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Properties

Label 123.3.c.a
Level $123$
Weight $3$
Character orbit 123.c
Analytic conductor $3.352$
Analytic rank $0$
Dimension $26$
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] = [123,3,Mod(83,123)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(123, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("123.83");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 123 = 3 \cdot 41 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 123.c (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: \(3.35150725163\)
Analytic rank: \(0\)
Dimension: \(26\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 26 q + 2 q^{3} - 52 q^{4} - 4 q^{7} - 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 26 q + 2 q^{3} - 52 q^{4} - 4 q^{7} - 6 q^{9} + 4 q^{10} - 6 q^{12} + 32 q^{13} + 10 q^{15} + 52 q^{16} - 20 q^{18} - 48 q^{19} + 60 q^{21} + 112 q^{22} + 16 q^{24} - 98 q^{25} - 88 q^{27} - 112 q^{28} - 22 q^{30} - 2 q^{31} - 38 q^{33} + 64 q^{34} + 160 q^{36} - 94 q^{37} + 76 q^{39} + 44 q^{40} - 72 q^{42} + 134 q^{43} - 68 q^{45} - 24 q^{46} - 198 q^{48} + 134 q^{49} + 74 q^{51} - 128 q^{52} - 22 q^{54} + 44 q^{55} + 16 q^{57} - 280 q^{58} + 378 q^{60} + 110 q^{61} - 202 q^{63} + 444 q^{64} + 20 q^{66} - 248 q^{67} + 200 q^{69} - 184 q^{70} - 100 q^{72} + 2 q^{73} - 106 q^{75} + 200 q^{76} - 56 q^{78} - 120 q^{79} + 162 q^{81} - 356 q^{84} - 44 q^{85} - 250 q^{87} - 184 q^{88} + 48 q^{90} - 16 q^{91} + 236 q^{93} - 372 q^{94} - 336 q^{96} + 200 q^{97} + 566 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
83.1 − 3.61374i −2.83399 − 0.984114i −9.05909 1.47034i −3.55633 + 10.2413i −2.52550 18.2822i 7.06304 + 5.57795i 5.31343
83.2 − 3.58087i 1.09842 − 2.79168i −8.82266 − 5.21390i −9.99666 − 3.93329i 12.1039 17.2693i −6.58696 − 6.13286i −18.6703
83.3 − 3.41812i 0.565625 + 2.94620i −7.68353 8.54886i 10.0704 − 1.93337i 1.46564 12.5907i −8.36014 + 3.33288i 29.2210
83.4 − 3.10997i 2.35731 + 1.85555i −5.67192 − 5.48886i 5.77071 − 7.33118i 1.29845 5.19961i 2.11386 + 8.74823i −17.0702
83.5 − 2.95938i −1.59123 + 2.54323i −4.75795 − 5.61647i 7.52638 + 4.70905i −7.28613 2.24305i −3.93599 − 8.09370i −16.6213
83.6 − 2.80939i 0.820098 − 2.88573i −3.89265 3.24075i −8.10713 − 2.30397i −11.6544 − 0.301588i −7.65488 − 4.73316i 9.10451
83.7 − 2.23701i 2.85743 − 0.913823i −1.00419 6.44774i −2.04423 − 6.39210i 7.64016 − 6.70163i 7.32985 − 5.22238i 14.4236
83.8 − 1.94464i −2.68856 + 1.33103i 0.218366 1.89490i 2.58837 + 5.22829i 8.73579 − 8.20321i 5.45674 − 7.15709i 3.68491
83.9 − 1.58077i 2.97866 − 0.357210i 1.50118 − 3.67894i −0.564664 − 4.70856i −7.61635 − 8.69608i 8.74480 − 2.12801i −5.81554
83.10 − 1.42772i −1.60360 − 2.53544i 1.96160 − 4.20695i −3.61991 + 2.28950i 1.57760 − 8.51153i −3.85695 + 8.13166i −6.00637
83.11 − 0.597648i 1.81938 + 2.38534i 3.64282 3.66632i 1.42560 − 1.08735i −1.27478 − 4.56771i −2.37973 + 8.67968i 2.19117
83.12 − 0.582311i −2.91788 − 0.697111i 3.66091 7.61434i −0.405935 + 1.69912i −10.9384 − 4.46104i 8.02807 + 4.06817i 4.43392
83.13 − 0.304779i 0.138340 + 2.99681i 3.90711 − 7.18182i 0.913363 − 0.0421630i 6.47400 − 2.40992i −8.96172 + 0.829155i −2.18886
83.14 0.304779i 0.138340 − 2.99681i 3.90711 7.18182i 0.913363 + 0.0421630i 6.47400 2.40992i −8.96172 − 0.829155i −2.18886
83.15 0.582311i −2.91788 + 0.697111i 3.66091 − 7.61434i −0.405935 − 1.69912i −10.9384 4.46104i 8.02807 − 4.06817i 4.43392
83.16 0.597648i 1.81938 − 2.38534i 3.64282 − 3.66632i 1.42560 + 1.08735i −1.27478 4.56771i −2.37973 − 8.67968i 2.19117
83.17 1.42772i −1.60360 + 2.53544i 1.96160 4.20695i −3.61991 − 2.28950i 1.57760 8.51153i −3.85695 − 8.13166i −6.00637
83.18 1.58077i 2.97866 + 0.357210i 1.50118 3.67894i −0.564664 + 4.70856i −7.61635 8.69608i 8.74480 + 2.12801i −5.81554
83.19 1.94464i −2.68856 − 1.33103i 0.218366 − 1.89490i 2.58837 − 5.22829i 8.73579 8.20321i 5.45674 + 7.15709i 3.68491
83.20 2.23701i 2.85743 + 0.913823i −1.00419 − 6.44774i −2.04423 + 6.39210i 7.64016 6.70163i 7.32985 + 5.22238i 14.4236
See all 26 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 83.26
Significant digits:
Format:

Inner twists

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

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 123.3.c.a ✓ 26
3.b odd 2 1 inner 123.3.c.a ✓ 26
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
123.3.c.a ✓ 26 1.a even 1 1 trivial
123.3.c.a ✓ 26 3.b odd 2 1 inner

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(123, [\chi])\).