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Properties

Label 525.3.c.e
Level $525$
Weight $3$
Character orbit 525.c
Analytic conductor $14.305$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [525,3,Mod(176,525)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(525, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0, 0]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("525.176");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 525.c (of order \(2\), degree \(1\), minimal)

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: no
Analytic conductor: \(14.3052138789\)
Analytic rank: \(0\)
Dimension: \(24\)
Twist minimal: no (minimal twist has level 105)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 24 q - 52 q^{4} + 22 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 24 q - 52 q^{4} + 22 q^{9} + 4 q^{16} - 72 q^{19} + 14 q^{21} + 156 q^{24} - 40 q^{31} + 144 q^{34} + 36 q^{36} - 62 q^{39} - 104 q^{46} + 168 q^{49} + 70 q^{51} - 60 q^{54} + 432 q^{61} + 364 q^{64} + 284 q^{66} - 404 q^{69} + 152 q^{76} - 108 q^{79} - 158 q^{81} - 112 q^{84} - 84 q^{91} - 808 q^{94} - 516 q^{96} - 582 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
176.1 − 3.57140i −1.65264 − 2.50375i −8.75491 0 −8.94190 + 5.90225i −2.64575 16.9817i −3.53755 + 8.27561i 0
176.2 − 3.57140i 1.65264 − 2.50375i −8.75491 0 −8.94190 − 5.90225i 2.64575 16.9817i −3.53755 − 8.27561i 0
176.3 − 3.21327i −2.29339 + 1.93400i −6.32511 0 6.21446 + 7.36929i −2.64575 7.47120i 1.51929 − 8.87084i 0
176.4 − 3.21327i 2.29339 + 1.93400i −6.32511 0 6.21446 − 7.36929i 2.64575 7.47120i 1.51929 + 8.87084i 0
176.5 − 2.80814i −2.99904 − 0.0756962i −3.88565 0 −0.212566 + 8.42174i 2.64575 − 0.321110i 8.98854 + 0.454033i 0
176.6 − 2.80814i 2.99904 − 0.0756962i −3.88565 0 −0.212566 − 8.42174i −2.64575 − 0.321110i 8.98854 − 0.454033i 0
176.7 − 1.87229i −0.302541 + 2.98471i 0.494516 0 5.58825 + 0.566446i 2.64575 − 8.41505i −8.81694 − 1.80599i 0
176.8 − 1.87229i 0.302541 + 2.98471i 0.494516 0 5.58825 − 0.566446i −2.64575 − 8.41505i −8.81694 + 1.80599i 0
176.9 − 1.50770i −2.15510 − 2.08699i 1.72685 0 −3.14656 + 3.24924i 2.64575 − 8.63435i 0.288904 + 8.99536i 0
176.10 − 1.50770i 2.15510 − 2.08699i 1.72685 0 −3.14656 − 3.24924i −2.64575 − 8.63435i 0.288904 − 8.99536i 0
176.11 − 0.505667i −2.83353 + 0.985457i 3.74430 0 0.498313 + 1.43282i −2.64575 − 3.91604i 7.05775 − 5.58464i 0
176.12 − 0.505667i 2.83353 + 0.985457i 3.74430 0 0.498313 − 1.43282i 2.64575 − 3.91604i 7.05775 + 5.58464i 0
176.13 0.505667i −2.83353 − 0.985457i 3.74430 0 0.498313 − 1.43282i −2.64575 3.91604i 7.05775 + 5.58464i 0
176.14 0.505667i 2.83353 − 0.985457i 3.74430 0 0.498313 + 1.43282i 2.64575 3.91604i 7.05775 − 5.58464i 0
176.15 1.50770i −2.15510 + 2.08699i 1.72685 0 −3.14656 − 3.24924i 2.64575 8.63435i 0.288904 − 8.99536i 0
176.16 1.50770i 2.15510 + 2.08699i 1.72685 0 −3.14656 + 3.24924i −2.64575 8.63435i 0.288904 + 8.99536i 0
176.17 1.87229i −0.302541 − 2.98471i 0.494516 0 5.58825 − 0.566446i 2.64575 8.41505i −8.81694 + 1.80599i 0
176.18 1.87229i 0.302541 − 2.98471i 0.494516 0 5.58825 + 0.566446i −2.64575 8.41505i −8.81694 − 1.80599i 0
176.19 2.80814i −2.99904 + 0.0756962i −3.88565 0 −0.212566 − 8.42174i 2.64575 0.321110i 8.98854 − 0.454033i 0
176.20 2.80814i 2.99904 + 0.0756962i −3.88565 0 −0.212566 + 8.42174i −2.64575 0.321110i 8.98854 + 0.454033i 0
See all 24 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 176.24
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
3.b odd 2 1 inner
5.b even 2 1 inner
15.d odd 2 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 525.3.c.e 24
3.b odd 2 1 inner 525.3.c.e 24
5.b even 2 1 inner 525.3.c.e 24
5.c odd 4 2 105.3.f.a ✓ 24
15.d odd 2 1 inner 525.3.c.e 24
15.e even 4 2 105.3.f.a ✓ 24
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
105.3.f.a ✓ 24 5.c odd 4 2
105.3.f.a ✓ 24 15.e even 4 2
525.3.c.e 24 1.a even 1 1 trivial
525.3.c.e 24 3.b odd 2 1 inner
525.3.c.e 24 5.b even 2 1 inner
525.3.c.e 24 15.d odd 2 1 inner

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{3}^{\mathrm{new}}(525, [\chi])\):

\( T_{2}^{12} + 37T_{2}^{10} + 510T_{2}^{8} + 3226T_{2}^{6} + 9293T_{2}^{4} + 10449T_{2}^{2} + 2116 \) Copy content Toggle raw display
\( T_{13}^{12} - 1403 T_{13}^{10} + 733300 T_{13}^{8} - 175885856 T_{13}^{6} + 19134397328 T_{13}^{4} + \cdots + 6291829755904 \) Copy content Toggle raw display