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Properties

Label 1183.2.c.j
Level $1183$
Weight $2$
Character orbit 1183.c
Analytic conductor $9.446$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1183,2,Mod(337,1183)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1183, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1183.337");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1183 = 7 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1183.c (of order \(2\), degree \(1\), 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: \(9.44630255912\)
Analytic rank: \(0\)
Dimension: \(24\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 24 q + 16 q^{3} - 30 q^{4} + 52 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 24 q + 16 q^{3} - 30 q^{4} + 52 q^{9} + 12 q^{10} - 26 q^{12} + 6 q^{14} + 26 q^{16} - 62 q^{17} - 8 q^{22} - 36 q^{23} - 64 q^{25} + 64 q^{27} + 30 q^{29} + 20 q^{30} - 8 q^{35} - 98 q^{36} - 90 q^{38} - 40 q^{40} + 4 q^{42} + 44 q^{43} + 22 q^{48} - 24 q^{49} - 36 q^{51} + 106 q^{53} - 52 q^{55} - 24 q^{56} + 44 q^{61} - 38 q^{62} - 4 q^{64} - 68 q^{66} + 68 q^{68} - 6 q^{69} - 80 q^{74} - 30 q^{75} - 24 q^{77} + 4 q^{79} + 72 q^{81} + 64 q^{82} + 54 q^{87} + 96 q^{88} + 52 q^{90} + 104 q^{92} - 88 q^{94} - 58 q^{95}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
337.1 − 2.62803i −1.76762 −4.90656 2.94291i 4.64535i 1.00000i 7.63852i 0.124466 7.73406
337.2 − 2.58557i 2.93994 −4.68518 1.26031i − 7.60143i − 1.00000i 6.94272i 5.64327 3.25863
337.3 − 2.47725i 0.982981 −4.13677 − 1.35413i − 2.43509i 1.00000i 5.29330i −2.03375 −3.35452
337.4 − 2.23724i 3.02592 −3.00523 3.28547i − 6.76971i 1.00000i 2.24893i 6.15622 7.35037
337.5 − 2.07140i −3.01646 −2.29068 − 2.69245i 6.24828i − 1.00000i 0.602118i 6.09903 −5.57713
337.6 − 2.06743i 2.11889 −2.27425 − 2.43928i − 4.38065i 1.00000i 0.566992i 1.48970 −5.04303
337.7 − 1.35819i 3.39737 0.155322 − 0.772491i − 4.61428i − 1.00000i − 2.92733i 8.54215 −1.04919
337.8 − 1.10989i 0.955760 0.768150 − 3.55862i − 1.06079i − 1.00000i − 3.07233i −2.08652 −3.94966
337.9 − 0.983820i −1.57171 1.03210 − 0.398447i 1.54628i 1.00000i − 2.98304i −0.529731 −0.392000
337.10 − 0.961590i −1.98737 1.07534 3.39320i 1.91103i − 1.00000i − 2.95722i 0.949635 3.26287
337.11 − 0.842530i 0.161973 1.29014 3.72786i − 0.136467i 1.00000i − 2.77204i −2.97376 3.14083
337.12 − 0.149660i 2.76031 1.97760 4.13443i − 0.413107i − 1.00000i − 0.595288i 4.61930 0.618759
337.13 0.149660i 2.76031 1.97760 − 4.13443i 0.413107i 1.00000i 0.595288i 4.61930 0.618759
337.14 0.842530i 0.161973 1.29014 − 3.72786i 0.136467i − 1.00000i 2.77204i −2.97376 3.14083
337.15 0.961590i −1.98737 1.07534 − 3.39320i − 1.91103i 1.00000i 2.95722i 0.949635 3.26287
337.16 0.983820i −1.57171 1.03210 0.398447i − 1.54628i − 1.00000i 2.98304i −0.529731 −0.392000
337.17 1.10989i 0.955760 0.768150 3.55862i 1.06079i 1.00000i 3.07233i −2.08652 −3.94966
337.18 1.35819i 3.39737 0.155322 0.772491i 4.61428i 1.00000i 2.92733i 8.54215 −1.04919
337.19 2.06743i 2.11889 −2.27425 2.43928i 4.38065i − 1.00000i − 0.566992i 1.48970 −5.04303
337.20 2.07140i −3.01646 −2.29068 2.69245i − 6.24828i 1.00000i − 0.602118i 6.09903 −5.57713
See all 24 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 337.24
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
13.b even 2 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 1183.2.c.j 24
13.b even 2 1 inner 1183.2.c.j 24
13.d odd 4 1 1183.2.a.q ✓ 12
13.d odd 4 1 1183.2.a.r yes 12
91.i even 4 1 8281.2.a.cn 12
91.i even 4 1 8281.2.a.cq 12
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1183.2.a.q ✓ 12 13.d odd 4 1
1183.2.a.r yes 12 13.d odd 4 1
1183.2.c.j 24 1.a even 1 1 trivial
1183.2.c.j 24 13.b even 2 1 inner
8281.2.a.cn 12 91.i even 4 1
8281.2.a.cq 12 91.i even 4 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{24} + 39 T_{2}^{22} + 661 T_{2}^{20} + 6390 T_{2}^{18} + 38898 T_{2}^{16} + 155486 T_{2}^{14} + \cdots + 841 \) acting on \(S_{2}^{\mathrm{new}}(1183, [\chi])\). Copy content Toggle raw display