LMFDB - Newform orbit 704.4.a.j

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [704,4,Mod(1,704)] 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("704.1"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(704, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 704 = 2^{6} \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	704.a (trivial)

Newform invariants

comment:select newform

sage:traces = [1,0,5,0,7] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	yes
Analytic conductor:	$41.5373446440$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 44)
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 + 5 q^{3} + 7 q^{5} - 26 q^{7} - 2 q^{9} + 11 q^{11} - 52 q^{13} + 35 q^{15} + 46 q^{17} + 96 q^{19} - 130 q^{21} + 27 q^{23} - 76 q^{25} - 145 q^{27} - 16 q^{29} - 293 q^{31} + 55 q^{33} - 182 q^{35}+ \cdots - 22 q^{99}+O(q^{100}) $

q + 5 * q^3 + 7 * q^5 - 26 * q^7 - 2 * q^9 + 11 * q^11 - 52 * q^13 + 35 * q^15 + 46 * q^17 + 96 * q^19 - 130 * q^21 + 27 * q^23 - 76 * q^25 - 145 * q^27 - 16 * q^29 - 293 * q^31 + 55 * q^33 - 182 * q^35 + 29 * q^37 - 260 * q^39 - 472 * q^41 + 110 * q^43 - 14 * q^45 - 224 * q^47 + 333 * q^49 + 230 * q^51 - 754 * q^53 + 77 * q^55 + 480 * q^57 - 825 * q^59 + 548 * q^61 + 52 * q^63 - 364 * q^65 + 123 * q^67 + 135 * q^69 + 1001 * q^71 - 1020 * q^73 - 380 * q^75 - 286 * q^77 + 526 * q^79 - 671 * q^81 + 158 * q^83 + 322 * q^85 - 80 * q^87 - 1217 * q^89 + 1352 * q^91 - 1465 * q^93 + 672 * q^95 - 263 * q^97 - 22 * 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

5.00000

7.00000

−26.0000

−2.00000

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	704.4.a.j		1
4.b	odd	2	1		704.4.a.c		1
8.b	even	2	1		44.4.a.a	✓	1
8.d	odd	2	1		176.4.a.e		1
24.f	even	2	1		1584.4.a.p		1
24.h	odd	2	1		396.4.a.e		1
40.f	even	2	1		1100.4.a.d		1
40.i	odd	4	2		1100.4.b.c		2
56.h	odd	2	1		2156.4.a.b		1
88.b	odd	2	1		484.4.a.a		1
88.g	even	2	1		1936.4.a.m		1

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
44.4.a.a	✓	1	8.b	even	2	1
176.4.a.e		1	8.d	odd	2	1
396.4.a.e		1	24.h	odd	2	1
484.4.a.a		1	88.b	odd	2	1
704.4.a.c		1	4.b	odd	2	1
704.4.a.j		1	1.a	even	1	1	trivial
1100.4.a.d		1	40.f	even	2	1
1100.4.b.c		2	40.i	odd	4	2
1584.4.a.p		1	24.f	even	2	1
1936.4.a.m		1	88.g	even	2	1
2156.4.a.b		1	56.h	odd	2	1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $S_{4}^{\mathrm{new}}(\Gamma_0(704))$:

$ T_{3} - 5 $

T3 - 5

$ T_{5} - 7 $

T5 - 7

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$ T $ T
$3$	$ T - 5 $ T - 5
$5$	$ T - 7 $ T - 7
$7$	$ T + 26 $ T + 26
$11$	$ T - 11 $ T - 11
$13$	$ T + 52 $ T + 52
$17$	$ T - 46 $ T - 46
$19$	$ T - 96 $ T - 96
$23$	$ T - 27 $ T - 27
$29$	$ T + 16 $ T + 16
$31$	$ T + 293 $ T + 293
$37$	$ T - 29 $ T - 29
$41$	$ T + 472 $ T + 472
$43$	$ T - 110 $ T - 110
$47$	$ T + 224 $ T + 224
$53$	$ T + 754 $ T + 754
$59$	$ T + 825 $ T + 825
$61$	$ T - 548 $ T - 548
$67$	$ T - 123 $ T - 123
$71$	$ T - 1001 $ T - 1001
$73$	$ T + 1020 $ T + 1020
$79$	$ T - 526 $ T - 526
$83$	$ T - 158 $ T - 158
$89$	$ T + 1217 $ T + 1217
$97$	$ T + 263 $ T + 263
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Elliptic curves over $\Q$
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Level:	\( N \)	\(=\)	\( 704 = 2^{6} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	704.a (trivial)

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