LMFDB - Newform orbit 1445.4.a.h

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1445,4,Mod(1,1445)] 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("1445.1"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1445, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 1445 = 5 \cdot 17^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1445.a (trivial)

Newform invariants

comment:select newform

sage:traces = [1,3,7,1,-5] 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:	$85.2577599583$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 85)
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 + 3 q^{2} + 7 q^{3} + q^{4} - 5 q^{5} + 21 q^{6} + 22 q^{7} - 21 q^{8} + 22 q^{9} - 15 q^{10} + 64 q^{11} + 7 q^{12} + 73 q^{13} + 66 q^{14} - 35 q^{15} - 71 q^{16} + 66 q^{18} - 49 q^{19} - 5 q^{20}+ \cdots + 1408 q^{99}+O(q^{100}) $

q + 3 * q^2 + 7 * q^3 + q^4 - 5 * q^5 + 21 * q^6 + 22 * q^7 - 21 * q^8 + 22 * q^9 - 15 * q^10 + 64 * q^11 + 7 * q^12 + 73 * q^13 + 66 * q^14 - 35 * q^15 - 71 * q^16 + 66 * q^18 - 49 * q^19 - 5 * q^20 + 154 * q^21 + 192 * q^22 - 110 * q^23 - 147 * q^24 + 25 * q^25 + 219 * q^26 - 35 * q^27 + 22 * q^28 - 155 * q^29 - 105 * q^30 + 197 * q^31 - 45 * q^32 + 448 * q^33 - 110 * q^35 + 22 * q^36 + 372 * q^37 - 147 * q^38 + 511 * q^39 + 105 * q^40 + 262 * q^41 + 462 * q^42 + 258 * q^43 + 64 * q^44 - 110 * q^45 - 330 * q^46 - 13 * q^47 - 497 * q^48 + 141 * q^49 + 75 * q^50 + 73 * q^52 - 653 * q^53 - 105 * q^54 - 320 * q^55 - 462 * q^56 - 343 * q^57 - 465 * q^58 - 333 * q^59 - 35 * q^60 + 355 * q^61 + 591 * q^62 + 484 * q^63 + 433 * q^64 - 365 * q^65 + 1344 * q^66 + 814 * q^67 - 770 * q^69 - 330 * q^70 - 47 * q^71 - 462 * q^72 + 437 * q^73 + 1116 * q^74 + 175 * q^75 - 49 * q^76 + 1408 * q^77 + 1533 * q^78 + 384 * q^79 + 355 * q^80 - 839 * q^81 + 786 * q^82 - 736 * q^83 + 154 * q^84 + 774 * q^86 - 1085 * q^87 - 1344 * q^88 + 511 * q^89 - 330 * q^90 + 1606 * q^91 - 110 * q^92 + 1379 * q^93 - 39 * q^94 + 245 * q^95 - 315 * q^96 - 537 * q^97 + 423 * q^98 + 1408 * 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

3.00000

7.00000

1.00000

−5.00000

21.0000

22.0000

−21.0000

22.0000

−15.0000

Atkin-Lehner signs

$ p $	Sign
$5$	$ +1 $
$17$	$ +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	1445.4.a.h		1
17.b	even	2	1		85.4.a.a	✓	1
51.c	odd	2	1		765.4.a.b		1
68.d	odd	2	1		1360.4.a.i		1
85.c	even	2	1		425.4.a.c		1
85.g	odd	4	2		425.4.b.a		2

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
85.4.a.a	✓	1	17.b	even	2	1
425.4.a.c		1	85.c	even	2	1
425.4.b.a		2	85.g	odd	4	2
765.4.a.b		1	51.c	odd	2	1
1360.4.a.i		1	68.d	odd	2	1
1445.4.a.h		1	1.a	even	1	1	trivial

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $S_{4}^{\mathrm{new}}(\Gamma_0(1445))$:

$ T_{2} - 3 $

T2 - 3

$ T_{3} - 7 $

T3 - 7

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$ T - 3 $ T - 3
$3$	$ T - 7 $ T - 7
$5$	$ T + 5 $ T + 5
$7$	$ T - 22 $ T - 22
$11$	$ T - 64 $ T - 64
$13$	$ T - 73 $ T - 73
$17$	$ T $ T
$19$	$ T + 49 $ T + 49
$23$	$ T + 110 $ T + 110
$29$	$ T + 155 $ T + 155
$31$	$ T - 197 $ T - 197
$37$	$ T - 372 $ T - 372
$41$	$ T - 262 $ T - 262
$43$	$ T - 258 $ T - 258
$47$	$ T + 13 $ T + 13
$53$	$ T + 653 $ T + 653
$59$	$ T + 333 $ T + 333
$61$	$ T - 355 $ T - 355
$67$	$ T - 814 $ T - 814
$71$	$ T + 47 $ T + 47
$73$	$ T - 437 $ T - 437
$79$	$ T - 384 $ T - 384
$83$	$ T + 736 $ T + 736
$89$	$ T - 511 $ T - 511
$97$	$ T + 537 $ T + 537
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Elliptic curves over $\Q$ over number fields
Genus 2 curves
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Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1445 = 5 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1445.a (trivial)

\(n\):		e.g. 2-40 or 80-90
Significant digits:
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