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Properties

Label 220.3.q.a
Level $220$
Weight $3$
Character orbit 220.q
Analytic conductor $5.995$
Analytic rank $0$
Dimension $48$
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [220,3,Mod(29,220)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(220, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 5, 7]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("220.29");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 220 = 2^{2} \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 220.q (of order \(10\), degree \(4\), 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: \(5.99456581593\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(12\) over \(\Q(\zeta_{10})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

$q$-expansion

The algebraic \(q\)-expansion of this newform has not been computed, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 48 q + 5 q^{5} + 20 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 48 q + 5 q^{5} + 20 q^{9} - 23 q^{15} - 7 q^{25} - 74 q^{31} + 155 q^{35} + 80 q^{39} - 20 q^{41} + 12 q^{45} + 102 q^{49} + 220 q^{51} - 69 q^{55} + 40 q^{59} - 290 q^{61} - 234 q^{69} - 406 q^{71} + 153 q^{75} - 280 q^{79} + 230 q^{81} - 465 q^{85} - 636 q^{89} + 512 q^{91} - 495 q^{95} - 382 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
29.1 0 −4.54114 − 1.47550i 0 0.670369 − 4.95486i 0 −1.65772 − 5.10192i 0 11.1636 + 8.11086i 0
29.2 0 −4.28374 − 1.39187i 0 3.70093 + 3.36201i 0 −1.02805 − 3.16403i 0 9.13194 + 6.63474i 0
29.3 0 −3.83667 − 1.24661i 0 −4.92332 + 0.872318i 0 −0.101776 − 0.313235i 0 5.88485 + 4.27559i 0
29.4 0 −2.12894 − 0.691734i 0 3.38343 − 3.68136i 0 3.76322 + 11.5820i 0 −3.22727 − 2.34475i 0
29.5 0 −0.914119 − 0.297015i 0 3.63827 + 3.42972i 0 1.31985 + 4.06207i 0 −6.53376 − 4.74705i 0
29.6 0 −0.279655 − 0.0908655i 0 −1.46713 + 4.77991i 0 −2.89276 − 8.90300i 0 −7.21120 − 5.23925i 0
29.7 0 0.279655 + 0.0908655i 0 −4.99933 − 0.0817530i 0 2.89276 + 8.90300i 0 −7.21120 − 5.23925i 0
29.8 0 0.914119 + 0.297015i 0 −2.13757 − 4.52004i 0 −1.31985 − 4.06207i 0 −6.53376 − 4.74705i 0
29.9 0 2.12894 + 0.691734i 0 4.54672 − 2.08023i 0 −3.76322 − 11.5820i 0 −3.22727 − 2.34475i 0
29.10 0 3.83667 + 1.24661i 0 −2.35101 + 4.41279i 0 0.101776 + 0.313235i 0 5.88485 + 4.27559i 0
29.11 0 4.28374 + 1.39187i 0 −2.05382 − 4.55871i 0 1.02805 + 3.16403i 0 9.13194 + 6.63474i 0
29.12 0 4.54114 + 1.47550i 0 4.91950 + 0.893576i 0 1.65772 + 5.10192i 0 11.1636 + 8.11086i 0
129.1 0 −4.54114 + 1.47550i 0 0.670369 + 4.95486i 0 −1.65772 + 5.10192i 0 11.1636 − 8.11086i 0
129.2 0 −4.28374 + 1.39187i 0 3.70093 − 3.36201i 0 −1.02805 + 3.16403i 0 9.13194 − 6.63474i 0
129.3 0 −3.83667 + 1.24661i 0 −4.92332 − 0.872318i 0 −0.101776 + 0.313235i 0 5.88485 − 4.27559i 0
129.4 0 −2.12894 + 0.691734i 0 3.38343 + 3.68136i 0 3.76322 − 11.5820i 0 −3.22727 + 2.34475i 0
129.5 0 −0.914119 + 0.297015i 0 3.63827 − 3.42972i 0 1.31985 − 4.06207i 0 −6.53376 + 4.74705i 0
129.6 0 −0.279655 + 0.0908655i 0 −1.46713 − 4.77991i 0 −2.89276 + 8.90300i 0 −7.21120 + 5.23925i 0
129.7 0 0.279655 − 0.0908655i 0 −4.99933 + 0.0817530i 0 2.89276 − 8.90300i 0 −7.21120 + 5.23925i 0
129.8 0 0.914119 − 0.297015i 0 −2.13757 + 4.52004i 0 −1.31985 + 4.06207i 0 −6.53376 + 4.74705i 0
See all 48 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 29.12
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
5.b even 2 1 inner
11.d odd 10 1 inner
55.h odd 10 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 220.3.q.a ✓ 48
5.b even 2 1 inner 220.3.q.a ✓ 48
11.d odd 10 1 inner 220.3.q.a ✓ 48
55.h odd 10 1 inner 220.3.q.a ✓ 48
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
220.3.q.a ✓ 48 1.a even 1 1 trivial
220.3.q.a ✓ 48 5.b even 2 1 inner
220.3.q.a ✓ 48 11.d odd 10 1 inner
220.3.q.a ✓ 48 55.h odd 10 1 inner

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(220, [\chi])\).