LMFDB - Newform orbit 105.4.a.b

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [105,4,Mod(1,105)] 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("105.1"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(105, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 105 = 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	105.a (trivial)

Newform invariants

comment:select newform

sage:traces = [1,5] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	yes
Analytic conductor:	$6.19520055060$
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 + 5 q^{2} - 3 q^{3} + 17 q^{4} + 5 q^{5} - 15 q^{6} + 7 q^{7} + 45 q^{8} + 9 q^{9} + 25 q^{10} + 12 q^{11} - 51 q^{12} + 30 q^{13} + 35 q^{14} - 15 q^{15} + 89 q^{16} - 134 q^{17} + 45 q^{18} - 92 q^{19}+ \cdots + 108 q^{99}+O(q^{100}) $

q + 5 * q^2 - 3 * q^3 + 17 * q^4 + 5 * q^5 - 15 * q^6 + 7 * q^7 + 45 * q^8 + 9 * q^9 + 25 * q^10 + 12 * q^11 - 51 * q^12 + 30 * q^13 + 35 * q^14 - 15 * q^15 + 89 * q^16 - 134 * q^17 + 45 * q^18 - 92 * q^19 + 85 * q^20 - 21 * q^21 + 60 * q^22 + 112 * q^23 - 135 * q^24 + 25 * q^25 + 150 * q^26 - 27 * q^27 + 119 * q^28 - 58 * q^29 - 75 * q^30 - 224 * q^31 + 85 * q^32 - 36 * q^33 - 670 * q^34 + 35 * q^35 + 153 * q^36 - 146 * q^37 - 460 * q^38 - 90 * q^39 + 225 * q^40 + 18 * q^41 - 105 * q^42 + 340 * q^43 + 204 * q^44 + 45 * q^45 + 560 * q^46 + 208 * q^47 - 267 * q^48 + 49 * q^49 + 125 * q^50 + 402 * q^51 + 510 * q^52 - 754 * q^53 - 135 * q^54 + 60 * q^55 + 315 * q^56 + 276 * q^57 - 290 * q^58 + 380 * q^59 - 255 * q^60 + 718 * q^61 - 1120 * q^62 + 63 * q^63 - 287 * q^64 + 150 * q^65 - 180 * q^66 + 412 * q^67 - 2278 * q^68 - 336 * q^69 + 175 * q^70 - 960 * q^71 + 405 * q^72 + 1066 * q^73 - 730 * q^74 - 75 * q^75 - 1564 * q^76 + 84 * q^77 - 450 * q^78 + 896 * q^79 + 445 * q^80 + 81 * q^81 + 90 * q^82 + 436 * q^83 - 357 * q^84 - 670 * q^85 + 1700 * q^86 + 174 * q^87 + 540 * q^88 - 1038 * q^89 + 225 * q^90 + 210 * q^91 + 1904 * q^92 + 672 * q^93 + 1040 * q^94 - 460 * q^95 - 255 * q^96 - 702 * q^97 + 245 * q^98 + 108 * 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

−3.00000

17.0000

5.00000

−15.0000

7.00000

45.0000

9.00000

25.0000

Atkin-Lehner signs

$ p $	Sign
$3$	$ +1 $
$5$	$ -1 $
$7$	$ -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	105.4.a.b	✓	1
3.b	odd	2	1		315.4.a.a		1
4.b	odd	2	1		1680.4.a.u		1
5.b	even	2	1		525.4.a.a		1
5.c	odd	4	2		525.4.d.a		2
7.b	odd	2	1		735.4.a.j		1
15.d	odd	2	1		1575.4.a.l		1
21.c	even	2	1		2205.4.a.b		1

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
105.4.a.b	✓	1	1.a	even	1	1	trivial
315.4.a.a		1	3.b	odd	2	1
525.4.a.a		1	5.b	even	2	1
525.4.d.a		2	5.c	odd	4	2
735.4.a.j		1	7.b	odd	2	1
1575.4.a.l		1	15.d	odd	2	1
1680.4.a.u		1	4.b	odd	2	1
2205.4.a.b		1	21.c	even	2	1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator $ T_{2} - 5 $ T2 - 5 acting on $S_{4}^{\mathrm{new}}(\Gamma_0(105))$.

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$ T - 5 $ T - 5
$3$	$ T + 3 $ T + 3
$5$	$ T - 5 $ T - 5
$7$	$ T - 7 $ T - 7
$11$	$ T - 12 $ T - 12
$13$	$ T - 30 $ T - 30
$17$	$ T + 134 $ T + 134
$19$	$ T + 92 $ T + 92
$23$	$ T - 112 $ T - 112
$29$	$ T + 58 $ T + 58
$31$	$ T + 224 $ T + 224
$37$	$ T + 146 $ T + 146
$41$	$ T - 18 $ T - 18
$43$	$ T - 340 $ T - 340
$47$	$ T - 208 $ T - 208
$53$	$ T + 754 $ T + 754
$59$	$ T - 380 $ T - 380
$61$	$ T - 718 $ T - 718
$67$	$ T - 412 $ T - 412
$71$	$ T + 960 $ T + 960
$73$	$ T - 1066 $ T - 1066
$79$	$ T - 896 $ T - 896
$83$	$ T - 436 $ T - 436
$89$	$ T + 1038 $ T + 1038
$97$	$ T + 702 $ T + 702
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Overview	Random
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Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	105.a (trivial)

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