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Properties

Label 2142.2.n.b
Level $2142$
Weight $2$
Character orbit 2142.n
Analytic conductor $17.104$
Analytic rank $0$
Dimension $48$
Inner twists $4$

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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] = [2142,2,Mod(251,2142)] 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("2142.251"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2142, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 2, 1])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 2142 = 2 \cdot 3^{2} \cdot 7 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2142.n (of order \(4\), degree \(2\), minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [48,48] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(17.1039561130\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(24\) over \(\Q(i)\)
Twist minimal: yes
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.

\(\operatorname{Tr}(f)(q) = \) \( 48 q + 48 q^{2} + 48 q^{4} + 48 q^{8} + 8 q^{11} + 48 q^{16} + 8 q^{22} + 8 q^{29} + 48 q^{32} - 24 q^{37} + 8 q^{44} + 8 q^{58} + 48 q^{64} + 32 q^{65} + 16 q^{67} + 48 q^{71} - 24 q^{74} + 32 q^{79} - 48 q^{85}+ \cdots + 96 q^{95}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
251.1 1.00000 0 1.00000 −2.82655 − 2.82655i 0 2.04043 − 1.68423i 1.00000 0 −2.82655 − 2.82655i
251.2 1.00000 0 1.00000 −2.38718 − 2.38718i 0 1.86555 + 1.87610i 1.00000 0 −2.38718 − 2.38718i
251.3 1.00000 0 1.00000 −2.35702 − 2.35702i 0 −0.977792 + 2.45844i 1.00000 0 −2.35702 − 2.35702i
251.4 1.00000 0 1.00000 −1.98331 − 1.98331i 0 1.59031 − 2.11445i 1.00000 0 −1.98331 − 1.98331i
251.5 1.00000 0 1.00000 −1.68087 − 1.68087i 0 −2.58694 − 0.554726i 1.00000 0 −1.68087 − 1.68087i
251.6 1.00000 0 1.00000 −1.66743 − 1.66743i 0 −2.47179 + 0.943542i 1.00000 0 −1.66743 − 1.66743i
251.7 1.00000 0 1.00000 −1.36769 − 1.36769i 0 −1.73335 − 1.99887i 1.00000 0 −1.36769 − 1.36769i
251.8 1.00000 0 1.00000 −1.36044 − 1.36044i 0 0.763586 + 2.53317i 1.00000 0 −1.36044 − 1.36044i
251.9 1.00000 0 1.00000 −1.14125 − 1.14125i 0 2.53515 + 0.756984i 1.00000 0 −1.14125 − 1.14125i
251.10 1.00000 0 1.00000 −0.389550 − 0.389550i 0 2.63523 − 0.235715i 1.00000 0 −0.389550 − 0.389550i
251.11 1.00000 0 1.00000 −0.203398 − 0.203398i 0 −0.534552 − 2.59119i 1.00000 0 −0.203398 − 0.203398i
251.12 1.00000 0 1.00000 −0.0168074 − 0.0168074i 0 −1.77295 + 1.96383i 1.00000 0 −0.0168074 − 0.0168074i
251.13 1.00000 0 1.00000 0.0168074 + 0.0168074i 0 −1.96383 + 1.77295i 1.00000 0 0.0168074 + 0.0168074i
251.14 1.00000 0 1.00000 0.203398 + 0.203398i 0 2.59119 + 0.534552i 1.00000 0 0.203398 + 0.203398i
251.15 1.00000 0 1.00000 0.389550 + 0.389550i 0 0.235715 − 2.63523i 1.00000 0 0.389550 + 0.389550i
251.16 1.00000 0 1.00000 1.14125 + 1.14125i 0 −0.756984 − 2.53515i 1.00000 0 1.14125 + 1.14125i
251.17 1.00000 0 1.00000 1.36044 + 1.36044i 0 −2.53317 − 0.763586i 1.00000 0 1.36044 + 1.36044i
251.18 1.00000 0 1.00000 1.36769 + 1.36769i 0 1.99887 + 1.73335i 1.00000 0 1.36769 + 1.36769i
251.19 1.00000 0 1.00000 1.66743 + 1.66743i 0 −0.943542 + 2.47179i 1.00000 0 1.66743 + 1.66743i
251.20 1.00000 0 1.00000 1.68087 + 1.68087i 0 0.554726 + 2.58694i 1.00000 0 1.68087 + 1.68087i
See all 48 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 251.24
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
7.b odd 2 1 inner
51.f odd 4 1 inner
357.l even 4 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 2142.2.n.b yes 48
3.b odd 2 1 2142.2.n.a ✓ 48
7.b odd 2 1 inner 2142.2.n.b yes 48
17.c even 4 1 2142.2.n.a ✓ 48
21.c even 2 1 2142.2.n.a ✓ 48
51.f odd 4 1 inner 2142.2.n.b yes 48
119.f odd 4 1 2142.2.n.a ✓ 48
357.l even 4 1 inner 2142.2.n.b yes 48
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
2142.2.n.a ✓ 48 3.b odd 2 1
2142.2.n.a ✓ 48 17.c even 4 1
2142.2.n.a ✓ 48 21.c even 2 1
2142.2.n.a ✓ 48 119.f odd 4 1
2142.2.n.b yes 48 1.a even 1 1 trivial
2142.2.n.b yes 48 7.b odd 2 1 inner
2142.2.n.b yes 48 51.f odd 4 1 inner
2142.2.n.b yes 48 357.l even 4 1 inner