↑

Properties

Label 483.3.b.a
Level $483$
Weight $3$
Character orbit 483.b
Analytic conductor $13.161$
Analytic rank $0$
Dimension $88$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [483,3,Mod(323,483)]
 
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, 0, 0]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("483.323");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 483 = 3 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 483.b (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: \(13.1607967686\)
Analytic rank: \(0\)
Dimension: \(88\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 88 q + 8 q^{3} - 176 q^{4} - 22 q^{6} + 20 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 88 q + 8 q^{3} - 176 q^{4} - 22 q^{6} + 20 q^{9} - 16 q^{10} - 18 q^{12} + 64 q^{13} + 20 q^{15} + 272 q^{16} - 38 q^{18} - 48 q^{19} - 28 q^{21} + 208 q^{22} + 228 q^{24} - 568 q^{25} - 88 q^{27} - 8 q^{30} + 8 q^{31} - 160 q^{33} - 32 q^{34} - 138 q^{36} - 136 q^{37} + 76 q^{39} - 48 q^{40} - 140 q^{42} + 424 q^{43} + 172 q^{45} + 334 q^{48} + 616 q^{49} + 288 q^{51} - 140 q^{52} - 240 q^{55} - 252 q^{57} - 380 q^{58} - 364 q^{60} + 312 q^{61} - 252 q^{64} + 44 q^{66} - 224 q^{67} + 168 q^{70} - 592 q^{72} + 216 q^{73} - 284 q^{75} + 328 q^{76} + 470 q^{78} - 8 q^{79} + 380 q^{81} - 548 q^{82} + 224 q^{84} - 712 q^{85} + 56 q^{87} - 896 q^{88} + 1136 q^{90} + 168 q^{91} - 236 q^{93} - 252 q^{94} - 546 q^{96} + 480 q^{97} - 248 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
323.1 − 3.91522i 2.99444 + 0.182631i −11.3290 3.69463i 0.715040 − 11.7239i 2.64575 28.6946i 8.93329 + 1.09375i 14.4653
323.2 − 3.81832i −0.852935 − 2.87620i −10.5796 − 8.03455i −10.9822 + 3.25678i 2.64575 25.1228i −7.54500 + 4.90642i −30.6785
323.3 − 3.81350i 1.34927 + 2.67946i −10.5428 − 8.89089i 10.2181 − 5.14542i −2.64575 24.9509i −5.35897 + 7.23059i −33.9054
323.4 − 3.80760i 0.823489 − 2.88476i −10.4978 3.06240i −10.9840 − 3.13552i −2.64575 24.7411i −7.64373 − 4.75114i 11.6604
323.5 − 3.55131i −2.80484 − 1.06437i −8.61182 3.99734i −3.77990 + 9.96086i −2.64575 16.3780i 6.73424 + 5.97076i 14.1958
323.6 − 3.53262i −2.99242 + 0.213088i −8.47941 − 4.02890i 0.752759 + 10.5711i 2.64575 15.8240i 8.90919 − 1.27530i −14.2326
323.7 − 3.45153i −2.03109 − 2.20786i −7.91305 7.97564i −7.62051 + 7.01037i 2.64575 13.5060i −0.749336 + 8.96875i 27.5281
323.8 − 3.39347i 2.67682 − 1.35449i −7.51566 − 5.14487i −4.59641 − 9.08372i −2.64575 11.9303i 5.33074 − 7.25143i −17.4590
323.9 − 3.36083i −2.11593 + 2.12669i −7.29519 8.80778i 7.14745 + 7.11130i 2.64575 11.0746i −0.0456396 − 8.99988i 29.6015
323.10 − 3.27803i 2.67440 + 1.35925i −6.74548 7.86031i 4.45568 − 8.76677i −2.64575 8.99976i 5.30485 + 7.27039i 25.7663
323.11 − 3.21551i 2.51763 − 1.63142i −6.33948 − 5.48903i −5.24584 − 8.09546i 2.64575 7.52260i 3.67694 − 8.21463i −17.6500
323.12 − 3.14953i 2.25271 + 1.98124i −5.91951 0.146549i 6.23996 − 7.09496i −2.64575 6.04554i 1.14940 + 8.92630i 0.461560
323.13 − 3.08330i 1.93849 − 2.28960i −5.50675 5.82279i −7.05953 − 5.97694i 2.64575 4.64575i −1.48454 − 8.87672i 17.9534
323.14 − 3.02799i −1.28052 + 2.71298i −5.16871 0.457760i 8.21488 + 3.87740i −2.64575 3.53885i −5.72053 − 6.94806i 1.38609
323.15 − 2.85750i −1.75729 − 2.43145i −4.16533 − 5.17933i −6.94788 + 5.02145i −2.64575 0.472440i −2.82389 + 8.54551i −14.8000
323.16 − 2.84584i −0.677666 + 2.92246i −4.09879 − 7.26917i 8.31684 + 1.92853i 2.64575 0.281139i −8.08154 − 3.96090i −20.6869
323.17 − 2.71288i −2.93253 − 0.632651i −3.35974 − 2.46348i −1.71631 + 7.95562i 2.64575 − 1.73695i 8.19950 + 3.71054i −6.68313
323.18 − 2.61938i −2.82217 + 1.01753i −2.86116 − 9.67682i 2.66530 + 7.39233i −2.64575 − 2.98305i 6.92926 − 5.74329i −25.3473
323.19 − 2.61925i 2.60097 − 1.49497i −2.86049 8.70818i −3.91570 − 6.81261i −2.64575 − 2.98467i 4.53014 − 7.77675i 22.8089
323.20 − 2.47284i −2.89906 + 0.771673i −2.11494 6.48523i 1.90823 + 7.16890i −2.64575 − 4.66144i 7.80904 − 4.47425i 16.0370
See all 88 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 323.88
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 483.3.b.a ✓ 88
3.b odd 2 1 inner 483.3.b.a ✓ 88
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
483.3.b.a ✓ 88 1.a even 1 1 trivial
483.3.b.a ✓ 88 3.b odd 2 1 inner

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(483, [\chi])\).