Newform 23.2.a.a

• Label: 23.2.a.a
• Level: 23
• Weight: 2
• Character orbit: 23.a
• Self dual: Yes
• Analytic conductor: 0.184
• Analytic rank: 0
• Dimension: 2
• CM: No
• Inner twists: 1

Newspace parameters

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

Newform invariants

Self dual:	Yes
Analytic conductor:	\(0.183655924649\)
Analytic rank:	\(0\)
Dimension:	\(2\)
Coefficient field:	\(\Q(\sqrt{5}) \)
Coefficient ring:	\(\Z[a_1, a_2]\)
Coefficient ring index:	\( 1 \)
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.

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

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

1.61803
−0.618034

−1.61803

2.23607

0.618034

−3.23607

−3.61803

−1.23607

2.23607

2.00000

5.23607

1.2

0.618034

−2.23607

−1.61803

1.23607

−1.38197

3.23607

−2.23607

2.00000

0.763932

Inner twists

This newform does not admit any (nontrivial) inner twists.

Atkin-Lehner signs

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

Hecke kernels

There are no other newforms in \(S_{2}^{\mathrm{new}}(\Gamma_0(23))\).