Newform orbit 4830.2.a.l

• Label: 4830.2.a.l
• Level: $4830$
• Weight: $2$
• Character orbit: 4830.a
• Self dual: yes
• Analytic conductor: $38.568$
• Analytic rank: $0$
• Dimension: $1$
• CM: no
• Inner twists: $1$

Newspace parameters

Level:	$N$	$=$	$4830 = 2 \cdot 3 \cdot 5 \cdot 7 \cdot 23$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	4830.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	$38.5677441763$
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

$f(q)$

$=$

q - q^2 + q^3 + q^4 - q^5 - q^6 + q^7 - q^8 + q^9 + q^10 + q^12 - 4 * q^13 - q^14 - q^15 + q^16 - q^18 + 2 * q^19 - q^20 + q^21 + q^23 - q^24 + q^25 + 4 * q^26 + q^27 + q^28 + 6 * q^29 + q^30 + 2 * q^31 - q^32 - q^35 + q^36 - 10 * q^37 - 2 * q^38 - 4 * q^39 + q^40 + 6 * q^41 - q^42 - 4 * q^43 - q^45 - q^46 + 6 * q^47 + q^48 + q^49 - q^50 - 4 * q^52 - 6 * q^53 - q^54 - q^56 + 2 * q^57 - 6 * q^58 + 12 * q^59 - q^60 - 10 * q^61 - 2 * q^62 + q^63 + q^64 + 4 * q^65 - 4 * q^67 + q^69 + q^70 - q^72 + 14 * q^73 + 10 * q^74 + q^75 + 2 * q^76 + 4 * q^78 + 8 * q^79 - q^80 + q^81 - 6 * q^82 + 6 * q^83 + q^84 + 4 * q^86 + 6 * q^87 + q^90 - 4 * q^91 + q^92 + 2 * q^93 - 6 * q^94 - 2 * q^95 - q^96 + 8 * q^97 - q^98

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.

Label  

$\iota_m(\nu)$

$a_{2}$

$a_{3}$

$a_{4}$

$a_{5}$

$a_{6}$

$a_{7}$

$a_{8}$

$a_{9}$

$a_{10}$

1.1

0

−1.00000

1.00000

1.00000

−1.00000

−1.00000

1.00000

−1.00000

1.00000

1.00000

Atkin-Lehner signs

$p$	Sign
$2$	$+1$
$3$	$-1$
$5$	$+1$
$7$	$-1$
$23$	$-1$

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	4830.2.a.l	✓	1

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
4830.2.a.l	✓	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 $S_{2}^{\mathrm{new}}(\Gamma_0(4830))$:

$T_{11}$

$T_{13} + 4$

$T_{17}$

$T_{19} - 2$

$T_{29} - 6$

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$T + 1$
$3$	$T - 1$
$5$	$T + 1$
$7$	$T - 1$
$11$	$T$