1 44.c even 2 1
1452.4.a.c 1 1.a even 1 1 trivial
1584.4.a.a 1 132.d odd 2 1
2112.4.a.a 1 88.g even 2 1
2112.4.a.n 1 88.b odd 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(1452))\):

\( T_{5} - 22 \) Copy content Toggle raw display
\( T_{7} - 20 \) Copy content Toggle raw display

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T \) Copy content Toggle raw display
$3$ \( T + 3 \) Copy content Toggle raw display
$5$ \( T - 22 \) Copy content Toggle raw display
$7$ \( T - 20 \) Copy content Toggle raw display
$11$ \( T \) Copy content Toggle raw display
$13$ \( T + 22 \) Copy content Toggle raw display
$17$ \( T + 110 \) Copy content Toggle raw display
$19$ \( T + 48 \) Copy content Toggle raw display
$23$ \( T - 72 \) Copy content Toggle raw display
$29$ \( T - 142 \) Copy content Toggle raw display
$31$ \( T - 184 \) Copy content Toggle raw display
$37$ \( T + 194 \) Copy content Toggle raw display
$41$ \( T - 482 \) Copy content Toggle raw display
$43$ \( T - 80 \) Copy content Toggle raw display
$47$ \( T - 392 \) Copy content Toggle raw display
$53$ \( T + 34 \) Copy content Toggle raw display
$59$ \( T + 108 \) Copy content Toggle raw display
$61$ \( T + 382 \) Copy content Toggle raw display
$67$ \( T - 84 \) Copy content Toggle raw display
$71$ \( T + 1040 \) Copy content Toggle raw display
$73$ \( T - 606 \) Copy content Toggle raw display
$79$ \( T - 1292 \) Copy content Toggle raw display
$83$ \( T + 356 \) Copy content Toggle raw display
$89$ \( T + 406 \) Copy content Toggle raw display
$97$ \( T - 1090 \) Copy content Toggle raw display
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