Newform orbit 1150.2.a.p

• Label: 1150.2.a.p
• Level: $1150$
• Weight: $2$
• Character orbit: 1150.a
• Self dual: yes
• Analytic conductor: $9.183$
• Analytic rank: $0$
• Dimension: $2$
• CM: no
• Inner twists: $1$

Newspace parameters

Level:	\( N \)	\(=\)	\( 1150 = 2 \cdot 5^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1150.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	\(9.18279623245\)
Analytic rank:	\(0\)
Dimension:	\(2\)
Coefficient field:	\(\Q(\sqrt{17}) \)
Defining polynomial:	\( x^{2} - x - 4 \)
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 \(\beta = \frac{1}{2}(1 + \sqrt{17})\). We also show the integral \(q\)-expansion of the trace form.

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

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

−1.56155
2.56155

1.00000

−1.56155

1.00000

0

−1.56155

2.56155

1.00000

−0.561553

0

1.2

1.00000

2.56155

1.00000

0

2.56155

−1.56155

1.00000

3.56155

0

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	1150.2.a.p	yes	2
4.b	odd	2	1		9200.2.a.bp		2
5.b	even	2	1		1150.2.a.k	✓	2
5.c	odd	4	2		1150.2.b.h		4
20.d	odd	2	1		9200.2.a.bw		2

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
1150.2.a.k	✓	2	5.b	even	2	1
1150.2.a.p	yes	2	1.a	even	1	1	trivial
1150.2.b.h		4	5.c	odd	4	2
9200.2.a.bp		2	4.b	odd	2	1
9200.2.a.bw		2	20.d	odd	2	1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(1150))\):

\( T_{3}^{2} - T_{3} - 4 \)

\( T_{7}^{2} - T_{7} - 4 \)

\( T_{11} + 1 \)

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	\( (T - 1)^{2} \)
$3$	\( T^{2} - T - 4 \)
$5$	\( T^{2} \)
$7$	\( T^{2} - T - 4 \)
$11$	\( (T + 1)^{2} \)