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Properties

Label 483.2.d.d
Level $483$
Weight $2$
Character orbit 483.d
Analytic conductor $3.857$
Analytic rank $0$
Dimension $44$
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] = [483,2,Mod(461,483)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(483, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("483.461");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 483 = 3 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 483.d (of order \(2\), degree \(1\), 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: \(3.85677441763\)
Analytic rank: \(0\)
Dimension: \(44\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 44 q - 76 q^{4} - 8 q^{7} + 20 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 44 q - 76 q^{4} - 8 q^{7} + 20 q^{9} + 4 q^{15} + 92 q^{16} + 4 q^{18} - 22 q^{21} + 12 q^{22} + 16 q^{25} + 16 q^{28} - 32 q^{30} - 112 q^{37} + 4 q^{39} - 12 q^{42} - 68 q^{43} + 4 q^{46} + 44 q^{49} + 32 q^{51} + 16 q^{57} + 28 q^{58} - 44 q^{60} - 10 q^{63} - 16 q^{64} + 108 q^{67} - 60 q^{70} + 112 q^{72} - 48 q^{78} + 40 q^{79} - 4 q^{81} - 26 q^{84} - 108 q^{85} + 8 q^{88} + 24 q^{91} + 4 q^{93} + 4 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
461.1 − 2.69219i −0.983586 + 1.42568i −5.24788 −3.85613 3.83820 + 2.64800i 2.38743 + 1.14025i 8.74391i −1.06512 − 2.80455i 10.3814i
461.2 − 2.69219i 0.983586 − 1.42568i −5.24788 3.85613 −3.83820 − 2.64800i 2.38743 − 1.14025i 8.74391i −1.06512 − 2.80455i − 10.3814i
461.3 − 2.66529i −1.68218 + 0.412627i −5.10378 3.04244 1.09977 + 4.48351i −2.34832 + 1.21877i 8.27248i 2.65948 − 1.38823i − 8.10899i
461.4 − 2.66529i 1.68218 − 0.412627i −5.10378 −3.04244 −1.09977 − 4.48351i −2.34832 − 1.21877i 8.27248i 2.65948 − 1.38823i 8.10899i
461.5 − 2.52935i −0.292165 − 1.70723i −4.39759 −0.707387 −4.31818 + 0.738987i −2.12498 + 1.57622i 6.06435i −2.82928 + 0.997587i 1.78923i
461.6 − 2.52935i 0.292165 + 1.70723i −4.39759 0.707387 4.31818 − 0.738987i −2.12498 − 1.57622i 6.06435i −2.82928 + 0.997587i − 1.78923i
461.7 − 2.33753i −1.20492 − 1.24426i −3.46403 −1.30830 −2.90848 + 2.81653i 1.98664 + 1.74736i 3.42222i −0.0963491 + 2.99845i 3.05818i
461.8 − 2.33753i 1.20492 + 1.24426i −3.46403 1.30830 2.90848 − 2.81653i 1.98664 − 1.74736i 3.42222i −0.0963491 + 2.99845i − 3.05818i
461.9 − 2.16117i −1.71298 + 0.256312i −2.67065 0.517542 0.553932 + 3.70204i 1.45986 − 2.20654i 1.44938i 2.86861 − 0.878114i − 1.11850i
461.10 − 2.16117i 1.71298 − 0.256312i −2.67065 −0.517542 −0.553932 − 3.70204i 1.45986 + 2.20654i 1.44938i 2.86861 − 0.878114i 1.11850i
461.11 − 1.85828i −0.542877 − 1.64477i −1.45321 2.02465 −3.05645 + 1.00882i −1.70901 − 2.01972i − 1.01610i −2.41057 + 1.78582i − 3.76237i
461.12 − 1.85828i 0.542877 + 1.64477i −1.45321 −2.02465 3.05645 − 1.00882i −1.70901 + 2.01972i − 1.01610i −2.41057 + 1.78582i 3.76237i
461.13 − 1.77247i −1.65077 − 0.524365i −1.14166 −3.73040 −0.929423 + 2.92594i −2.02732 − 1.69999i − 1.52139i 2.45008 + 1.73121i 6.61202i
461.14 − 1.77247i 1.65077 + 0.524365i −1.14166 3.73040 0.929423 − 2.92594i −2.02732 + 1.69999i − 1.52139i 2.45008 + 1.73121i − 6.61202i
461.15 − 1.64139i −1.53811 + 0.796381i −0.694157 −0.500649 1.30717 + 2.52463i −0.751445 + 2.53680i − 2.14340i 1.73155 − 2.44984i 0.821759i
461.16 − 1.64139i 1.53811 − 0.796381i −0.694157 0.500649 −1.30717 − 2.52463i −0.751445 − 2.53680i − 2.14340i 1.73155 − 2.44984i − 0.821759i
461.17 − 0.714425i −0.852976 − 1.50746i 1.48960 −0.589252 −1.07697 + 0.609388i 2.38371 − 1.14801i − 2.49306i −1.54486 + 2.57165i 0.420976i
461.18 − 0.714425i 0.852976 + 1.50746i 1.48960 0.589252 1.07697 − 0.609388i 2.38371 + 1.14801i − 2.49306i −1.54486 + 2.57165i − 0.420976i
461.19 − 0.549000i −1.68022 − 0.420554i 1.69860 3.60956 −0.230884 + 0.922440i 1.38729 − 2.25287i − 2.03053i 2.64627 + 1.41325i − 1.98165i
461.20 − 0.549000i 1.68022 + 0.420554i 1.69860 −3.60956 0.230884 − 0.922440i 1.38729 + 2.25287i − 2.03053i 2.64627 + 1.41325i 1.98165i
See all 44 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 461.44
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 483.2.d.d ✓ 44
3.b odd 2 1 inner 483.2.d.d ✓ 44
7.b odd 2 1 inner 483.2.d.d ✓ 44
21.c even 2 1 inner 483.2.d.d ✓ 44
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
483.2.d.d ✓ 44 1.a even 1 1 trivial
483.2.d.d ✓ 44 3.b odd 2 1 inner
483.2.d.d ✓ 44 7.b odd 2 1 inner
483.2.d.d ✓ 44 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 \(S_{2}^{\mathrm{new}}(483, [\chi])\):

\( T_{2}^{22} + 41 T_{2}^{20} + 728 T_{2}^{18} + 7327 T_{2}^{16} + 45911 T_{2}^{14} + 184992 T_{2}^{12} + \cdots + 576 \) Copy content Toggle raw display
\( T_{5}^{22} - 59 T_{5}^{20} + 1395 T_{5}^{18} - 16866 T_{5}^{16} + 110742 T_{5}^{14} - 393352 T_{5}^{12} + \cdots - 1536 \) Copy content Toggle raw display