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Properties

Label 8752.2.a.v
Level $8752$
Weight $2$
Character orbit 8752.a
Self dual yes
Analytic conductor $69.885$
Analytic rank $0$
Dimension $25$
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] = [8752,2,Mod(1,8752)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8752, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 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("8752.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 8752 = 2^{4} \cdot 547 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8752.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: \(69.8850718490\)
Analytic rank: \(0\)
Dimension: \(25\)
Twist minimal: no (minimal twist has level 547)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

The dimension is sufficiently large that we do not compute an algebraic \(q\)-expansion, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 25 q - 8 q^{3} + 29 q^{5} - 5 q^{7} + 29 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 25 q - 8 q^{3} + 29 q^{5} - 5 q^{7} + 29 q^{9} - 10 q^{11} + 19 q^{13} - 5 q^{15} + 40 q^{17} - 8 q^{21} - 26 q^{23} + 36 q^{25} - 11 q^{27} + 30 q^{29} + 5 q^{31} + 10 q^{33} - 11 q^{35} + 26 q^{37} + 17 q^{39} + 9 q^{41} + 10 q^{43} + 64 q^{45} - 28 q^{47} + 20 q^{49} + 9 q^{51} + 80 q^{53} + q^{55} - 8 q^{57} + 2 q^{59} + 22 q^{61} + 9 q^{63} + 30 q^{65} + 16 q^{67} + 22 q^{69} + q^{71} + 2 q^{73} + 31 q^{75} + 67 q^{77} + 34 q^{79} - 11 q^{81} - 15 q^{83} + 15 q^{85} + 29 q^{87} + 38 q^{89} + 41 q^{91} - 4 q^{93} + 46 q^{95} - 2 q^{97} + 41 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Display 100 coefficients 10 coefficients

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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1.1 0 −3.24523 0 −0.595274 0 −1.62460 0 7.53151 0
1.2 0 −3.21746 0 1.65792 0 0.657486 0 7.35203 0
1.3 0 −3.07069 0 3.05017 0 4.64964 0 6.42911 0
1.4 0 −2.42262 0 −0.826438 0 −0.383471 0 2.86911 0
1.5 0 −2.24632 0 3.59228 0 1.86730 0 2.04594 0
1.6 0 −2.22215 0 0.712381 0 −4.39659 0 1.93796 0
1.7 0 −2.12625 0 4.42221 0 −1.19553 0 1.52095 0
1.8 0 −2.04968 0 −2.59497 0 −1.28808 0 1.20118 0
1.9 0 −1.64314 0 3.20489 0 0.477395 0 −0.300096 0
1.10 0 −1.40134 0 1.41612 0 −3.63098 0 −1.03623 0
1.11 0 −0.987380 0 2.62354 0 1.48197 0 −2.02508 0
1.12 0 −0.795018 0 1.19609 0 2.78278 0 −2.36795 0
1.13 0 −0.778073 0 −1.92511 0 4.90203 0 −2.39460 0
1.14 0 −0.649055 0 −2.10046 0 −0.493203 0 −2.57873 0
1.15 0 0.110475 0 3.86083 0 −3.07681 0 −2.98780 0
1.16 0 0.533377 0 1.81354 0 −3.82860 0 −2.71551 0
1.17 0 0.821475 0 0.420015 0 −4.69301 0 −2.32518 0
1.18 0 1.07595 0 −0.586151 0 −0.547575 0 −1.84234 0
1.19 0 1.52830 0 2.94110 0 4.64869 0 −0.664306 0
1.20 0 1.63498 0 −2.81730 0 2.32432 0 −0.326830 0
See all 25 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.25
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(2\) \(-1\)
\(547\) \(1\)

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 8752.2.a.v 25
4.b odd 2 1 547.2.a.c ✓ 25
12.b even 2 1 4923.2.a.n 25
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
547.2.a.c ✓ 25 4.b odd 2 1
4923.2.a.n 25 12.b even 2 1
8752.2.a.v 25 1.a even 1 1 trivial

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(8752))\):

\( T_{3}^{25} + 8 T_{3}^{24} - 20 T_{3}^{23} - 311 T_{3}^{22} - 159 T_{3}^{21} + 4979 T_{3}^{20} + \cdots - 25088 \) Copy content Toggle raw display
\( T_{5}^{25} - 29 T_{5}^{24} + 340 T_{5}^{23} - 1865 T_{5}^{22} + 2290 T_{5}^{21} + 29052 T_{5}^{20} + \cdots - 3804416 \) Copy content Toggle raw display
\( T_{7}^{25} + 5 T_{7}^{24} - 85 T_{7}^{23} - 465 T_{7}^{22} + 2784 T_{7}^{21} + 17422 T_{7}^{20} + \cdots - 2553344 \) Copy content Toggle raw display
\( T_{11}^{25} + 10 T_{11}^{24} - 86 T_{11}^{23} - 1174 T_{11}^{22} + 1669 T_{11}^{21} + 54292 T_{11}^{20} + \cdots - 2284779388 \) Copy content Toggle raw display