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Properties

Label 280.3.o.a
Level $280$
Weight $3$
Character orbit 280.o
Analytic conductor $7.629$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [280,3,Mod(211,280)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(280, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 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("280.211");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 280.o (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: \(7.62944740209\)
Analytic rank: \(0\)
Dimension: \(48\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 48 q - 2 q^{2} + 10 q^{4} + 24 q^{6} - 26 q^{8} + 144 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 48 q - 2 q^{2} + 10 q^{4} + 24 q^{6} - 26 q^{8} + 144 q^{9} + 20 q^{10} + 32 q^{11} - 60 q^{12} - 14 q^{14} + 18 q^{16} + 54 q^{18} - 64 q^{19} - 32 q^{22} - 52 q^{24} - 240 q^{25} - 156 q^{26} + 192 q^{27} - 70 q^{28} - 80 q^{30} - 42 q^{32} - 32 q^{33} - 120 q^{34} + 158 q^{36} - 100 q^{38} + 80 q^{40} - 96 q^{41} - 96 q^{43} - 20 q^{44} - 16 q^{46} + 60 q^{48} - 336 q^{49} + 10 q^{50} + 192 q^{51} + 56 q^{52} + 428 q^{54} + 14 q^{56} + 160 q^{57} + 564 q^{58} - 576 q^{59} - 60 q^{60} + 64 q^{62} - 14 q^{64} - 132 q^{66} - 160 q^{67} + 36 q^{68} + 58 q^{72} + 272 q^{74} + 300 q^{76} - 180 q^{78} + 320 q^{80} + 656 q^{81} - 412 q^{82} - 196 q^{84} + 332 q^{86} + 820 q^{88} + 240 q^{90} + 544 q^{92} - 244 q^{94} - 1444 q^{96} + 14 q^{98} + 224 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
211.1 −1.99983 − 0.0258973i 1.35796 3.99866 + 0.103581i − 2.23607i −2.71569 − 0.0351674i − 2.64575i −7.99396 − 0.310698i −7.15595 −0.0579081 + 4.47176i
211.2 −1.99983 + 0.0258973i 1.35796 3.99866 − 0.103581i 2.23607i −2.71569 + 0.0351674i 2.64575i −7.99396 + 0.310698i −7.15595 −0.0579081 − 4.47176i
211.3 −1.98012 − 0.281305i 4.41807 3.84173 + 1.11403i − 2.23607i −8.74831 − 1.24283i 2.64575i −7.29370 − 3.28662i 10.5194 −0.629017 + 4.42768i
211.4 −1.98012 + 0.281305i 4.41807 3.84173 − 1.11403i 2.23607i −8.74831 + 1.24283i − 2.64575i −7.29370 + 3.28662i 10.5194 −0.629017 − 4.42768i
211.5 −1.91631 − 0.572487i −5.75711 3.34452 + 2.19413i 2.23607i 11.0324 + 3.29587i 2.64575i −5.15304 − 6.11933i 24.1443 1.28012 − 4.28501i
211.6 −1.91631 + 0.572487i −5.75711 3.34452 − 2.19413i − 2.23607i 11.0324 − 3.29587i − 2.64575i −5.15304 + 6.11933i 24.1443 1.28012 + 4.28501i
211.7 −1.88400 − 0.671219i −2.90764 3.09893 + 2.52916i − 2.23607i 5.47799 + 1.95166i 2.64575i −4.14077 − 6.84500i −0.545650 −1.50089 + 4.21276i
211.8 −1.88400 + 0.671219i −2.90764 3.09893 − 2.52916i 2.23607i 5.47799 − 1.95166i − 2.64575i −4.14077 + 6.84500i −0.545650 −1.50089 − 4.21276i
211.9 −1.77932 − 0.913247i −0.659330 2.33196 + 3.24992i 2.23607i 1.17316 + 0.602132i − 2.64575i −1.18132 − 7.91230i −8.56528 2.04208 − 3.97868i
211.10 −1.77932 + 0.913247i −0.659330 2.33196 − 3.24992i − 2.23607i 1.17316 − 0.602132i 2.64575i −1.18132 + 7.91230i −8.56528 2.04208 + 3.97868i
211.11 −1.61871 − 1.17464i 1.42287 1.24046 + 3.80280i 2.23607i −2.30322 − 1.67135i 2.64575i 2.45894 − 7.61273i −6.97544 2.62656 − 3.61955i
211.12 −1.61871 + 1.17464i 1.42287 1.24046 − 3.80280i − 2.23607i −2.30322 + 1.67135i − 2.64575i 2.45894 + 7.61273i −6.97544 2.62656 + 3.61955i
211.13 −1.60808 − 1.18915i −3.26743 1.17184 + 3.82450i − 2.23607i 5.25428 + 3.88546i − 2.64575i 2.66348 − 7.54360i 1.67607 −2.65902 + 3.59578i
211.14 −1.60808 + 1.18915i −3.26743 1.17184 − 3.82450i 2.23607i 5.25428 − 3.88546i 2.64575i 2.66348 + 7.54360i 1.67607 −2.65902 − 3.59578i
211.15 −1.12561 − 1.65318i 0.876007 −1.46600 + 3.72167i − 2.23607i −0.986042 − 1.44820i 2.64575i 7.80274 − 1.76558i −8.23261 −3.69662 + 2.51694i
211.16 −1.12561 + 1.65318i 0.876007 −1.46600 − 3.72167i 2.23607i −0.986042 + 1.44820i − 2.64575i 7.80274 + 1.76558i −8.23261 −3.69662 − 2.51694i
211.17 −1.09759 − 1.67191i −4.45791 −1.59058 + 3.67016i 2.23607i 4.89297 + 7.45323i − 2.64575i 7.88199 − 1.36903i 10.8730 3.73851 − 2.45429i
211.18 −1.09759 + 1.67191i −4.45791 −1.59058 − 3.67016i − 2.23607i 4.89297 − 7.45323i 2.64575i 7.88199 + 1.36903i 10.8730 3.73851 + 2.45429i
211.19 −0.656544 − 1.88917i 4.90012 −3.13790 + 2.48064i 2.23607i −3.21715 − 9.25715i 2.64575i 6.74652 + 4.29936i 15.0112 4.22430 − 1.46808i
211.20 −0.656544 + 1.88917i 4.90012 −3.13790 − 2.48064i − 2.23607i −3.21715 + 9.25715i − 2.64575i 6.74652 − 4.29936i 15.0112 4.22430 + 1.46808i
See all 48 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 211.48
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
8.d odd 2 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 280.3.o.a ✓ 48
4.b odd 2 1 1120.3.o.a 48
8.b even 2 1 1120.3.o.a 48
8.d odd 2 1 inner 280.3.o.a ✓ 48
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
280.3.o.a ✓ 48 1.a even 1 1 trivial
280.3.o.a ✓ 48 8.d odd 2 1 inner
1120.3.o.a 48 4.b odd 2 1
1120.3.o.a 48 8.b even 2 1

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(280, [\chi])\).