Newform orbit 1584.4.a.y

• Label: 1584.4.a.y
• Level: $1584$
• Weight: $4$
• Character orbit: 1584.a
• Self dual: yes
• Analytic conductor: $93.459$
• Analytic rank: $1$
• Dimension: $2$
• CM: no
• Inner twists: $1$

Newspace parameters

Level:	\( N \)	\(=\)	\( 1584 = 2^{4} \cdot 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1584.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	\(93.4590254491\)
Analytic rank:	\(1\)
Dimension:	\(2\)
Coefficient field:	\(\Q(\sqrt{31}) \)
Defining polynomial:	\( x^{2} - 31 \)
Coefficient ring:	\(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index:	\( 2 \)
Twist minimal:	no (minimal twist has level 396)
Fricke sign:	\(-1\)
Sato-Tate group:	$\mathrm{SU}(2)$

$q$-expansion

Coefficients of the \(q\)-expansion are expressed in terms of \(\beta = 2\sqrt{31}\). We also show the integral \(q\)-expansion of the trace form.

\(f(q)\)	\(=\)	q + (b - 6) * q^5 + (-b + 12) * q^7 - 11 * q^11 + (5*b - 4) * q^13 + (-6*b + 14) * q^17 + (2*b + 34) * q^19 + (-7*b - 134) * q^23 + (-12*b + 35) * q^25 + (4*b + 130) * q^29 + (-14*b - 56) * q^31 + (18*b - 196) * q^35 + (-22*b + 158) * q^37 + (8*b + 62) * q^41 + 74 * q^43 + (11*b - 286) * q^47 + (-24*b - 75) * q^49 + (45*b + 38) * q^53 + (-11*b + 66) * q^55 + (6*b - 432) * q^59 + (51*b - 68) * q^61 + (-34*b + 644) * q^65 + (-40*b + 256) * q^67 + (-35*b - 362) * q^71 + (-12*b + 486) * q^73 + (11*b - 132) * q^77 + (5*b + 264) * q^79 + (22*b - 1056) * q^83 + (50*b - 828) * q^85 + (-112*b + 144) * q^89 + (64*b - 668) * q^91 + (22*b + 44) * q^95 + (-72*b + 250) * q^97
\(\operatorname{Tr}(f)(q)\)	\(=\)	2 * q - 12 * q^5 + 24 * q^7 - 22 * q^11 - 8 * q^13 + 28 * q^17 + 68 * q^19 - 268 * q^23 + 70 * q^25 + 260 * q^29 - 112 * q^31 - 392 * q^35 + 316 * q^37 + 124 * q^41 + 148 * q^43 - 572 * q^47 - 150 * q^49 + 76 * q^53 + 132 * q^55 - 864 * q^59 - 136 * q^61 + 1288 * q^65 + 512 * q^67 - 724 * q^71 + 972 * q^73 - 264 * q^77 + 528 * q^79 - 2112 * q^83 - 1656 * q^85 + 288 * q^89 - 1336 * q^91 + 88 * q^95 + 500 * 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

−5.56776
5.56776

0

0

0

−17.1355

0

23.1355

0

0

0

1.2

0

0

0

5.13553

0

0.864471

0

0

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	1584.4.a.y		2
3.b	odd	2	1		1584.4.a.bi		2
4.b	odd	2	1		396.4.a.h	✓	2
12.b	even	2	1		396.4.a.j	yes	2

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
396.4.a.h	✓	2	4.b	odd	2	1
396.4.a.j	yes	2	12.b	even	2	1
1584.4.a.y		2	1.a	even	1	1	trivial
1584.4.a.bi		2	3.b	odd	2	1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(1584))\):

\( T_{5}^{2} + 12T_{5} - 88 \)

\( T_{7}^{2} - 24T_{7} + 20 \)

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	\( T^{2} \)
$3$	\( T^{2} \)
$5$	\( T^{2} + 12T - 88 \)
$7$	\( T^{2} - 24T + 20 \)
$11$	\( (T + 11)^{2} \)