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Properties

Label 1440.3.v.a
Level $1440$
Weight $3$
Character orbit 1440.v
Analytic conductor $39.237$
Analytic rank $0$
Dimension $96$
Inner twists $8$

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Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [1440,3,Mod(143,1440)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1440.143"); S:= CuspForms(chi, 3); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1440, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 2, 2, 3])) N = Newforms(chi, 3, names="a")
 
Level: \( N \) \(=\) \( 1440 = 2^{5} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1440.v (of order \(4\), degree \(2\), not minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(39.2371580679\)
Analytic rank: \(0\)
Dimension: \(96\)
Relative dimension: \(48\) over \(\Q(i)\)
Twist minimal: no (minimal twist has level 360)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 96 q - 256 q^{43} - 64 q^{97}+O(q^{100}) \) Copy content Toggle raw display

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.

Copy content comment:embeddings in the coefficient field
 
Copy content gp:mfembed(f)
 
Label   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
143.1 0 0 0 −4.90198 − 0.985206i 0 −7.83545 − 7.83545i 0 0 0
143.2 0 0 0 −4.90198 − 0.985206i 0 7.83545 + 7.83545i 0 0 0
143.3 0 0 0 −4.81735 − 1.33908i 0 −5.79392 − 5.79392i 0 0 0
143.4 0 0 0 −4.81735 − 1.33908i 0 5.79392 + 5.79392i 0 0 0
143.5 0 0 0 −4.81378 + 1.35186i 0 −1.83250 − 1.83250i 0 0 0
143.6 0 0 0 −4.81378 + 1.35186i 0 1.83250 + 1.83250i 0 0 0
143.7 0 0 0 −4.54158 − 2.09143i 0 −3.96746 − 3.96746i 0 0 0
143.8 0 0 0 −4.54158 − 2.09143i 0 3.96746 + 3.96746i 0 0 0
143.9 0 0 0 −4.04972 + 2.93254i 0 −8.86028 − 8.86028i 0 0 0
143.10 0 0 0 −4.04972 + 2.93254i 0 8.86028 + 8.86028i 0 0 0
143.11 0 0 0 −3.63146 − 3.43694i 0 −3.39005 − 3.39005i 0 0 0
143.12 0 0 0 −3.63146 − 3.43694i 0 3.39005 + 3.39005i 0 0 0
143.13 0 0 0 −3.62942 + 3.43908i 0 −1.49960 − 1.49960i 0 0 0
143.14 0 0 0 −3.62942 + 3.43908i 0 1.49960 + 1.49960i 0 0 0
143.15 0 0 0 −3.25584 + 3.79467i 0 −2.37222 − 2.37222i 0 0 0
143.16 0 0 0 −3.25584 + 3.79467i 0 2.37222 + 2.37222i 0 0 0
143.17 0 0 0 −1.73055 − 4.69097i 0 −8.09918 − 8.09918i 0 0 0
143.18 0 0 0 −1.73055 − 4.69097i 0 8.09918 + 8.09918i 0 0 0
143.19 0 0 0 −1.15118 + 4.86567i 0 −6.37207 − 6.37207i 0 0 0
143.20 0 0 0 −1.15118 + 4.86567i 0 6.37207 + 6.37207i 0 0 0
See all 96 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 143.48
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
3.b odd 2 1 inner
5.c odd 4 1 inner
8.d odd 2 1 inner
15.e even 4 1 inner
24.f even 2 1 inner
40.k even 4 1 inner
120.q odd 4 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 1440.3.v.a 96
3.b odd 2 1 inner 1440.3.v.a 96
4.b odd 2 1 360.3.r.a ✓ 96
5.c odd 4 1 inner 1440.3.v.a 96
8.b even 2 1 360.3.r.a ✓ 96
8.d odd 2 1 inner 1440.3.v.a 96
12.b even 2 1 360.3.r.a ✓ 96
15.e even 4 1 inner 1440.3.v.a 96
20.e even 4 1 360.3.r.a ✓ 96
24.f even 2 1 inner 1440.3.v.a 96
24.h odd 2 1 360.3.r.a ✓ 96
40.i odd 4 1 360.3.r.a ✓ 96
40.k even 4 1 inner 1440.3.v.a 96
60.l odd 4 1 360.3.r.a ✓ 96
120.q odd 4 1 inner 1440.3.v.a 96
120.w even 4 1 360.3.r.a ✓ 96
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
360.3.r.a ✓ 96 4.b odd 2 1
360.3.r.a ✓ 96 8.b even 2 1
360.3.r.a ✓ 96 12.b even 2 1
360.3.r.a ✓ 96 20.e even 4 1
360.3.r.a ✓ 96 24.h odd 2 1
360.3.r.a ✓ 96 40.i odd 4 1
360.3.r.a ✓ 96 60.l odd 4 1
360.3.r.a ✓ 96 120.w even 4 1
1440.3.v.a 96 1.a even 1 1 trivial
1440.3.v.a 96 3.b odd 2 1 inner
1440.3.v.a 96 5.c odd 4 1 inner
1440.3.v.a 96 8.d odd 2 1 inner
1440.3.v.a 96 15.e even 4 1 inner
1440.3.v.a 96 24.f even 2 1 inner
1440.3.v.a 96 40.k even 4 1 inner
1440.3.v.a 96 120.q odd 4 1 inner

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(1440, [\chi])\).