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Properties

Label 1183.2.e.j
Level $1183$
Weight $2$
Character orbit 1183.e
Analytic conductor $9.446$
Analytic rank $0$
Dimension $24$
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] = [1183,2,Mod(170,1183)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1183, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1183.170");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1183 = 7 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1183.e (of order \(3\), 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: \(9.44630255912\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(\zeta_{3})\)
Twist minimal: no (minimal twist has level 91)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 24 q - 6 q^{3} - 8 q^{4} - 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 24 q - 6 q^{3} - 8 q^{4} - 2 q^{9} - 24 q^{10} + 2 q^{12} + 8 q^{14} - 16 q^{16} - 34 q^{17} + 60 q^{22} - 6 q^{23} + 10 q^{25} + 24 q^{27} + 4 q^{29} - 22 q^{30} - 24 q^{35} - 52 q^{36} - 38 q^{38} - 2 q^{40} + 32 q^{42} + 44 q^{43} - 76 q^{48} + 12 q^{49} - 8 q^{51} - 16 q^{53} + 60 q^{55} + 54 q^{56} + 10 q^{61} + 164 q^{62} - 4 q^{64} - 68 q^{66} - 22 q^{68} + 28 q^{69} - 66 q^{74} - 2 q^{75} + 38 q^{77} - 70 q^{79} + 28 q^{81} - 10 q^{82} + 20 q^{87} + 28 q^{88} - 132 q^{92} + 2 q^{94} - 4 q^{95}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
170.1 −1.29430 + 2.24179i −0.259233 − 0.449005i −2.35043 − 4.07106i −0.806027 + 1.39608i 1.34210 2.13104 + 1.56802i 6.99143 1.36560 − 2.36528i −2.08648 − 3.61389i
170.2 −1.15163 + 1.99469i 0.736680 + 1.27597i −1.65252 − 2.86225i −0.423646 + 0.733776i −3.39354 −1.00088 − 2.44913i 3.00585 0.414604 − 0.718115i −0.975769 − 1.69008i
170.3 −0.689527 + 1.19430i −1.44060 − 2.49520i 0.0491037 + 0.0850501i −0.402974 + 0.697972i 3.97334 −1.26180 − 2.32548i −2.89354 −2.65067 + 4.59109i −0.555723 − 0.962541i
170.4 −0.672613 + 1.16500i −1.02505 − 1.77544i 0.0951832 + 0.164862i −1.78389 + 3.08979i 2.75785 2.62255 − 0.349630i −2.94654 −0.601462 + 1.04176i −2.39973 − 4.15646i
170.5 −0.249993 + 0.433001i −0.424801 − 0.735776i 0.875007 + 1.51556i 0.521238 − 0.902810i 0.424789 −2.40155 + 1.11021i −1.87496 1.13909 − 1.97296i 0.260612 + 0.451393i
170.6 −0.0904119 + 0.156598i 0.913006 + 1.58137i 0.983651 + 1.70373i −1.34332 + 2.32670i −0.330186 −1.64912 + 2.06892i −0.717383 −0.167162 + 0.289532i −0.242904 − 0.420723i
170.7 0.0904119 − 0.156598i 0.913006 + 1.58137i 0.983651 + 1.70373i 1.34332 − 2.32670i 0.330186 1.64912 − 2.06892i 0.717383 −0.167162 + 0.289532i −0.242904 − 0.420723i
170.8 0.249993 − 0.433001i −0.424801 − 0.735776i 0.875007 + 1.51556i −0.521238 + 0.902810i −0.424789 2.40155 − 1.11021i 1.87496 1.13909 − 1.97296i 0.260612 + 0.451393i
170.9 0.672613 − 1.16500i −1.02505 − 1.77544i 0.0951832 + 0.164862i 1.78389 − 3.08979i −2.75785 −2.62255 + 0.349630i 2.94654 −0.601462 + 1.04176i −2.39973 − 4.15646i
170.10 0.689527 − 1.19430i −1.44060 − 2.49520i 0.0491037 + 0.0850501i 0.402974 − 0.697972i −3.97334 1.26180 + 2.32548i 2.89354 −2.65067 + 4.59109i −0.555723 − 0.962541i
170.11 1.15163 − 1.99469i 0.736680 + 1.27597i −1.65252 − 2.86225i 0.423646 − 0.733776i 3.39354 1.00088 + 2.44913i −3.00585 0.414604 − 0.718115i −0.975769 − 1.69008i
170.12 1.29430 − 2.24179i −0.259233 − 0.449005i −2.35043 − 4.07106i 0.806027 − 1.39608i −1.34210 −2.13104 − 1.56802i −6.99143 1.36560 − 2.36528i −2.08648 − 3.61389i
508.1 −1.29430 − 2.24179i −0.259233 + 0.449005i −2.35043 + 4.07106i −0.806027 − 1.39608i 1.34210 2.13104 − 1.56802i 6.99143 1.36560 + 2.36528i −2.08648 + 3.61389i
508.2 −1.15163 − 1.99469i 0.736680 − 1.27597i −1.65252 + 2.86225i −0.423646 − 0.733776i −3.39354 −1.00088 + 2.44913i 3.00585 0.414604 + 0.718115i −0.975769 + 1.69008i
508.3 −0.689527 − 1.19430i −1.44060 + 2.49520i 0.0491037 − 0.0850501i −0.402974 − 0.697972i 3.97334 −1.26180 + 2.32548i −2.89354 −2.65067 − 4.59109i −0.555723 + 0.962541i
508.4 −0.672613 − 1.16500i −1.02505 + 1.77544i 0.0951832 − 0.164862i −1.78389 − 3.08979i 2.75785 2.62255 + 0.349630i −2.94654 −0.601462 − 1.04176i −2.39973 + 4.15646i
508.5 −0.249993 − 0.433001i −0.424801 + 0.735776i 0.875007 − 1.51556i 0.521238 + 0.902810i 0.424789 −2.40155 − 1.11021i −1.87496 1.13909 + 1.97296i 0.260612 − 0.451393i
508.6 −0.0904119 − 0.156598i 0.913006 − 1.58137i 0.983651 − 1.70373i −1.34332 − 2.32670i −0.330186 −1.64912 − 2.06892i −0.717383 −0.167162 − 0.289532i −0.242904 + 0.420723i
508.7 0.0904119 + 0.156598i 0.913006 − 1.58137i 0.983651 − 1.70373i 1.34332 + 2.32670i 0.330186 1.64912 + 2.06892i 0.717383 −0.167162 − 0.289532i −0.242904 + 0.420723i
508.8 0.249993 + 0.433001i −0.424801 + 0.735776i 0.875007 − 1.51556i −0.521238 − 0.902810i −0.424789 2.40155 + 1.11021i 1.87496 1.13909 + 1.97296i 0.260612 − 0.451393i
See all 24 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 170.12
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
7.c even 3 1 inner
13.b even 2 1 inner
91.r even 6 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 1183.2.e.j 24
7.c even 3 1 inner 1183.2.e.j 24
7.c even 3 1 8281.2.a.cp 12
7.d odd 6 1 8281.2.a.co 12
13.b even 2 1 inner 1183.2.e.j 24
13.f odd 12 1 91.2.k.b ✓ 12
13.f odd 12 1 91.2.u.b yes 12
39.k even 12 1 819.2.bm.f 12
39.k even 12 1 819.2.do.e 12
91.r even 6 1 inner 1183.2.e.j 24
91.r even 6 1 8281.2.a.cp 12
91.s odd 6 1 8281.2.a.co 12
91.w even 12 1 637.2.k.i 12
91.w even 12 1 637.2.q.i 12
91.x odd 12 1 91.2.u.b yes 12
91.x odd 12 1 637.2.q.g 12
91.ba even 12 1 637.2.q.i 12
91.ba even 12 1 637.2.u.g 12
91.bc even 12 1 637.2.k.i 12
91.bc even 12 1 637.2.u.g 12
91.bd odd 12 1 91.2.k.b ✓ 12
91.bd odd 12 1 637.2.q.g 12
273.bv even 12 1 819.2.do.e 12
273.bw even 12 1 819.2.bm.f 12
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
91.2.k.b ✓ 12 13.f odd 12 1
91.2.k.b ✓ 12 91.bd odd 12 1
91.2.u.b yes 12 13.f odd 12 1
91.2.u.b yes 12 91.x odd 12 1
637.2.k.i 12 91.w even 12 1
637.2.k.i 12 91.bc even 12 1
637.2.q.g 12 91.x odd 12 1
637.2.q.g 12 91.bd odd 12 1
637.2.q.i 12 91.w even 12 1
637.2.q.i 12 91.ba even 12 1
637.2.u.g 12 91.ba even 12 1
637.2.u.g 12 91.bc even 12 1
819.2.bm.f 12 39.k even 12 1
819.2.bm.f 12 273.bw even 12 1
819.2.do.e 12 39.k even 12 1
819.2.do.e 12 273.bv even 12 1
1183.2.e.j 24 1.a even 1 1 trivial
1183.2.e.j 24 7.c even 3 1 inner
1183.2.e.j 24 13.b even 2 1 inner
1183.2.e.j 24 91.r even 6 1 inner
8281.2.a.co 12 7.d odd 6 1
8281.2.a.co 12 91.s odd 6 1
8281.2.a.cp 12 7.c even 3 1
8281.2.a.cp 12 91.r even 6 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(1183, [\chi])\):

\( T_{2}^{24} + 16 T_{2}^{22} + 168 T_{2}^{20} + 1014 T_{2}^{18} + 4420 T_{2}^{16} + 11868 T_{2}^{14} + \cdots + 1 \) Copy content Toggle raw display
\( T_{3}^{12} + 3 T_{3}^{11} + 14 T_{3}^{10} + 17 T_{3}^{9} + 69 T_{3}^{8} + 75 T_{3}^{7} + 233 T_{3}^{6} + \cdots + 49 \) Copy content Toggle raw display