Newform orbit 462.6.a.a

• Label: 462.6.a.a
• Level: $462$
• Weight: $6$
• Character orbit: 462.a
• Self dual: yes
• Analytic conductor: $74.097$
• Analytic rank: $1$
• Dimension: $1$
• CM: no
• Inner twists: $1$

Newspace parameters

Level:	\( N \)	\(=\)	\( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	462.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	\(74.0973247536\)
Analytic rank:	\(1\)
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

\(f(q)\)

\(=\)

\( q - 4 q^{2} - 9 q^{3} + 16 q^{4} - 78 q^{5} + 36 q^{6} + 49 q^{7} - 64 q^{8} + 81 q^{9}+O(q^{10}) \)

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

−4.00000

−9.00000

16.0000

−78.0000

36.0000

49.0000

−64.0000

81.0000

312.000

Atkin-Lehner signs

\( p \)	Sign
\(2\)	\(1\)
\(3\)	\(1\)
\(7\)	\(-1\)
\(11\)	\(-1\)

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	462.6.a.a	✓	1

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
462.6.a.a	✓	1	1.a	even	1	1	trivial

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{5} + 78 \) acting on \(S_{6}^{\mathrm{new}}(\Gamma_0(462))\).

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	\( T + 4 \)
$3$	\( T + 9 \)
$5$	\( T + 78 \)
$7$	\( T - 49 \)
$11$	\( T - 121 \)