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Properties

Label 2031.4.a.d
Level $2031$
Weight $4$
Character orbit 2031.a
Self dual yes
Analytic conductor $119.833$
Analytic rank $0$
Dimension $94$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [2031,4,Mod(1,2031)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2031, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("2031.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2031 = 3 \cdot 677 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2031.a (trivial)

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: yes
Analytic conductor: \(119.832879222\)
Analytic rank: \(0\)
Dimension: \(94\)
Twist minimal: yes
Fricke sign: \(+1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

The algebraic \(q\)-expansion of this newform has not been computed, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 94 q + 19 q^{2} + 282 q^{3} + 409 q^{4} + 84 q^{5} + 57 q^{6} + 39 q^{7} + 228 q^{8} + 846 q^{9} + 145 q^{10} + 357 q^{11} + 1227 q^{12} + 271 q^{13} + 366 q^{14} + 252 q^{15} + 1865 q^{16} + 690 q^{17}+ \cdots + 3213 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1.1 −5.47214 3.00000 21.9443 21.3352 −16.4164 −0.0652059 −76.3050 9.00000 −116.749
1.2 −5.45637 3.00000 21.7719 −6.07049 −16.3691 10.9617 −75.1446 9.00000 33.1228
1.3 −5.27921 3.00000 19.8701 11.0881 −15.8376 −17.2827 −62.6647 9.00000 −58.5362
1.4 −5.16569 3.00000 18.6843 17.7056 −15.4971 11.4525 −55.1919 9.00000 −91.4614
1.5 −5.10408 3.00000 18.0516 −3.79340 −15.3122 −8.15158 −51.3044 9.00000 19.3618
1.6 −5.10333 3.00000 18.0440 −16.6972 −15.3100 −10.1248 −51.2578 9.00000 85.2116
1.7 −5.02302 3.00000 17.2308 −13.6796 −15.0691 −35.1340 −46.3664 9.00000 68.7130
1.8 −4.91474 3.00000 16.1547 −10.0566 −14.7442 −7.95652 −40.0782 9.00000 49.4258
1.9 −4.76129 3.00000 14.6699 −4.67891 −14.2839 −10.6034 −31.7573 9.00000 22.2776
1.10 −4.72829 3.00000 14.3567 4.12529 −14.1849 15.0339 −30.0563 9.00000 −19.5056
1.11 −4.55506 3.00000 12.7486 8.74592 −13.6652 18.2953 −21.6301 9.00000 −39.8382
1.12 −4.50669 3.00000 12.3103 −0.307147 −13.5201 −10.6842 −19.4251 9.00000 1.38422
1.13 −4.45057 3.00000 11.8076 −1.33582 −13.3517 34.8098 −16.9459 9.00000 5.94516
1.14 −4.31352 3.00000 10.6064 −16.4491 −12.9406 −15.0796 −11.2430 9.00000 70.9536
1.15 −4.22592 3.00000 9.85844 −6.75739 −12.6778 30.5747 −7.85362 9.00000 28.5562
1.16 −4.09444 3.00000 8.76443 −8.00283 −12.2833 3.11074 −3.12990 9.00000 32.7671
1.17 −3.94499 3.00000 7.56296 15.3322 −11.8350 −27.0568 1.72411 9.00000 −60.4854
1.18 −3.73151 3.00000 5.92420 21.2295 −11.1945 17.7615 7.74587 9.00000 −79.2182
1.19 −3.42427 3.00000 3.72561 7.87027 −10.2728 −22.7257 14.6366 9.00000 −26.9499
1.20 −3.26684 3.00000 2.67224 21.8684 −9.80052 −22.0772 17.4049 9.00000 −71.4405
See all 94 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.94
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(3\) \( -1 \)
\(677\) \( -1 \)

Inner twists

This newform does not admit any (nontrivial) inner twists.

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 2031.4.a.d ✓ 94
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
2031.4.a.d ✓ 94 1.a even 1 1 trivial