Newform orbit 1450.2.a.n

• Label: 1450.2.a.n
• Level: $1450$
• Weight: $2$
• Character orbit: 1450.a
• Self dual: yes
• Analytic conductor: $11.578$
• Analytic rank: $0$
• Dimension: $2$
• CM: no
• Inner twists: $1$

Newspace parameters

Level:	\( N \)	\(=\)	\( 1450 = 2 \cdot 5^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1450.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	\(11.5783082931\)
Analytic rank:	\(0\)
Dimension:	\(2\)
Coefficient field:	\(\Q(\sqrt{13}) \)
Defining polynomial:	\( x^{2} - x - 3 \)
Coefficient ring:	\(\Z[a_1, a_2, a_3]\)
Coefficient ring index:	\( 1 \)
Twist minimal:	no (minimal twist has level 290)
Fricke sign:	\(-1\)
Sato-Tate group:	$\mathrm{SU}(2)$

$q$-expansion

Coefficients of the \(q\)-expansion are expressed in terms of \(\beta = \frac{1}{2}(1 + \sqrt{13})\). We also show the integral \(q\)-expansion of the trace form.

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

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

2.30278
−1.30278

1.00000

−2.30278

1.00000

0

−2.30278

−3.30278

1.00000

2.30278

0

1.2

1.00000

1.30278

1.00000

0

1.30278

0.302776

1.00000

−1.30278

0

Atkin-Lehner signs

\( p \)	Sign
\(2\)	\(-1\)
\(5\)	\(1\)
\(29\)	\(1\)

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	1450.2.a.n		2
5.b	even	2	1		290.2.a.c	✓	2
5.c	odd	4	2		1450.2.b.h		4
15.d	odd	2	1		2610.2.a.s		2
20.d	odd	2	1		2320.2.a.j		2
40.e	odd	2	1		9280.2.a.bb		2
40.f	even	2	1		9280.2.a.x		2
145.d	even	2	1		8410.2.a.s		2

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
290.2.a.c	✓	2	5.b	even	2	1
1450.2.a.n		2	1.a	even	1	1	trivial
1450.2.b.h		4	5.c	odd	4	2
2320.2.a.j		2	20.d	odd	2	1
2610.2.a.s		2	15.d	odd	2	1
8410.2.a.s		2	145.d	even	2	1
9280.2.a.x		2	40.f	even	2	1
9280.2.a.bb		2	40.e	odd	2	1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(1450))\):

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

\( T_{7}^{2} + 3T_{7} - 1 \)

\( T_{13}^{2} - T_{13} - 3 \)

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	\( (T - 1)^{2} \)
$3$	\( T^{2} + T - 3 \)
$5$	\( T^{2} \)
$7$	\( T^{2} + 3T - 1 \)
$11$	\( T^{2} - 2T - 12 \)