LMFDB - Newform orbit 176.6.a.j

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [176,6,Mod(1,176)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(176, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 6, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("176.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$N$	$=$	$176 = 2^{4} \cdot 11$
Weight:	$k$	$=$	$6$
Character orbit:	$[\chi]$	$=$	176.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:	$28.2275522871$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	3.3.1784453.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$x^{3} - 368x - 2705$ x^3 - 368*x - 2705
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$2^{2}$
Twist minimal:	no (minimal twist has level 88)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

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

\iota_m(\nu)

a_{2}

a_{3}

a_{4}

a_{5}

a_{6}

a_{7}

a_{8}

a_{9}

a_{10}

1.1

−10.4642
22.1399
−11.6758

−25.3952

−2.46146

−36.9338

401.918

1.2

−3.36210

105.922

−123.284

−231.696

1.3

14.7573

−47.4604

48.2178

−25.2213

Atkin-Lehner signs

$p$	Sign
$2$	$+1$
$11$	$+1$

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	176.6.a.j		3
4.b	odd	2	1		88.6.a.b	✓	3
8.b	even	2	1		704.6.a.s		3
8.d	odd	2	1		704.6.a.r		3
12.b	even	2	1		792.6.a.f		3
44.c	even	2	1		968.6.a.c		3

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
88.6.a.b	✓	3	4.b	odd	2	1
176.6.a.j		3	1.a	even	1	1	trivial
704.6.a.r		3	8.d	odd	2	1
704.6.a.s		3	8.b	even	2	1
792.6.a.f		3	12.b	even	2	1
968.6.a.c		3	44.c	even	2	1

This newform subspace can be constructed as the kernel of the linear operator $T_{3}^{3} + 14T_{3}^{2} - 339T_{3} - 1260$ T3^3 + 14*T3^2 - 339*T3 - 1260 acting on $S_{6}^{\mathrm{new}}(\Gamma_0(176))$ .

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$T^{3}$ T^3
$3$	$T^{3} + 14 T^{2} + \cdots - 1260$ T^3 + 14T^2 - 339T - 1260
$5$	$T^{3} - 56 T^{2} + \cdots - 12374$ T^3 - 56T^2 - 5171T - 12374
$7$	$T^{3} + 112 T^{2} + \cdots - 219552$ T^3 + 112T^2 - 3172T - 219552
$11$	$(T + 121)^{3}$ (T + 121)^3
$13$	$T^{3} - 450 T^{2} + \cdots + 51255776$ T^3 - 450T^2 - 361592T + 51255776
$17$	$T^{3} - 1274 T^{2} + \cdots - 54141048$ T^3 - 1274T^2 + 482476T - 54141048
$19$	$T^{3} + \cdots - 4934825280$ T^3 + 2416T^2 - 1801184T - 4934825280
$23$	$T^{3} + 4042 T^{2} + \cdots + 645194920$ T^3 + 4042T^2 + 3092989T + 645194920
$29$	$T^{3} + \cdots + 34612290944$ T^3 - 2086T^2 - 20370768T + 34612290944
$31$	$T^{3} + \cdots - 2443760880$ T^3 + 10034T^2 + 23377421T - 2443760880
$37$	$T^{3} + 2916 T^{2} + \cdots - 548244166$ T^3 + 2916T^2 - 1967795T - 548244166
$41$	$T^{3} + \cdots + 19244597856$ T^3 + 9450T^2 + 24464968T + 19244597856
$43$	$T^{3} + \cdots + 106822549552$ T^3 + 17296T^2 + 87058804T + 106822549552
$47$	$T^{3} + \cdots - 584697794560$ T^3 + 22312T^2 - 210607936T - 584697794560
$53$	$T^{3} + \cdots - 16689929059320$ T^3 + 50990T^2 + 52943132T - 16689929059320
$59$	$T^{3} + \cdots + 16036070192844$ T^3 - 16654T^2 - 1122414835T + 16036070192844
$61$	$T^{3} + \cdots - 29532796072736$ T^3 + 50674T^2 - 499131248T - 29532796072736
$67$	$T^{3} + \cdots + 84021494680468$ T^3 - 59966T^2 - 1176114491T + 84021494680468
$71$	$T^{3} + \cdots + 75746574829848$ T^3 - 16954T^2 - 4476401267T + 75746574829848
$73$	$T^{3} + \cdots - 348170414631776$ T^3 + 50850T^2 - 6345561992T - 348170414631776
$79$	$T^{3} + \cdots + 118332099622976$ T^3 + 7580T^2 - 5926902300T + 118332099622976
$83$	$T^{3} + \cdots + 82355829648$ T^3 + 1664T^2 - 268034812T + 82355829648
$89$	$T^{3} + \cdots - 28304140091626$ T^3 + 41920T^2 - 821234155T - 28304140091626
$97$	$T^{3} + \cdots - 19\!\cdots\!26$ T^3 + 93356T^2 - 22679687915T - 1962823039303426
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Elliptic curves over $\Q$
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Genus 2 curves over $\Q$
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Abelian varieties over $\F_{q}$

$f(q)$	$=$	$q + (\beta_{2} - 5) q^{3} + ( - \beta_{2} + \beta_1 + 19) q^{5} + (2 \beta_{2} - \beta_1 - 38) q^{7} + ( - 11 \beta_{2} - 3 \beta_1 + 52) q^{9} - 121 q^{11} + ( - 18 \beta_{2} - 7 \beta_1 + 156) q^{13}+ \cdots + (1331 \beta_{2} + 363 \beta_1 - 6292) q^{99}+O(q^{100})$ q + (b2 - 5) * q^3 + (-b2 + b1 + 19) * q^5 + (2b2 - b1 - 38) q^7 + (-11b2 - 3b1 + 52) * q^9 - 121 * q^11 + (-18b2 - 7b1 + 156) * q^13 + (-19b2 - 325) q^15 + (-4b2 + 3b1 + 426) * q^17 + (-76b2 - 15b1 - 780) * q^19 + (-6b2 - 3b1 + 690) * q^21 + (-67b2 + 10b1 - 1325) * q^23 + (65b2 + 75b1 + 1346) * q^25 + (7b2 + 42b1 - 2135) * q^27 + (-86b2 - 56b1 + 724) * q^29 + (61b2 + 38b1 - 3365) * q^31 + (-121b2 + 605) q^33 + (-70b2 - 89b1 - 5062) * q^35 + (105b2 + 7b1 - 1007) * q^37 + (572b2 + 75b1 - 5920) * q^39 + (102b2 + 13b1 - 3184) * q^41 + (170b2 - 14b1 - 5822) * q^43 + (32b2 - 186b1 - 8122) * q^45 + (248b2 - 246b1 - 7520) * q^47 + (36b2 + 100b1 - 10523) * q^49 + (318b2 + 3b1 - 3090) * q^51 + (1060b2 - 254b1 - 17350) * q^53 + (121b2 - 121b1 - 2299) * q^55 + (336b2 + 273b1 - 17220) * q^57 + (-1685b2 + 118b1 + 6113) * q^59 + (614b2 + 448b1 - 17096) * q^61 + (372b2 + 270b1 + 4044) * q^63 + (-144b2 - 361b1 - 20056) * q^65 + (-2065b2 + 346b1 + 20677) * q^67 + (-1363b2 + 171b1 - 11065) * q^69 + (2167b2 + 660b1 + 4929) * q^71 + (-3582b2 - 563b1 - 15756) * q^73 + (-2344b2 - 420b1 + 13820) * q^75 + (-242b2 + 121b1 + 4598) * q^77 + (-1022b2 - 962b1 - 2186) * q^79 + (-1352b2 + 582b1 + 1609) * q^81 + (-398b2 - 184b1 - 422) * q^83 + (-150b2 + 589b1 + 20654) * q^85 + (3704b2 + 426b1 - 29080) * q^87 + (1817b2 - 123b1 - 14579) * q^89 + (968b2 + 534b1 + 11952) * q^91 + (-5403b2 - 297b1 + 34815) * q^93 + (1704b2 - 2075b1 - 55540) * q^95 + (7555b2 - 703b1 - 33637) * q^97 + (1331b2 + 363b1 - 6292) * q^99
$\operatorname{Tr}(f)(q)$	$=$	$3 q - 14 q^{3} + 56 q^{5} - 112 q^{7} + 145 q^{9} - 363 q^{11} + 450 q^{13} - 994 q^{15} + 1274 q^{17} - 2416 q^{19} + 2064 q^{21} - 4042 q^{23} + 4103 q^{25} - 6398 q^{27} + 2086 q^{29} - 10034 q^{31}+ \cdots - 17545 q^{99}+O(q^{100})$ 3 * q - 14 * q^3 + 56 * q^5 - 112 * q^7 + 145 * q^9 - 363 * q^11 + 450 * q^13 - 994 * q^15 + 1274 * q^17 - 2416 * q^19 + 2064 * q^21 - 4042 * q^23 + 4103 * q^25 - 6398 * q^27 + 2086 * q^29 - 10034 * q^31 + 1694 * q^33 - 15256 * q^35 - 2916 * q^37 - 17188 * q^39 - 9450 * q^41 - 17296 * q^43 - 24334 * q^45 - 22312 * q^47 - 31533 * q^49 - 8952 * q^51 - 50990 * q^53 - 6776 * q^55 - 51324 * q^57 + 16654 * q^59 - 50674 * q^61 + 12504 * q^63 - 60312 * q^65 + 59966 * q^67 - 34558 * q^69 + 16954 * q^71 - 50850 * q^73 + 39116 * q^75 + 13552 * q^77 - 7580 * q^79 + 3475 * q^81 - 1664 * q^83 + 61812 * q^85 - 83536 * q^87 - 41920 * q^89 + 36824 * q^91 + 99042 * q^93 - 164916 * q^95 - 93356 * q^97 - 17545 * q^99

$\beta_{1}$	$=$	$4\nu$ 4*v
$\beta_{2}$	$=$	$\nu^{2} - 11\nu - 245$ v^2 - 11*v - 245

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