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Properties

Label 280.3.m.a
Level $280$
Weight $3$
Character orbit 280.m
Analytic conductor $7.629$
Analytic rank $0$
Dimension $64$
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] = [280,3,Mod(181,280)]
 
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([0, 1, 0, 1]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("280.181");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 280.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: \(7.62944740209\)
Analytic rank: \(0\)
Dimension: \(64\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 64 q - 2 q^{2} - 6 q^{4} + 10 q^{8} + 192 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 64 q - 2 q^{2} - 6 q^{4} + 10 q^{8} + 192 q^{9} + 34 q^{14} - 14 q^{16} + 70 q^{18} + 44 q^{22} + 64 q^{23} + 320 q^{25} - 90 q^{28} - 302 q^{32} - 50 q^{36} - 120 q^{42} + 16 q^{44} - 284 q^{46} - 32 q^{49} - 10 q^{50} + 178 q^{56} + 192 q^{57} - 76 q^{58} + 140 q^{60} - 320 q^{63} - 318 q^{64} + 120 q^{70} - 384 q^{71} + 662 q^{72} + 224 q^{74} - 740 q^{78} - 320 q^{79} + 608 q^{81} - 160 q^{84} + 392 q^{86} - 320 q^{88} + 196 q^{92} - 534 q^{98}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
181.1 −1.98653 − 0.231770i −1.12438 3.89257 + 0.920834i −2.23607 2.23361 + 0.260598i 0.945845 + 6.93580i −7.51926 − 2.73144i −7.73577 4.44201 + 0.518254i
181.2 −1.98653 − 0.231770i 1.12438 3.89257 + 0.920834i 2.23607 −2.23361 − 0.260598i 0.945845 − 6.93580i −7.51926 − 2.73144i −7.73577 −4.44201 − 0.518254i
181.3 −1.98653 + 0.231770i −1.12438 3.89257 − 0.920834i −2.23607 2.23361 − 0.260598i 0.945845 − 6.93580i −7.51926 + 2.73144i −7.73577 4.44201 − 0.518254i
181.4 −1.98653 + 0.231770i 1.12438 3.89257 − 0.920834i 2.23607 −2.23361 + 0.260598i 0.945845 + 6.93580i −7.51926 + 2.73144i −7.73577 −4.44201 + 0.518254i
181.5 −1.83882 − 0.786591i −4.48764 2.76255 + 2.89281i −2.23607 8.25199 + 3.52994i −3.96209 − 5.77077i −2.80438 − 7.49236i 11.1389 4.11174 + 1.75887i
181.6 −1.83882 − 0.786591i 4.48764 2.76255 + 2.89281i 2.23607 −8.25199 − 3.52994i −3.96209 + 5.77077i −2.80438 − 7.49236i 11.1389 −4.11174 − 1.75887i
181.7 −1.83882 + 0.786591i −4.48764 2.76255 − 2.89281i −2.23607 8.25199 − 3.52994i −3.96209 + 5.77077i −2.80438 + 7.49236i 11.1389 4.11174 − 1.75887i
181.8 −1.83882 + 0.786591i 4.48764 2.76255 − 2.89281i 2.23607 −8.25199 + 3.52994i −3.96209 − 5.77077i −2.80438 + 7.49236i 11.1389 −4.11174 + 1.75887i
181.9 −1.81506 − 0.839965i −3.33682 2.58892 + 3.04918i 2.23607 6.05655 + 2.80281i −6.90897 − 1.12524i −2.13785 − 7.70906i 2.13440 −4.05861 − 1.87822i
181.10 −1.81506 − 0.839965i 3.33682 2.58892 + 3.04918i −2.23607 −6.05655 − 2.80281i −6.90897 + 1.12524i −2.13785 − 7.70906i 2.13440 4.05861 + 1.87822i
181.11 −1.81506 + 0.839965i −3.33682 2.58892 − 3.04918i 2.23607 6.05655 − 2.80281i −6.90897 + 1.12524i −2.13785 + 7.70906i 2.13440 −4.05861 + 1.87822i
181.12 −1.81506 + 0.839965i 3.33682 2.58892 − 3.04918i −2.23607 −6.05655 + 2.80281i −6.90897 − 1.12524i −2.13785 + 7.70906i 2.13440 4.05861 − 1.87822i
181.13 −1.67311 − 1.09576i −2.13352 1.59860 + 3.66667i 2.23607 3.56962 + 2.33784i 6.25095 + 3.15049i 1.34318 − 7.88644i −4.44807 −3.74119 − 2.45020i
181.14 −1.67311 − 1.09576i 2.13352 1.59860 + 3.66667i −2.23607 −3.56962 − 2.33784i 6.25095 − 3.15049i 1.34318 − 7.88644i −4.44807 3.74119 + 2.45020i
181.15 −1.67311 + 1.09576i −2.13352 1.59860 − 3.66667i 2.23607 3.56962 − 2.33784i 6.25095 − 3.15049i 1.34318 + 7.88644i −4.44807 −3.74119 + 2.45020i
181.16 −1.67311 + 1.09576i 2.13352 1.59860 − 3.66667i −2.23607 −3.56962 + 2.33784i 6.25095 + 3.15049i 1.34318 + 7.88644i −4.44807 3.74119 − 2.45020i
181.17 −1.03304 − 1.71255i −4.54931 −1.86566 + 3.53827i −2.23607 4.69962 + 7.79093i 6.26297 − 3.12653i 7.98676 − 0.460138i 11.6962 2.30995 + 3.82938i
181.18 −1.03304 − 1.71255i 4.54931 −1.86566 + 3.53827i 2.23607 −4.69962 − 7.79093i 6.26297 + 3.12653i 7.98676 − 0.460138i 11.6962 −2.30995 − 3.82938i
181.19 −1.03304 + 1.71255i −4.54931 −1.86566 − 3.53827i −2.23607 4.69962 − 7.79093i 6.26297 + 3.12653i 7.98676 + 0.460138i 11.6962 2.30995 − 3.82938i
181.20 −1.03304 + 1.71255i 4.54931 −1.86566 − 3.53827i 2.23607 −4.69962 + 7.79093i 6.26297 − 3.12653i 7.98676 + 0.460138i 11.6962 −2.30995 + 3.82938i
See all 64 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 181.64
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
7.b odd 2 1 inner
8.b even 2 1 inner
56.h 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.m.a ✓ 64
4.b odd 2 1 1120.3.m.a 64
7.b odd 2 1 inner 280.3.m.a ✓ 64
8.b even 2 1 inner 280.3.m.a ✓ 64
8.d odd 2 1 1120.3.m.a 64
28.d even 2 1 1120.3.m.a 64
56.e even 2 1 1120.3.m.a 64
56.h odd 2 1 inner 280.3.m.a ✓ 64
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
280.3.m.a ✓ 64 1.a even 1 1 trivial
280.3.m.a ✓ 64 7.b odd 2 1 inner
280.3.m.a ✓ 64 8.b even 2 1 inner
280.3.m.a ✓ 64 56.h odd 2 1 inner
1120.3.m.a 64 4.b odd 2 1
1120.3.m.a 64 8.d odd 2 1
1120.3.m.a 64 28.d even 2 1
1120.3.m.a 64 56.e even 2 1

Hecke kernels

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