LMFDB - Newform orbit 2366.4.a.c

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2366,4,Mod(1,2366)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2366, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 4, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("2366.1"); S:= CuspForms(chi, 4); N := Newforms(S);

Level:	$N$	$=$	$2366 = 2 \cdot 7 \cdot 13^{2}$
Weight:	$k$	$=$	$4$
Character orbit:	$[\chi]$	$=$	2366.a (trivial)

Newform invariants

comment:select newform

sage:traces = [1,-2,-2,4,12] 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:	$139.598519074$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$1$
Twist minimal:	no (minimal twist has level 14)
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} + 12 q^{5} + 4 q^{6} - 7 q^{7} - 8 q^{8} - 23 q^{9} - 24 q^{10} - 48 q^{11} - 8 q^{12} + 14 q^{14} - 24 q^{15} + 16 q^{16} - 114 q^{17} + 46 q^{18} - 2 q^{19} + 48 q^{20}+ \cdots + 1104 q^{99}+O(q^{100})

q - 2 * q^2 - 2 * q^3 + 4 * q^4 + 12 * q^5 + 4 * q^6 - 7 * q^7 - 8 * q^8 - 23 * q^9 - 24 * q^10 - 48 * q^11 - 8 * q^12 + 14 * q^14 - 24 * q^15 + 16 * q^16 - 114 * q^17 + 46 * q^18 - 2 * q^19 + 48 * q^20 + 14 * q^21 + 96 * q^22 - 120 * q^23 + 16 * q^24 + 19 * q^25 + 100 * q^27 - 28 * q^28 - 54 * q^29 + 48 * q^30 - 236 * q^31 - 32 * q^32 + 96 * q^33 + 228 * q^34 - 84 * q^35 - 92 * q^36 - 146 * q^37 + 4 * q^38 - 96 * q^40 - 126 * q^41 - 28 * q^42 - 376 * q^43 - 192 * q^44 - 276 * q^45 + 240 * q^46 + 12 * q^47 - 32 * q^48 + 49 * q^49 - 38 * q^50 + 228 * q^51 + 174 * q^53 - 200 * q^54 - 576 * q^55 + 56 * q^56 + 4 * q^57 + 108 * q^58 - 138 * q^59 - 96 * q^60 + 380 * q^61 + 472 * q^62 + 161 * q^63 + 64 * q^64 - 192 * q^66 + 484 * q^67 - 456 * q^68 + 240 * q^69 + 168 * q^70 - 576 * q^71 + 184 * q^72 + 1150 * q^73 + 292 * q^74 - 38 * q^75 - 8 * q^76 + 336 * q^77 + 776 * q^79 + 192 * q^80 + 421 * q^81 + 252 * q^82 - 378 * q^83 + 56 * q^84 - 1368 * q^85 + 752 * q^86 + 108 * q^87 + 384 * q^88 + 390 * q^89 + 552 * q^90 - 480 * q^92 + 472 * q^93 - 24 * q^94 - 24 * q^95 + 64 * q^96 + 1330 * q^97 - 98 * q^98 + 1104 * 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

4.00000

12.0000

4.00000

−7.00000

−8.00000

−23.0000

−24.0000

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	2366.4.a.c		1
13.b	even	2	1		14.4.a.b	✓	1
39.d	odd	2	1		126.4.a.d		1
52.b	odd	2	1		112.4.a.e		1
65.d	even	2	1		350.4.a.f		1
65.h	odd	4	2		350.4.c.g		2
91.b	odd	2	1		98.4.a.e		1
91.r	even	6	2		98.4.c.c		2
91.s	odd	6	2		98.4.c.b		2
104.e	even	2	1		448.4.a.k		1
104.h	odd	2	1		448.4.a.g		1
143.d	odd	2	1		1694.4.a.b		1
156.h	even	2	1		1008.4.a.r		1
273.g	even	2	1		882.4.a.b		1
273.w	odd	6	2		882.4.g.p		2
273.ba	even	6	2		882.4.g.v		2
364.h	even	2	1		784.4.a.h		1
455.h	odd	2	1		2450.4.a.i		1

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
14.4.a.b	✓	1	13.b	even	2	1
98.4.a.e		1	91.b	odd	2	1
98.4.c.b		2	91.s	odd	6	2
98.4.c.c		2	91.r	even	6	2
112.4.a.e		1	52.b	odd	2	1
126.4.a.d		1	39.d	odd	2	1
350.4.a.f		1	65.d	even	2	1
350.4.c.g		2	65.h	odd	4	2
448.4.a.g		1	104.h	odd	2	1
448.4.a.k		1	104.e	even	2	1
784.4.a.h		1	364.h	even	2	1
882.4.a.b		1	273.g	even	2	1
882.4.g.p		2	273.w	odd	6	2
882.4.g.v		2	273.ba	even	6	2
1008.4.a.r		1	156.h	even	2	1
1694.4.a.b		1	143.d	odd	2	1
2366.4.a.c		1	1.a	even	1	1	trivial
2450.4.a.i		1	455.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 $S_{4}^{\mathrm{new}}(\Gamma_0(2366))$ :

T_{3} + 2

T3 + 2

T_{5} - 12

T5 - 12

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$T + 2$ T + 2
$3$	$T + 2$ T + 2
$5$	$T - 12$ T - 12
$7$	$T + 7$ T + 7
$11$	$T + 48$ T + 48
$13$	$T$ T
$17$	$T + 114$ T + 114
$19$	$T + 2$ T + 2
$23$	$T + 120$ T + 120
$29$	$T + 54$ T + 54
$31$	$T + 236$ T + 236
$37$	$T + 146$ T + 146
$41$	$T + 126$ T + 126
$43$	$T + 376$ T + 376
$47$	$T - 12$ T - 12
$53$	$T - 174$ T - 174
$59$	$T + 138$ T + 138
$61$	$T - 380$ T - 380
$67$	$T - 484$ T - 484
$71$	$T + 576$ T + 576
$73$	$T - 1150$ T - 1150
$79$	$T - 776$ T - 776
$83$	$T + 378$ T + 378
$89$	$T - 390$ T - 390
$97$	$T - 1330$ T - 1330
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