↑

Properties

Label 531.3.b.a
Level $531$
Weight $3$
Character orbit 531.b
Analytic conductor $14.469$
Analytic rank $0$
Dimension $40$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [531,3,Mod(296,531)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(531, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("531.296");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 531 = 3^{2} \cdot 59 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 531.b (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: \(14.4687020375\)
Analytic rank: \(0\)
Dimension: \(40\)
Twist minimal: yes
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.

\(\operatorname{Tr}(f)(q) = \) \( 40 q - 80 q^{4} + 16 q^{7}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 40 q - 80 q^{4} + 16 q^{7} - 48 q^{10} + 240 q^{16} - 48 q^{22} - 152 q^{25} - 128 q^{28} - 48 q^{31} + 128 q^{34} - 64 q^{37} + 208 q^{40} - 96 q^{43} + 32 q^{46} + 152 q^{49} - 48 q^{52} + 288 q^{55} + 16 q^{58} - 32 q^{61} - 400 q^{64} - 280 q^{67} - 776 q^{70} + 232 q^{73} + 432 q^{76} + 344 q^{79} + 480 q^{82} + 296 q^{85} + 120 q^{88} + 168 q^{91} - 864 q^{94} - 504 q^{97}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
296.1 − 3.88572i 0 −11.0988 4.94070i 0 1.25666 27.5841i 0 19.1982
296.2 − 3.79369i 0 −10.3921 0.115947i 0 −4.68018 24.2494i 0 0.439867
296.3 − 3.73249i 0 −9.93151 − 8.39519i 0 7.72933 22.1393i 0 −31.3350
296.4 − 3.48146i 0 −8.12056 − 6.38989i 0 11.5262 14.3456i 0 −22.2461
296.5 − 3.24601i 0 −6.53658 0.185457i 0 −2.64874 8.23377i 0 0.601995
296.6 − 3.09181i 0 −5.55926 − 3.60522i 0 −12.5126 4.82093i 0 −11.1466
296.7 − 2.89875i 0 −4.40277 7.11303i 0 −3.90934 1.16753i 0 20.6189
296.8 − 2.85325i 0 −4.14103 1.11921i 0 6.26430 0.402383i 0 3.19338
296.9 − 2.63172i 0 −2.92597 6.78735i 0 0.812170 − 2.82656i 0 17.8624
296.10 − 2.46015i 0 −2.05232 − 3.29018i 0 2.59149 − 4.79158i 0 −8.09433
296.11 − 1.85203i 0 0.569979 − 7.58729i 0 −7.03781 − 8.46375i 0 −14.0519
296.12 − 1.82251i 0 0.678446 − 6.07732i 0 3.80355 − 8.52653i 0 −11.0760
296.13 − 1.81283i 0 0.713651 4.90638i 0 8.89220 − 8.54504i 0 8.89443
296.14 − 1.31552i 0 2.26940 − 5.55152i 0 6.30347 − 8.24754i 0 −7.30315
296.15 − 1.23530i 0 2.47402 3.52553i 0 −7.85301 − 7.99739i 0 4.35510
296.16 − 0.987014i 0 3.02580 0.952948i 0 −9.89269 − 6.93457i 0 0.940573
296.17 − 0.579054i 0 3.66470 2.27847i 0 −2.29028 − 4.43827i 0 1.31936
296.18 − 0.419921i 0 3.82367 8.11094i 0 −8.94555 − 3.28532i 0 3.40595
296.19 − 0.238582i 0 3.94308 0.111821i 0 6.64755 − 1.89508i 0 0.0266785
296.20 − 0.0430442i 0 3.99815 9.20714i 0 11.9433 − 0.344273i 0 0.396314
See all 40 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 296.40
Significant digits:
Format:

Inner twists

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

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 531.3.b.a ✓ 40
3.b odd 2 1 inner 531.3.b.a ✓ 40
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
531.3.b.a ✓ 40 1.a even 1 1 trivial
531.3.b.a ✓ 40 3.b odd 2 1 inner

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(531, [\chi])\).