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Properties

Label 1440.2.bv.b
Level $1440$
Weight $2$
Character orbit 1440.bv
Analytic conductor $11.498$
Analytic rank $0$
Dimension $92$
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] = [1440,2,Mod(241,1440)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1440, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 3, 4, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1440.241");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1440 = 2^{5} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1440.bv (of order \(6\), degree \(2\), not 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: \(11.4984578911\)
Analytic rank: \(0\)
Dimension: \(92\)
Relative dimension: \(46\) over \(\Q(\zeta_{6})\)
Twist minimal: no (minimal twist has level 360)
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.

\(\operatorname{Tr}(f)(q) = \) \( 92 q + 8 q^{7} + 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 92 q + 8 q^{7} + 6 q^{9} + 12 q^{17} - 28 q^{23} + 46 q^{25} - 8 q^{31} - 14 q^{33} + 24 q^{39} - 18 q^{41} + 36 q^{47} - 30 q^{49} - 20 q^{55} - 34 q^{57} + 32 q^{63} + 12 q^{65} + 8 q^{71} - 4 q^{73} - 20 q^{79} + 18 q^{81} + 48 q^{87} - 24 q^{89} + 18 q^{95} - 14 q^{97}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
241.1 0 −1.73199 − 0.0140878i 0 −0.866025 + 0.500000i 0 −1.38868 + 2.40527i 0 2.99960 + 0.0488000i 0
241.2 0 −1.72914 − 0.100320i 0 −0.866025 + 0.500000i 0 2.03225 − 3.51996i 0 2.97987 + 0.346937i 0
241.3 0 −1.69766 + 0.343430i 0 0.866025 − 0.500000i 0 2.54751 − 4.41241i 0 2.76411 − 1.16605i 0
241.4 0 −1.65748 − 0.502749i 0 0.866025 − 0.500000i 0 −0.375568 + 0.650502i 0 2.49449 + 1.66660i 0
241.5 0 −1.64326 − 0.547444i 0 0.866025 − 0.500000i 0 1.03266 − 1.78863i 0 2.40061 + 1.79919i 0
241.6 0 −1.64287 + 0.548626i 0 −0.866025 + 0.500000i 0 0.740799 − 1.28310i 0 2.39802 − 1.80264i 0
241.7 0 −1.64095 + 0.554332i 0 0.866025 − 0.500000i 0 −1.02186 + 1.76992i 0 2.38543 − 1.81926i 0
241.8 0 −1.55032 + 0.772347i 0 0.866025 − 0.500000i 0 −1.31554 + 2.27859i 0 1.80696 − 2.39476i 0
241.9 0 −1.42280 − 0.987751i 0 −0.866025 + 0.500000i 0 −0.647320 + 1.12119i 0 1.04869 + 2.81074i 0
241.10 0 −1.36869 − 1.06146i 0 −0.866025 + 0.500000i 0 −2.36602 + 4.09807i 0 0.746600 + 2.90561i 0
241.11 0 −1.32635 − 1.11391i 0 0.866025 − 0.500000i 0 −0.206718 + 0.358047i 0 0.518424 + 2.95487i 0
241.12 0 −1.26532 + 1.18278i 0 −0.866025 + 0.500000i 0 0.166325 − 0.288084i 0 0.202086 − 2.99319i 0
241.13 0 −1.19560 − 1.25321i 0 −0.866025 + 0.500000i 0 1.81917 − 3.15090i 0 −0.141089 + 2.99668i 0
241.14 0 −1.15336 + 1.29220i 0 −0.866025 + 0.500000i 0 −0.807871 + 1.39927i 0 −0.339538 − 2.98072i 0
241.15 0 −0.994723 + 1.41793i 0 0.866025 − 0.500000i 0 0.293997 − 0.509218i 0 −1.02105 − 2.82090i 0
241.16 0 −0.904267 − 1.47726i 0 0.866025 − 0.500000i 0 0.852557 − 1.47667i 0 −1.36460 + 2.67168i 0
241.17 0 −0.615144 − 1.61913i 0 −0.866025 + 0.500000i 0 1.58270 − 2.74131i 0 −2.24320 + 1.99200i 0
241.18 0 −0.493847 − 1.66016i 0 0.866025 − 0.500000i 0 −2.00777 + 3.47755i 0 −2.51223 + 1.63973i 0
241.19 0 −0.443022 + 1.67443i 0 0.866025 − 0.500000i 0 −2.04026 + 3.53383i 0 −2.60746 − 1.48362i 0
241.20 0 −0.417024 + 1.68110i 0 0.866025 − 0.500000i 0 0.764350 − 1.32389i 0 −2.65218 − 1.40212i 0
See all 92 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 241.46
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
8.b even 2 1 inner
9.c even 3 1 inner
72.n even 6 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 1440.2.bv.b 92
3.b odd 2 1 4320.2.bv.b 92
4.b odd 2 1 360.2.bf.b ✓ 92
8.b even 2 1 inner 1440.2.bv.b 92
8.d odd 2 1 360.2.bf.b ✓ 92
9.c even 3 1 inner 1440.2.bv.b 92
9.d odd 6 1 4320.2.bv.b 92
12.b even 2 1 1080.2.bf.b 92
24.f even 2 1 1080.2.bf.b 92
24.h odd 2 1 4320.2.bv.b 92
36.f odd 6 1 360.2.bf.b ✓ 92
36.h even 6 1 1080.2.bf.b 92
72.j odd 6 1 4320.2.bv.b 92
72.l even 6 1 1080.2.bf.b 92
72.n even 6 1 inner 1440.2.bv.b 92
72.p odd 6 1 360.2.bf.b ✓ 92
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
360.2.bf.b ✓ 92 4.b odd 2 1
360.2.bf.b ✓ 92 8.d odd 2 1
360.2.bf.b ✓ 92 36.f odd 6 1
360.2.bf.b ✓ 92 72.p odd 6 1
1080.2.bf.b 92 12.b even 2 1
1080.2.bf.b 92 24.f even 2 1
1080.2.bf.b 92 36.h even 6 1
1080.2.bf.b 92 72.l even 6 1
1440.2.bv.b 92 1.a even 1 1 trivial
1440.2.bv.b 92 8.b even 2 1 inner
1440.2.bv.b 92 9.c even 3 1 inner
1440.2.bv.b 92 72.n even 6 1 inner
4320.2.bv.b 92 3.b odd 2 1
4320.2.bv.b 92 9.d odd 6 1
4320.2.bv.b 92 24.h odd 2 1
4320.2.bv.b 92 72.j odd 6 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{7}^{46} - 4 T_{7}^{45} + 96 T_{7}^{44} - 320 T_{7}^{43} + 5075 T_{7}^{42} - 15252 T_{7}^{41} + \cdots + 5524530586624 \) acting on \(S_{2}^{\mathrm{new}}(1440, [\chi])\). Copy content Toggle raw display