↑

Properties

Label 280.2.bg.a
Level $280$
Weight $2$
Character orbit 280.bg
Analytic conductor $2.236$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [280,2,Mod(9,280)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(280, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 3, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("280.9");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 280.bg (of order \(6\), degree \(2\), 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: \(2.23581125660\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

$q$-expansion

The dimension is sufficiently large that we do not compute an algebraic \(q\)-expansion, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 24 q + 14 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 24 q + 14 q^{9} - 2 q^{11} + 12 q^{15} - 10 q^{19} - 10 q^{21} - 2 q^{25} + 12 q^{29} + 4 q^{31} - 28 q^{35} + 20 q^{39} + 24 q^{41} - 8 q^{45} - 30 q^{49} - 12 q^{55} - 48 q^{59} - 18 q^{61} - 26 q^{65} - 60 q^{69} + 16 q^{71} - 14 q^{75} - 44 q^{79} + 12 q^{81} - 44 q^{85} + 30 q^{89} + 44 q^{91} - 26 q^{95} - 44 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
9.1 0 −2.63533 + 1.52151i 0 −2.07968 + 0.821533i 0 0.629537 + 2.56976i 0 3.12998 − 5.42128i 0
9.2 0 −2.20343 + 1.27215i 0 −0.474541 − 2.18513i 0 2.64391 + 0.0988222i 0 1.73675 − 3.00813i 0
9.3 0 −1.82577 + 1.05411i 0 1.46656 − 1.68796i 0 −1.44930 − 2.21349i 0 0.722285 − 1.25103i 0
9.4 0 −1.76528 + 1.01918i 0 2.04540 + 0.903506i 0 −2.27974 + 1.34267i 0 0.577473 − 1.00021i 0
9.5 0 −0.650755 + 0.375714i 0 −0.702823 + 2.12274i 0 0.543003 − 2.58943i 0 −1.21768 + 2.10908i 0
9.6 0 −0.277116 + 0.159993i 0 −2.00685 − 0.986173i 0 −1.50695 − 2.17465i 0 −1.44880 + 2.50940i 0
9.7 0 0.277116 − 0.159993i 0 1.85748 + 1.24490i 0 1.50695 + 2.17465i 0 −1.44880 + 2.50940i 0
9.8 0 0.650755 − 0.375714i 0 −1.48694 + 1.67003i 0 −0.543003 + 2.58943i 0 −1.21768 + 2.10908i 0
9.9 0 1.76528 − 1.01918i 0 −1.80516 − 1.31962i 0 2.27974 − 1.34267i 0 0.577473 − 1.00021i 0
9.10 0 1.82577 − 1.05411i 0 0.728531 − 2.11406i 0 1.44930 + 2.21349i 0 0.722285 − 1.25103i 0
9.11 0 2.20343 − 1.27215i 0 2.12965 − 0.681602i 0 −2.64391 − 0.0988222i 0 1.73675 − 3.00813i 0
9.12 0 2.63533 − 1.52151i 0 0.328373 + 2.21183i 0 −0.629537 − 2.56976i 0 3.12998 − 5.42128i 0
249.1 0 −2.63533 − 1.52151i 0 −2.07968 − 0.821533i 0 0.629537 − 2.56976i 0 3.12998 + 5.42128i 0
249.2 0 −2.20343 − 1.27215i 0 −0.474541 + 2.18513i 0 2.64391 − 0.0988222i 0 1.73675 + 3.00813i 0
249.3 0 −1.82577 − 1.05411i 0 1.46656 + 1.68796i 0 −1.44930 + 2.21349i 0 0.722285 + 1.25103i 0
249.4 0 −1.76528 − 1.01918i 0 2.04540 − 0.903506i 0 −2.27974 − 1.34267i 0 0.577473 + 1.00021i 0
249.5 0 −0.650755 − 0.375714i 0 −0.702823 − 2.12274i 0 0.543003 + 2.58943i 0 −1.21768 − 2.10908i 0
249.6 0 −0.277116 − 0.159993i 0 −2.00685 + 0.986173i 0 −1.50695 + 2.17465i 0 −1.44880 − 2.50940i 0
249.7 0 0.277116 + 0.159993i 0 1.85748 − 1.24490i 0 1.50695 − 2.17465i 0 −1.44880 − 2.50940i 0
249.8 0 0.650755 + 0.375714i 0 −1.48694 − 1.67003i 0 −0.543003 − 2.58943i 0 −1.21768 − 2.10908i 0
See all 24 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 9.12
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
5.b even 2 1 inner
7.c even 3 1 inner
35.j even 6 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 280.2.bg.a ✓ 24
4.b odd 2 1 560.2.bw.f 24
5.b even 2 1 inner 280.2.bg.a ✓ 24
5.c odd 4 1 1400.2.q.n 12
5.c odd 4 1 1400.2.q.o 12
7.c even 3 1 inner 280.2.bg.a ✓ 24
7.c even 3 1 1960.2.g.f 12
7.d odd 6 1 1960.2.g.e 12
20.d odd 2 1 560.2.bw.f 24
28.g odd 6 1 560.2.bw.f 24
35.i odd 6 1 1960.2.g.e 12
35.j even 6 1 inner 280.2.bg.a ✓ 24
35.j even 6 1 1960.2.g.f 12
35.k even 12 1 9800.2.a.cw 6
35.k even 12 1 9800.2.a.cy 6
35.l odd 12 1 1400.2.q.n 12
35.l odd 12 1 1400.2.q.o 12
35.l odd 12 1 9800.2.a.cv 6
35.l odd 12 1 9800.2.a.cx 6
140.p odd 6 1 560.2.bw.f 24
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
280.2.bg.a ✓ 24 1.a even 1 1 trivial
280.2.bg.a ✓ 24 5.b even 2 1 inner
280.2.bg.a ✓ 24 7.c even 3 1 inner
280.2.bg.a ✓ 24 35.j even 6 1 inner
560.2.bw.f 24 4.b odd 2 1
560.2.bw.f 24 20.d odd 2 1
560.2.bw.f 24 28.g odd 6 1
560.2.bw.f 24 140.p odd 6 1
1400.2.q.n 12 5.c odd 4 1
1400.2.q.n 12 35.l odd 12 1
1400.2.q.o 12 5.c odd 4 1
1400.2.q.o 12 35.l odd 12 1
1960.2.g.e 12 7.d odd 6 1
1960.2.g.e 12 35.i odd 6 1
1960.2.g.f 12 7.c even 3 1
1960.2.g.f 12 35.j even 6 1
9800.2.a.cv 6 35.l odd 12 1
9800.2.a.cw 6 35.k even 12 1
9800.2.a.cx 6 35.l odd 12 1
9800.2.a.cy 6 35.k even 12 1

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(280, [\chi])\).