Newform orbit 1452.4.a.m

• Label: 1452.4.a.m
• Level: $1452$
• Weight: $4$
• Character orbit: 1452.a
• Self dual: yes
• Analytic conductor: $85.671$
• Analytic rank: $0$
• Dimension: $2$
• CM: no
• Inner twists: $1$

Newspace parameters

Level:	\( N \)	\(=\)	\( 1452 = 2^{2} \cdot 3 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1452.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	\(85.6707733283\)
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 - 3 * q^3 + (11*b - 5) * q^5 + (-4*b + 13) * q^7 + 9 * q^9 + (-14*b + 51) * q^13 + (-33*b + 15) * q^15 + (-21*b + 16) * q^17 + (93*b - 85) * q^19 + (12*b - 39) * q^21 + 185 * q^23 + (11*b + 21) * q^25 - 27 * q^27 + (60*b - 118) * q^29 + (-209*b + 154) * q^31 + (119*b - 109) * q^35 + (154*b - 107) * q^37 + (42*b - 153) * q^39 + (-96*b + 235) * q^41 + (298*b + 5) * q^43 + (99*b - 45) * q^45 + (33*b - 388) * q^47 + (-88*b - 158) * q^49 + (63*b - 48) * q^51 + (-77*b + 312) * q^53 + (-279*b + 255) * q^57 + (11*b + 295) * q^59 + (357*b + 69) * q^61 + (-36*b + 117) * q^63 + (477*b - 409) * q^65 + (407*b - 575) * q^67 - 555 * q^69 + (99*b + 201) * q^71 + (-342*b - 456) * q^73 + (-33*b - 63) * q^75 + (336*b - 355) * q^79 + 81 * q^81 + (-266*b - 219) * q^83 + (50*b - 311) * q^85 + (-180*b + 354) * q^87 + (-220*b + 419) * q^89 + (-330*b + 719) * q^91 + (627*b - 462) * q^93 + (-377*b + 1448) * q^95 + (11*b + 151) * q^97
\(\operatorname{Tr}(f)(q)\)	\(=\)	2 * q - 6 * q^3 + q^5 + 22 * q^7 + 18 * q^9 + 88 * q^13 - 3 * q^15 + 11 * q^17 - 77 * q^19 - 66 * q^21 + 370 * q^23 + 53 * q^25 - 54 * q^27 - 176 * q^29 + 99 * q^31 - 99 * q^35 - 60 * q^37 - 264 * q^39 + 374 * q^41 + 308 * q^43 + 9 * q^45 - 743 * q^47 - 404 * q^49 - 33 * q^51 + 547 * q^53 + 231 * q^57 + 601 * q^59 + 495 * q^61 + 198 * q^63 - 341 * q^65 - 743 * q^67 - 1110 * q^69 + 501 * q^71 - 1254 * q^73 - 159 * q^75 - 374 * q^79 + 162 * q^81 - 704 * q^83 - 572 * q^85 + 528 * q^87 + 618 * q^89 + 1108 * q^91 - 297 * q^93 + 2519 * q^95 + 313 * 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

−0.618034
1.61803

0

−3.00000

0

−11.7984

0

15.4721

0

9.00000

0

1.2

0

−3.00000

0

12.7984

0

6.52786

0

9.00000

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	1452.4.a.m		2
11.b	odd	2	1		1452.4.a.l		2
11.d	odd	10	2		132.4.i.a	✓	4
33.f	even	10	2		396.4.j.a		4

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
132.4.i.a	✓	4	11.d	odd	10	2
396.4.j.a		4	33.f	even	10	2
1452.4.a.l		2	11.b	odd	2	1
1452.4.a.m		2	1.a	even	1	1	trivial

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(1452))\):

\( T_{5}^{2} - T_{5} - 151 \)

\( T_{7}^{2} - 22T_{7} + 101 \)

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	\( T^{2} \)
$3$	\( (T + 3)^{2} \)
$5$	\( T^{2} - T - 151 \)
$7$	\( T^{2} - 22T + 101 \)
$11$	\( T^{2} \)