LMFDB - Newform orbit 182.4.a.c

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [182,4,Mod(1,182)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("182.1"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(182, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 182 = 2 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	182.a (trivial)

Newform invariants

comment:select newform

sage:traces = [1,2,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$10.7383476210$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

$q$-expansion

comment:q-expansion

sage:f.q_expansion() # note that sage often uses an isomorphic number field

gp:mfcoefs(f, 20)

$f(q)$

$=$

$ q + 2 q^{2} - 2 q^{3} + 4 q^{4} - 5 q^{5} - 4 q^{6} - 7 q^{7} + 8 q^{8} - 23 q^{9} - 10 q^{10} - 36 q^{11} - 8 q^{12} - 13 q^{13} - 14 q^{14} + 10 q^{15} + 16 q^{16} + 26 q^{17} - 46 q^{18} - 47 q^{19}+ \cdots + 828 q^{99}+O(q^{100}) $

q + 2 * q^2 - 2 * q^3 + 4 * q^4 - 5 * q^5 - 4 * q^6 - 7 * q^7 + 8 * q^8 - 23 * q^9 - 10 * q^10 - 36 * q^11 - 8 * q^12 - 13 * q^13 - 14 * q^14 + 10 * q^15 + 16 * q^16 + 26 * q^17 - 46 * q^18 - 47 * q^19 - 20 * q^20 + 14 * q^21 - 72 * q^22 - 99 * q^23 - 16 * q^24 - 100 * q^25 - 26 * q^26 + 100 * q^27 - 28 * q^28 - 61 * q^29 + 20 * q^30 - 23 * q^31 + 32 * q^32 + 72 * q^33 + 52 * q^34 + 35 * q^35 - 92 * q^36 - 50 * q^37 - 94 * q^38 + 26 * q^39 - 40 * q^40 + 70 * q^41 + 28 * q^42 - 19 * q^43 - 144 * q^44 + 115 * q^45 - 198 * q^46 + 191 * q^47 - 32 * q^48 + 49 * q^49 - 200 * q^50 - 52 * q^51 - 52 * q^52 + 195 * q^53 + 200 * q^54 + 180 * q^55 - 56 * q^56 + 94 * q^57 - 122 * q^58 + 264 * q^59 + 40 * q^60 + 310 * q^61 - 46 * q^62 + 161 * q^63 + 64 * q^64 + 65 * q^65 + 144 * q^66 - 190 * q^67 + 104 * q^68 + 198 * q^69 + 70 * q^70 - 166 * q^71 - 184 * q^72 + 873 * q^73 - 100 * q^74 + 200 * q^75 - 188 * q^76 + 252 * q^77 + 52 * q^78 - 1191 * q^79 - 80 * q^80 + 421 * q^81 + 140 * q^82 + 259 * q^83 + 56 * q^84 - 130 * q^85 - 38 * q^86 + 122 * q^87 - 288 * q^88 - 635 * q^89 + 230 * q^90 + 91 * q^91 - 396 * q^92 + 46 * q^93 + 382 * q^94 + 235 * q^95 - 64 * q^96 + 133 * q^97 + 98 * q^98 + 828 * q^99

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

2.00000

−2.00000

4.00000

−5.00000

−4.00000

−7.00000

8.00000

−23.0000

−10.0000

Atkin-Lehner signs

$ p $	Sign
$2$	$ -1 $
$7$	$ +1 $
$13$	$ +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	182.4.a.c	✓	1
3.b	odd	2	1		1638.4.a.e		1
4.b	odd	2	1		1456.4.a.f		1
7.b	odd	2	1		1274.4.a.g		1
13.b	even	2	1		2366.4.a.b		1

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
182.4.a.c	✓	1	1.a	even	1	1	trivial
1274.4.a.g		1	7.b	odd	2	1
1456.4.a.f		1	4.b	odd	2	1
1638.4.a.e		1	3.b	odd	2	1
2366.4.a.b		1	13.b	even	2	1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator $ T_{3} + 2 $ T3 + 2 acting on $S_{4}^{\mathrm{new}}(\Gamma_0(182))$.

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$ T - 2 $ T - 2
$3$	$ T + 2 $ T + 2
$5$	$ T + 5 $ T + 5
$7$	$ T + 7 $ T + 7
$11$	$ T + 36 $ T + 36
$13$	$ T + 13 $ T + 13
$17$	$ T - 26 $ T - 26
$19$	$ T + 47 $ T + 47
$23$	$ T + 99 $ T + 99
$29$	$ T + 61 $ T + 61
$31$	$ T + 23 $ T + 23
$37$	$ T + 50 $ T + 50
$41$	$ T - 70 $ T - 70
$43$	$ T + 19 $ T + 19
$47$	$ T - 191 $ T - 191
$53$	$ T - 195 $ T - 195
$59$	$ T - 264 $ T - 264
$61$	$ T - 310 $ T - 310
$67$	$ T + 190 $ T + 190
$71$	$ T + 166 $ T + 166
$73$	$ T - 873 $ T - 873
$79$	$ T + 1191 $ T + 1191
$83$	$ T - 259 $ T - 259
$89$	$ T + 635 $ T + 635
$97$	$ T - 133 $ T - 133
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Level:	\( N \)	\(=\)	\( 182 = 2 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	182.a (trivial)

\(n\):		e.g. 2-40 or 990-1000
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