↑

Properties

Label 2352.2.k.j
Level $2352$
Weight $2$
Character orbit 2352.k
Analytic conductor $18.781$
Analytic rank $0$
Dimension $24$
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [2352,2,Mod(881,2352)] 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("2352.881"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2352, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 1, 1])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 2352 = 2^{4} \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2352.k (of order \(2\), degree \(1\), not minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [24,0,0,0,0,0,0,0,0,0,0,0,0,0,16,0,0,0,0,0,0,0,0,0,8,0,0,0,0, 0,0,0,0,0,0,0,16] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(37)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(18.7808145554\)
Analytic rank: \(0\)
Dimension: \(24\)
Twist minimal: no (minimal twist has level 1176)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 24 q + 16 q^{15} + 8 q^{25} + 16 q^{37} + 64 q^{39} - 16 q^{43} - 48 q^{51} + 48 q^{57} - 16 q^{67} + 80 q^{81} - 64 q^{85} - 32 q^{93} + 56 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
881.1 0 −1.72171 − 0.188994i 0 −4.01535 0 0 0 2.92856 + 0.650785i 0
881.2 0 −1.72171 + 0.188994i 0 −4.01535 0 0 0 2.92856 − 0.650785i 0
881.3 0 −1.71558 − 0.238292i 0 1.32383 0 0 0 2.88643 + 0.817619i 0
881.4 0 −1.71558 + 0.238292i 0 1.32383 0 0 0 2.88643 − 0.817619i 0
881.5 0 −1.48931 − 0.884275i 0 0.992103 0 0 0 1.43612 + 2.63393i 0
881.6 0 −1.48931 + 0.884275i 0 0.992103 0 0 0 1.43612 − 2.63393i 0
881.7 0 −0.698115 − 1.58513i 0 −0.489061 0 0 0 −2.02527 + 2.21321i 0
881.8 0 −0.698115 + 1.58513i 0 −0.489061 0 0 0 −2.02527 − 2.21321i 0
881.9 0 −0.615077 − 1.61916i 0 −1.31193 0 0 0 −2.24336 + 1.99182i 0
881.10 0 −0.615077 + 1.61916i 0 −1.31193 0 0 0 −2.24336 − 1.99182i 0
881.11 0 −0.0935860 − 1.72952i 0 3.34363 0 0 0 −2.98248 + 0.323718i 0
881.12 0 −0.0935860 + 1.72952i 0 3.34363 0 0 0 −2.98248 − 0.323718i 0
881.13 0 0.0935860 − 1.72952i 0 −3.34363 0 0 0 −2.98248 − 0.323718i 0
881.14 0 0.0935860 + 1.72952i 0 −3.34363 0 0 0 −2.98248 + 0.323718i 0
881.15 0 0.615077 − 1.61916i 0 1.31193 0 0 0 −2.24336 − 1.99182i 0
881.16 0 0.615077 + 1.61916i 0 1.31193 0 0 0 −2.24336 + 1.99182i 0
881.17 0 0.698115 − 1.58513i 0 0.489061 0 0 0 −2.02527 − 2.21321i 0
881.18 0 0.698115 + 1.58513i 0 0.489061 0 0 0 −2.02527 + 2.21321i 0
881.19 0 1.48931 − 0.884275i 0 −0.992103 0 0 0 1.43612 − 2.63393i 0
881.20 0 1.48931 + 0.884275i 0 −0.992103 0 0 0 1.43612 + 2.63393i 0
See all 24 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 881.24
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
3.b odd 2 1 inner
7.b odd 2 1 inner
21.c even 2 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 2352.2.k.j 24
3.b odd 2 1 inner 2352.2.k.j 24
4.b odd 2 1 1176.2.k.b ✓ 24
7.b odd 2 1 inner 2352.2.k.j 24
12.b even 2 1 1176.2.k.b ✓ 24
21.c even 2 1 inner 2352.2.k.j 24
28.d even 2 1 1176.2.k.b ✓ 24
28.f even 6 2 1176.2.u.c 48
28.g odd 6 2 1176.2.u.c 48
84.h odd 2 1 1176.2.k.b ✓ 24
84.j odd 6 2 1176.2.u.c 48
84.n even 6 2 1176.2.u.c 48
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1176.2.k.b ✓ 24 4.b odd 2 1
1176.2.k.b ✓ 24 12.b even 2 1
1176.2.k.b ✓ 24 28.d even 2 1
1176.2.k.b ✓ 24 84.h odd 2 1
1176.2.u.c 48 28.f even 6 2
1176.2.u.c 48 28.g odd 6 2
1176.2.u.c 48 84.j odd 6 2
1176.2.u.c 48 84.n even 6 2
2352.2.k.j 24 1.a even 1 1 trivial
2352.2.k.j 24 3.b odd 2 1 inner
2352.2.k.j 24 7.b odd 2 1 inner
2352.2.k.j 24 21.c even 2 1 inner

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(2352, [\chi])\):

\( T_{5}^{12} - 32T_{5}^{10} + 316T_{5}^{8} - 1056T_{5}^{6} + 1476T_{5}^{4} - 832T_{5}^{2} + 128 \) Copy content Toggle raw display
\( T_{13}^{12} + 104T_{13}^{10} + 3668T_{13}^{8} + 50704T_{13}^{6} + 227716T_{13}^{4} + 185472T_{13}^{2} + 41472 \) Copy content Toggle raw display