LMFDB - Newform orbit 182.4.a.a

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,-2,7] 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:	$0$
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} + 7 q^{3} + 4 q^{4} - 14 q^{6} + 7 q^{7} - 8 q^{8} + 22 q^{9} + 39 q^{11} + 28 q^{12} + 13 q^{13} - 14 q^{14} + 16 q^{16} + 24 q^{17} - 44 q^{18} + 38 q^{19} + 49 q^{21} - 78 q^{22} + 39 q^{23}+ \cdots + 858 q^{99}+O(q^{100}) $

q - 2 * q^2 + 7 * q^3 + 4 * q^4 - 14 * q^6 + 7 * q^7 - 8 * q^8 + 22 * q^9 + 39 * q^11 + 28 * q^12 + 13 * q^13 - 14 * q^14 + 16 * q^16 + 24 * q^17 - 44 * q^18 + 38 * q^19 + 49 * q^21 - 78 * q^22 + 39 * q^23 - 56 * q^24 - 125 * q^25 - 26 * q^26 - 35 * q^27 + 28 * q^28 - 96 * q^29 + 227 * q^31 - 32 * q^32 + 273 * q^33 - 48 * q^34 + 88 * q^36 + 425 * q^37 - 76 * q^38 + 91 * q^39 - 105 * q^41 - 98 * q^42 + 344 * q^43 + 156 * q^44 - 78 * q^46 + 99 * q^47 + 112 * q^48 + 49 * q^49 + 250 * q^50 + 168 * q^51 + 52 * q^52 - 540 * q^53 + 70 * q^54 - 56 * q^56 + 266 * q^57 + 192 * q^58 + 114 * q^59 - 565 * q^61 - 454 * q^62 + 154 * q^63 + 64 * q^64 - 546 * q^66 - 385 * q^67 + 96 * q^68 + 273 * q^69 - 156 * q^71 - 176 * q^72 - 673 * q^73 - 850 * q^74 - 875 * q^75 + 152 * q^76 + 273 * q^77 - 182 * q^78 + 749 * q^79 - 839 * q^81 + 210 * q^82 - 1044 * q^83 + 196 * q^84 - 688 * q^86 - 672 * q^87 - 312 * q^88 - 690 * q^89 + 91 * q^91 + 156 * q^92 + 1589 * q^93 - 198 * q^94 - 224 * q^96 + 317 * q^97 - 98 * q^98 + 858 * 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

7.00000

4.00000

−14.0000

7.00000

−8.00000

22.0000

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.a	✓	1
3.b	odd	2	1		1638.4.a.j		1
4.b	odd	2	1		1456.4.a.b		1
7.b	odd	2	1		1274.4.a.a		1
13.b	even	2	1		2366.4.a.g		1

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

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator $ T_{3} - 7 $ T3 - 7 acting on $S_{4}^{\mathrm{new}}(\Gamma_0(182))$.

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$ T + 2 $ T + 2
$3$	$ T - 7 $ T - 7
$5$	$ T $ T
$7$	$ T - 7 $ T - 7
$11$	$ T - 39 $ T - 39
$13$	$ T - 13 $ T - 13
$17$	$ T - 24 $ T - 24
$19$	$ T - 38 $ T - 38
$23$	$ T - 39 $ T - 39
$29$	$ T + 96 $ T + 96
$31$	$ T - 227 $ T - 227
$37$	$ T - 425 $ T - 425
$41$	$ T + 105 $ T + 105
$43$	$ T - 344 $ T - 344
$47$	$ T - 99 $ T - 99
$53$	$ T + 540 $ T + 540
$59$	$ T - 114 $ T - 114
$61$	$ T + 565 $ T + 565
$67$	$ T + 385 $ T + 385
$71$	$ T + 156 $ T + 156
$73$	$ T + 673 $ T + 673
$79$	$ T - 749 $ T - 749
$83$	$ T + 1044 $ T + 1044
$89$	$ T + 690 $ T + 690
$97$	$ T - 317 $ T - 317
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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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