Newform orbit 1452.2.a.j

• Label: 1452.2.a.j
• Level: $1452$
• Weight: $2$
• Character orbit: 1452.a
• Self dual: yes
• Analytic conductor: $11.594$
• Analytic rank: $0$
• Dimension: $2$
• CM: no
• Inner twists: $1$

Newspace parameters

Level:	\( N \)	\(=\)	\( 1452 = 2^{2} \cdot 3 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1452.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	\(11.5942783735\)
Analytic rank:	\(0\)
Dimension:	\(2\)
Coefficient field:	\(\Q(\sqrt{5}) \)
Defining polynomial:	\( x^{2} - x - 1 \)
Coefficient ring:	\(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index:	\( 1 \)
Twist minimal:	no (minimal twist has level 132)
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^3 + (-3*b + 1) * q^5 + (-2*b + 3) * q^7 + q^9 + (-2*b - 3) * q^13 + (3*b - 1) * q^15 + (-b + 4) * q^17 + (-5*b + 3) * q^19 + (2*b - 3) * q^21 + (-2*b + 3) * q^23 + (3*b + 5) * q^25 - q^27 + (4*b - 2) * q^29 + (b - 8) * q^31 + (-5*b + 9) * q^35 + (2*b - 7) * q^37 + (2*b + 3) * q^39 + (4*b + 3) * q^41 + (4*b + 3) * q^43 + (-3*b + 1) * q^45 + (b + 2) * q^47 + (-8*b + 6) * q^49 + (b - 4) * q^51 + (9*b - 8) * q^53 + (5*b - 3) * q^57 + (-3*b + 7) * q^59 + (-b - 1) * q^61 + (-2*b + 3) * q^63 + (13*b + 3) * q^65 + (3*b - 5) * q^67 + (2*b - 3) * q^69 + (b - 3) * q^71 + 2*b * q^73 + (-3*b - 5) * q^75 + (2*b + 11) * q^79 + q^81 + (4*b + 9) * q^83 + (-10*b + 7) * q^85 + (-4*b + 2) * q^87 + q^89 + (4*b - 5) * q^91 + (-b + 8) * q^93 + (b + 18) * q^95 + (-5*b + 3) * q^97
\(\operatorname{Tr}(f)(q)\)	\(=\)	2 * q - 2 * q^3 - q^5 + 4 * q^7 + 2 * q^9 - 8 * q^13 + q^15 + 7 * q^17 + q^19 - 4 * q^21 + 4 * q^23 + 13 * q^25 - 2 * q^27 - 15 * q^31 + 13 * q^35 - 12 * q^37 + 8 * q^39 + 10 * q^41 + 10 * q^43 - q^45 + 5 * q^47 + 4 * q^49 - 7 * q^51 - 7 * q^53 - q^57 + 11 * q^59 - 3 * q^61 + 4 * q^63 + 19 * q^65 - 7 * q^67 - 4 * q^69 - 5 * q^71 + 2 * q^73 - 13 * q^75 + 24 * q^79 + 2 * q^81 + 22 * q^83 + 4 * q^85 + 2 * q^89 - 6 * q^91 + 15 * q^93 + 37 * q^95 + q^97

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

0

−1.00000

0

−3.85410

0

−0.236068

0

1.00000

0

1.2

0

−1.00000

0

2.85410

0

4.23607

0

1.00000

0

Atkin-Lehner signs

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

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	1452.2.a.j		2
3.b	odd	2	1		4356.2.a.v		2
4.b	odd	2	1		5808.2.a.cc		2
11.b	odd	2	1		1452.2.a.i		2
11.c	even	5	2		132.2.i.b	✓	4
11.c	even	5	2		1452.2.i.o		4
11.d	odd	10	2		1452.2.i.j		4
11.d	odd	10	2		1452.2.i.p		4
33.d	even	2	1		4356.2.a.s		2
33.h	odd	10	2		396.2.j.c		4
44.c	even	2	1		5808.2.a.cf		2
44.h	odd	10	2		528.2.y.a		4

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
132.2.i.b	✓	4	11.c	even	5	2
396.2.j.c		4	33.h	odd	10	2
528.2.y.a		4	44.h	odd	10	2
1452.2.a.i		2	11.b	odd	2	1
1452.2.a.j		2	1.a	even	1	1	trivial
1452.2.i.j		4	11.d	odd	10	2
1452.2.i.o		4	11.c	even	5	2
1452.2.i.p		4	11.d	odd	10	2
4356.2.a.s		2	33.d	even	2	1
4356.2.a.v		2	3.b	odd	2	1
5808.2.a.cc		2	4.b	odd	2	1
5808.2.a.cf		2	44.c	even	2	1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(1452))\):

\( T_{5}^{2} + T_{5} - 11 \)

\( T_{7}^{2} - 4T_{7} - 1 \)

Hecke characteristic polynomials

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