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Properties

Label 833.2.g.i
Level $833$
Weight $2$
Character orbit 833.g
Analytic conductor $6.652$
Analytic rank $0$
Dimension $32$
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] = [833,2,Mod(344,833)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(833, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([0, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("833.344");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 833 = 7^{2} \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 833.g (of order \(4\), 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: \(6.65153848837\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(16\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 32 q - 24 q^{4}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 32 q - 24 q^{4} - 8 q^{11} + 40 q^{16} - 24 q^{18} - 16 q^{22} - 8 q^{23} - 16 q^{29} - 8 q^{30} + 16 q^{37} - 24 q^{39} + 72 q^{44} - 32 q^{46} + 96 q^{50} - 8 q^{51} - 96 q^{57} - 32 q^{58} - 40 q^{64} + 48 q^{65} - 48 q^{71} + 32 q^{72} - 24 q^{74} + 64 q^{78} + 24 q^{79} - 48 q^{81} - 48 q^{85} - 104 q^{86} + 48 q^{88} + 8 q^{92} + 24 q^{95} + 80 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
344.1 − 2.67213i −0.758823 + 0.758823i −5.14029 −0.658915 + 0.658915i 2.02768 + 2.02768i 0 8.39128i 1.84838i 1.76071 + 1.76071i
344.2 − 2.67213i 0.758823 − 0.758823i −5.14029 0.658915 − 0.658915i −2.02768 − 2.02768i 0 8.39128i 1.84838i −1.76071 − 1.76071i
344.3 − 2.02246i −2.03527 + 2.03527i −2.09033 −0.245668 + 0.245668i 4.11624 + 4.11624i 0 0.182694i − 5.28461i 0.496853 + 0.496853i
344.4 − 2.02246i 2.03527 − 2.03527i −2.09033 0.245668 − 0.245668i −4.11624 − 4.11624i 0 0.182694i − 5.28461i −0.496853 − 0.496853i
344.5 − 1.49985i −0.483085 + 0.483085i −0.249543 −1.03501 + 1.03501i 0.724554 + 0.724554i 0 − 2.62542i 2.53326i 1.55236 + 1.55236i
344.6 − 1.49985i 0.483085 − 0.483085i −0.249543 1.03501 − 1.03501i −0.724554 − 0.724554i 0 − 2.62542i 2.53326i −1.55236 − 1.55236i
344.7 − 0.493689i −0.223308 + 0.223308i 1.75627 −2.23906 + 2.23906i 0.110245 + 0.110245i 0 − 1.85443i 2.90027i 1.10540 + 1.10540i
344.8 − 0.493689i 0.223308 − 0.223308i 1.75627 2.23906 − 2.23906i −0.110245 − 0.110245i 0 − 1.85443i 2.90027i −1.10540 − 1.10540i
344.9 0.0886998i −1.86051 + 1.86051i 1.99213 −0.268744 + 0.268744i −0.165027 − 0.165027i 0 0.354101i − 3.92298i −0.0238375 − 0.0238375i
344.10 0.0886998i 1.86051 − 1.86051i 1.99213 0.268744 − 0.268744i 0.165027 + 0.165027i 0 0.354101i − 3.92298i 0.0238375 + 0.0238375i
344.11 0.927558i −1.74406 + 1.74406i 1.13964 −0.286687 + 0.286687i −1.61772 − 1.61772i 0 2.91219i − 3.08349i −0.265919 − 0.265919i
344.12 0.927558i 1.74406 − 1.74406i 1.13964 0.286687 − 0.286687i 1.61772 + 1.61772i 0 2.91219i − 3.08349i 0.265919 + 0.265919i
344.13 1.25863i −0.169216 + 0.169216i 0.415851 −2.95480 + 2.95480i −0.212981 − 0.212981i 0 3.04066i 2.94273i −3.71899 − 3.71899i
344.14 1.25863i 0.169216 − 0.169216i 0.415851 2.95480 − 2.95480i 0.212981 + 0.212981i 0 3.04066i 2.94273i 3.71899 + 3.71899i
344.15 2.41324i −0.683213 + 0.683213i −3.82372 −0.731836 + 0.731836i −1.64876 − 1.64876i 0 − 4.40108i 2.06644i −1.76610 − 1.76610i
344.16 2.41324i 0.683213 − 0.683213i −3.82372 0.731836 − 0.731836i 1.64876 + 1.64876i 0 − 4.40108i 2.06644i 1.76610 + 1.76610i
540.1 − 2.41324i −0.683213 − 0.683213i −3.82372 −0.731836 − 0.731836i −1.64876 + 1.64876i 0 4.40108i − 2.06644i −1.76610 + 1.76610i
540.2 − 2.41324i 0.683213 + 0.683213i −3.82372 0.731836 + 0.731836i 1.64876 − 1.64876i 0 4.40108i − 2.06644i 1.76610 − 1.76610i
540.3 − 1.25863i −0.169216 − 0.169216i 0.415851 −2.95480 − 2.95480i −0.212981 + 0.212981i 0 − 3.04066i − 2.94273i −3.71899 + 3.71899i
540.4 − 1.25863i 0.169216 + 0.169216i 0.415851 2.95480 + 2.95480i 0.212981 − 0.212981i 0 − 3.04066i − 2.94273i 3.71899 − 3.71899i
See all 32 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 344.16
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
7.b odd 2 1 inner
17.c even 4 1 inner
119.f odd 4 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 833.2.g.i ✓ 32
7.b odd 2 1 inner 833.2.g.i ✓ 32
7.c even 3 2 833.2.o.h 64
7.d odd 6 2 833.2.o.h 64
17.c even 4 1 inner 833.2.g.i ✓ 32
119.f odd 4 1 inner 833.2.g.i ✓ 32
119.m odd 12 2 833.2.o.h 64
119.n even 12 2 833.2.o.h 64
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
833.2.g.i ✓ 32 1.a even 1 1 trivial
833.2.g.i ✓ 32 7.b odd 2 1 inner
833.2.g.i ✓ 32 17.c even 4 1 inner
833.2.g.i ✓ 32 119.f odd 4 1 inner
833.2.o.h 64 7.c even 3 2
833.2.o.h 64 7.d odd 6 2
833.2.o.h 64 119.m odd 12 2
833.2.o.h 64 119.n even 12 2

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(833, [\chi])\):

\( T_{2}^{16} + 22T_{2}^{14} + 187T_{2}^{12} + 780T_{2}^{10} + 1685T_{2}^{8} + 1836T_{2}^{6} + 891T_{2}^{4} + 134T_{2}^{2} + 1 \) Copy content Toggle raw display
\( T_{3}^{32} + 156 T_{3}^{28} + 7978 T_{3}^{24} + 140464 T_{3}^{20} + 308403 T_{3}^{16} + 204976 T_{3}^{12} + \cdots + 1 \) Copy content Toggle raw display