↑

Properties

Label 1020.3.m.a
Level $1020$
Weight $3$
Character orbit 1020.m
Analytic conductor $27.793$
Analytic rank $0$
Dimension $44$
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] = [1020,3,Mod(341,1020)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1020, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 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("1020.341");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1020 = 2^{2} \cdot 3 \cdot 5 \cdot 17 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1020.m (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: \(27.7929869648\)
Analytic rank: \(0\)
Dimension: \(44\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 44 q - 8 q^{7} + 16 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 44 q - 8 q^{7} + 16 q^{9} - 32 q^{13} + 88 q^{19} - 8 q^{21} - 220 q^{25} - 12 q^{27} - 80 q^{31} - 4 q^{33} - 120 q^{37} - 84 q^{39} + 120 q^{43} + 40 q^{45} + 380 q^{49} + 112 q^{57} + 216 q^{61} + 36 q^{63} - 304 q^{67} - 240 q^{69} + 272 q^{73} + 40 q^{79} - 16 q^{81} + 560 q^{87} - 560 q^{91} + 124 q^{93} + 40 q^{97} - 196 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
341.1 0 −2.99131 − 0.228179i 0 2.23607i 0 −8.67537 0 8.89587 + 1.36511i 0
341.2 0 −2.99131 + 0.228179i 0 − 2.23607i 0 −8.67537 0 8.89587 − 1.36511i 0
341.3 0 −2.93458 − 0.623110i 0 − 2.23607i 0 9.62567 0 8.22347 + 3.65713i 0
341.4 0 −2.93458 + 0.623110i 0 2.23607i 0 9.62567 0 8.22347 − 3.65713i 0
341.5 0 −2.87806 − 0.846636i 0 2.23607i 0 1.98524 0 7.56642 + 4.87333i 0
341.6 0 −2.87806 + 0.846636i 0 − 2.23607i 0 1.98524 0 7.56642 − 4.87333i 0
341.7 0 −2.57286 − 1.54286i 0 2.23607i 0 −7.51195 0 4.23918 + 7.93910i 0
341.8 0 −2.57286 + 1.54286i 0 − 2.23607i 0 −7.51195 0 4.23918 − 7.93910i 0
341.9 0 −2.35672 − 1.85630i 0 − 2.23607i 0 9.80085 0 2.10830 + 8.74958i 0
341.10 0 −2.35672 + 1.85630i 0 2.23607i 0 9.80085 0 2.10830 − 8.74958i 0
341.11 0 −2.14982 − 2.09243i 0 − 2.23607i 0 −10.7430 0 0.243458 + 8.99671i 0
341.12 0 −2.14982 + 2.09243i 0 2.23607i 0 −10.7430 0 0.243458 − 8.99671i 0
341.13 0 −2.14509 − 2.09729i 0 − 2.23607i 0 −2.46304 0 0.202789 + 8.99772i 0
341.14 0 −2.14509 + 2.09729i 0 2.23607i 0 −2.46304 0 0.202789 − 8.99772i 0
341.15 0 −1.87322 − 2.34330i 0 2.23607i 0 9.61791 0 −1.98209 + 8.77903i 0
341.16 0 −1.87322 + 2.34330i 0 − 2.23607i 0 9.61791 0 −1.98209 − 8.77903i 0
341.17 0 −0.703067 − 2.91645i 0 2.23607i 0 −7.68331 0 −8.01139 + 4.10092i 0
341.18 0 −0.703067 + 2.91645i 0 − 2.23607i 0 −7.68331 0 −8.01139 − 4.10092i 0
341.19 0 −0.641776 − 2.93055i 0 2.23607i 0 3.43971 0 −8.17625 + 3.76151i 0
341.20 0 −0.641776 + 2.93055i 0 − 2.23607i 0 3.43971 0 −8.17625 − 3.76151i 0
See all 44 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 341.44
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 1020.3.m.a ✓ 44
3.b odd 2 1 inner 1020.3.m.a ✓ 44
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1020.3.m.a ✓ 44 1.a even 1 1 trivial
1020.3.m.a ✓ 44 3.b odd 2 1 inner

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(1020, [\chi])\).