Newform orbit 432.9.o.b

• Label: 432.9.o.b
• Level: $432$
• Weight: $9$
• Character orbit: 432.o
• Analytic conductor: $175.988$
• Analytic rank: $0$
• Dimension: $32$
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	432.o (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(175.987559546\)
Analytic rank:	\(0\)
Dimension:	\(32\)
Relative dimension:	\(16\) over \(\Q(\zeta_{6})\)
Twist minimal:	no (minimal twist has level 144)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

$q$-expansion

The algebraic \(q\)-expansion of this newform has not been computed, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) 32 * q - 147 * q^5 + 2769 * q^7 + 17082 * q^11 + 1685 * q^13 + 6402 * q^17 - 4941 * q^23 - 1080803 * q^25 + 639219 * q^29 - 920745 * q^31 - 2765636 * q^37 + 2229390 * q^41 - 1788381 * q^47 + 13397285 * q^49 + 16055532 * q^53 - 42176466 * q^59 - 6097553 * q^61 - 14325141 * q^65 - 1476300 * q^67 + 44269442 * q^73 + 22487769 * q^77 - 65644341 * q^79 + 67089393 * q^83 + 28601250 * q^85 - 133904424 * q^89 + 7225380 * q^95 + 74963282 * 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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
127.1		0			0			0		−498.228	−	862.955i		0		−2852.71	−	1647.01i		0			0			0
127.2		0			0			0		−496.920	−	860.691i		0		−302.260	−	174.510i		0			0			0
127.3		0			0			0		−424.979	−	736.085i		0		−392.812	−	226.790i		0			0			0
127.4		0			0			0		−341.539	−	591.564i		0		2776.29	+	1602.89i		0			0			0
127.5		0			0			0		−231.039	−	400.171i		0		1072.97	+	619.477i		0			0			0
127.6		0			0			0		−204.161	−	353.617i		0		−3493.95	−	2017.23i		0			0			0
127.7		0			0			0		−116.277	−	201.398i		0		2549.44	+	1471.92i		0			0			0
127.8		0			0			0		−59.6077	−	103.244i		0		2053.57	+	1185.63i		0			0			0
127.9		0			0			0		33.9007	+	58.7177i		0		2633.24	+	1520.30i		0			0			0
127.10		0			0			0		152.622	+	264.349i		0		−517.677	−	298.881i		0			0			0
127.11		0			0			0		192.240	+	332.970i		0		−2901.79	−	1675.35i		0			0			0
127.12		0			0			0		195.960	+	339.413i		0		−2555.55	−	1475.45i		0			0			0
127.13		0			0			0		234.980	+	406.997i		0		260.631	+	150.475i		0			0			0
127.14		0			0			0		354.193	+	613.480i		0		−728.814	−	420.781i		0			0			0
127.15		0			0			0		527.884	+	914.322i		0		−246.626	−	142.389i		0			0			0
127.16		0			0			0		607.471	+	1052.17i		0		4030.55	+	2327.04i		0			0			0
415.1		0			0			0		−498.228	+	862.955i		0		−2852.71	+	1647.01i		0			0			0
415.2		0			0			0		−496.920	+	860.691i		0		−302.260	+	174.510i		0			0			0
415.3		0			0			0		−424.979	+	736.085i		0		−392.812	+	226.790i		0			0			0
415.4		0			0			0		−341.539	+	591.564i		0		2776.29	−	1602.89i		0			0			0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
36.f	odd	6	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	432.9.o.b		32
3.b	odd	2	1		144.9.o.a	✓	32
4.b	odd	2	1		432.9.o.a		32
9.c	even	3	1		432.9.o.a		32
9.d	odd	6	1		144.9.o.c	yes	32
12.b	even	2	1		144.9.o.c	yes	32
36.f	odd	6	1	inner	432.9.o.b		32
36.h	even	6	1		144.9.o.a	✓	32

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
144.9.o.a	✓	32	3.b	odd	2	1
144.9.o.a	✓	32	36.h	even	6	1
144.9.o.c	yes	32	9.d	odd	6	1
144.9.o.c	yes	32	12.b	even	2	1
432.9.o.a		32	4.b	odd	2	1
432.9.o.a		32	9.c	even	3	1
432.9.o.b		32	1.a	even	1	1	trivial
432.9.o.b		32	36.f	odd	6	1	inner