Newform orbit 230.2.a.c

• Label: 230.2.a.c
• Level: $230$
• Weight: $2$
• Character orbit: 230.a
• Self dual: yes
• Analytic conductor: $1.837$
• Analytic rank: $0$
• Dimension: $2$
• CM: no
• Inner twists: $1$

Newspace parameters

Level:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	230.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	\(1.83655924649\)
Analytic rank:	\(0\)
Dimension:	\(2\)
Coefficient field:	\(\Q(\sqrt{5}) \)
Defining polynomial:	\( x^{2} - x - 1 \)
Coefficient ring:	\(\Z[a_1, a_2, a_3]\)
Coefficient ring index:	\( 1 \)
Twist minimal:	yes
Fricke sign:	\(-1\)
Sato-Tate group:	$\mathrm{SU}(2)$

$q$-expansion

Coefficients of the \(q\)-expansion are expressed in terms of \(\beta = \frac{1}{2}(1 + \sqrt{5})\). We also show the integral \(q\)-expansion of the trace form.

\(f(q)\)	\(=\)	\( q + q^{2} + \beta q^{3} + q^{4} + q^{5} + \beta q^{6} + ( - \beta + 1) q^{7} + q^{8} + (\beta - 2) q^{9}+O(q^{10}) \)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} + q^{3} + 2 q^{4} + 2 q^{5} + q^{6} + q^{7} + 2 q^{8} - 3 q^{9}+O(q^{10}) \)

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

−0.618034
1.61803

1.00000

−0.618034

1.00000

1.00000

−0.618034

1.61803

1.00000

−2.61803

1.00000

1.2

1.00000

1.61803

1.00000

1.00000

1.61803

−0.618034

1.00000

−0.381966

1.00000

Atkin-Lehner signs

\( p \)	Sign
\(2\)	\(-1\)
\(5\)	\(-1\)
\(23\)	\(-1\)

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	230.2.a.c	✓	2
3.b	odd	2	1		2070.2.a.u		2
4.b	odd	2	1		1840.2.a.l		2
5.b	even	2	1		1150.2.a.j		2
5.c	odd	4	2		1150.2.b.i		4
8.b	even	2	1		7360.2.a.bh		2
8.d	odd	2	1		7360.2.a.bn		2
20.d	odd	2	1		9200.2.a.bu		2
23.b	odd	2	1		5290.2.a.o		2

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
230.2.a.c	✓	2	1.a	even	1	1	trivial
1150.2.a.j		2	5.b	even	2	1
1150.2.b.i		4	5.c	odd	4	2
1840.2.a.l		2	4.b	odd	2	1
2070.2.a.u		2	3.b	odd	2	1
5290.2.a.o		2	23.b	odd	2	1
7360.2.a.bh		2	8.b	even	2	1
7360.2.a.bn		2	8.d	odd	2	1
9200.2.a.bu		2	20.d	odd	2	1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{3}^{2} - T_{3} - 1 \) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(230))\).

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	\( (T - 1)^{2} \)
$3$	\( T^{2} - T - 1 \)
$5$	\( (T - 1)^{2} \)
$7$	\( T^{2} - T - 1 \)
$11$	\( T^{2} - T - 11 \)