Newform orbit 532.2.a.c

• Label: 532.2.a.c
• Level: $532$
• Weight: $2$
• Character orbit: 532.a
• Self dual: yes
• Analytic conductor: $4.248$
• Analytic rank: $0$
• Dimension: $2$
• CM: no
• Inner twists: $1$

Newspace parameters

Level:	\( N \)	\(=\)	\( 532 = 2^{2} \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	532.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	\(4.24804138753\)
Analytic rank:	\(0\)
Dimension:	\(2\)
Coefficient field:	\(\Q(\sqrt{21}) \)
Defining polynomial:	\( x^{2} - x - 5 \)
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 \(\beta = \frac{1}{2}(1 + \sqrt{21})\). We also show the integral \(q\)-expansion of the trace form.

\(f(q)\)	\(=\)	q - b * q^3 + 3 * q^5 + q^7 + (b + 2) * q^9 + (-b - 1) * q^11 - q^13 - 3*b * q^15 + (b + 1) * q^17 + q^19 - b * q^21 + (2*b - 1) * q^23 + 4 * q^25 - 5 * q^27 + (b + 1) * q^29 + (3*b - 1) * q^31 + (2*b + 5) * q^33 + 3 * q^35 + 5 * q^37 + b * q^39 + (-b - 1) * q^41 + 2 * q^43 + (3*b + 6) * q^45 + (2*b + 5) * q^47 + q^49 + (-2*b - 5) * q^51 - 3*b * q^53 + (-3*b - 3) * q^55 - b * q^57 + (4*b + 1) * q^59 - q^61 + (b + 2) * q^63 - 3 * q^65 + (-3*b - 1) * q^67 + (-b - 10) * q^69 + (-4*b - 1) * q^71 + (3*b + 8) * q^73 - 4*b * q^75 + (-b - 1) * q^77 - 10 * q^79 + (2*b - 6) * q^81 + (3*b + 6) * q^83 + (3*b + 3) * q^85 + (-2*b - 5) * q^87 + (2*b + 2) * q^89 - q^91 + (-2*b - 15) * q^93 + 3 * q^95 - 7 * q^97 + (-4*b - 7) * q^99
\(\operatorname{Tr}(f)(q)\)	\(=\)	2 * q - q^3 + 6 * q^5 + 2 * q^7 + 5 * q^9 - 3 * q^11 - 2 * q^13 - 3 * q^15 + 3 * q^17 + 2 * q^19 - q^21 + 8 * q^25 - 10 * q^27 + 3 * q^29 + q^31 + 12 * q^33 + 6 * q^35 + 10 * q^37 + q^39 - 3 * q^41 + 4 * q^43 + 15 * q^45 + 12 * q^47 + 2 * q^49 - 12 * q^51 - 3 * q^53 - 9 * q^55 - q^57 + 6 * q^59 - 2 * q^61 + 5 * q^63 - 6 * q^65 - 5 * q^67 - 21 * q^69 - 6 * q^71 + 19 * q^73 - 4 * q^75 - 3 * q^77 - 20 * q^79 - 10 * q^81 + 15 * q^83 + 9 * q^85 - 12 * q^87 + 6 * q^89 - 2 * q^91 - 32 * q^93 + 6 * q^95 - 14 * q^97 - 18 * q^99

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

2.79129
−1.79129

0

−2.79129

0

3.00000

0

1.00000

0

4.79129

0

1.2

0

1.79129

0

3.00000

0

1.00000

0

0.208712

0

Atkin-Lehner signs

\( p \)	Sign
\(2\)	\( -1 \)
\(7\)	\( -1 \)
\(19\)	\( -1 \)

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	532.2.a.c	✓	2
3.b	odd	2	1		4788.2.a.g		2
4.b	odd	2	1		2128.2.a.k		2
7.b	odd	2	1		3724.2.a.e		2
8.b	even	2	1		8512.2.a.t		2
8.d	odd	2	1		8512.2.a.m		2

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
532.2.a.c	✓	2	1.a	even	1	1	trivial
2128.2.a.k		2	4.b	odd	2	1
3724.2.a.e		2	7.b	odd	2	1
4788.2.a.g		2	3.b	odd	2	1
8512.2.a.m		2	8.d	odd	2	1
8512.2.a.t		2	8.b	even	2	1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{3}^{2} + T_{3} - 5 \) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(532))\).

Hecke characteristic polynomials

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