Newform orbit 432.7.o.c

• Label: 432.7.o.c
• Level: $432$
• Weight: $7$
• Character orbit: 432.o
• Analytic conductor: $99.383$
• Analytic rank: $0$
• Dimension: $24$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	432.o (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(99.3833641238\)
Analytic rank:	\(0\)
Dimension:	\(24\)
Relative dimension:	\(12\) over \(\Q(\zeta_{6})\)
Twist minimal:	no (minimal twist has level 144)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

$q$-expansion

The dimension is sufficiently large that we do not compute an algebraic \(q\)-expansion, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 24 q + 72 q^{5} + 360 q^{7}+O(q^{10}) \)

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		−119.170	−	206.408i		0		297.697	+	171.875i		0			0			0
127.2		0			0			0		−73.7563	−	127.750i		0		−190.108	−	109.759i		0			0			0
127.3		0			0			0		−60.1651	−	104.209i		0		−336.978	−	194.554i		0			0			0
127.4		0			0			0		−52.2018	−	90.4162i		0		−145.321	−	83.9012i		0			0			0
127.5		0			0			0		−44.4894	−	77.0579i		0		295.893	+	170.834i		0			0			0
127.6		0			0			0		9.36320	+	16.2175i		0		390.758	+	225.604i		0			0			0
127.7		0			0			0		22.4186	+	38.8302i		0		44.0273	+	25.4192i		0			0			0
127.8		0			0			0		37.9246	+	65.6873i		0		492.804	+	284.521i		0			0			0
127.9		0			0			0		39.8643	+	69.0470i		0		−343.678	−	198.423i		0			0			0
127.10		0			0			0		81.8187	+	141.714i		0		−30.8728	−	17.8244i		0			0			0
127.11		0			0			0		82.8778	+	143.549i		0		−552.707	−	319.106i		0			0			0
127.12		0			0			0		111.515	+	193.150i		0		258.486	+	149.237i		0			0			0
415.1		0			0			0		−119.170	+	206.408i		0		297.697	−	171.875i		0			0			0
415.2		0			0			0		−73.7563	+	127.750i		0		−190.108	+	109.759i		0			0			0
415.3		0			0			0		−60.1651	+	104.209i		0		−336.978	+	194.554i		0			0			0
415.4		0			0			0		−52.2018	+	90.4162i		0		−145.321	+	83.9012i		0			0			0
415.5		0			0			0		−44.4894	+	77.0579i		0		295.893	−	170.834i		0			0			0
415.6		0			0			0		9.36320	−	16.2175i		0		390.758	−	225.604i		0			0			0
415.7		0			0			0		22.4186	−	38.8302i		0		44.0273	−	25.4192i		0			0			0
415.8		0			0			0		37.9246	−	65.6873i		0		492.804	−	284.521i		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	432.7.o.c		24
3.b	odd	2	1		144.7.o.a	✓	24
4.b	odd	2	1		432.7.o.b		24
9.c	even	3	1		432.7.o.b		24
9.d	odd	6	1		144.7.o.c	yes	24
12.b	even	2	1		144.7.o.c	yes	24
36.f	odd	6	1	inner	432.7.o.c		24
36.h	even	6	1		144.7.o.a	✓	24

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
144.7.o.a	✓	24	3.b	odd	2	1
144.7.o.a	✓	24	36.h	even	6	1
144.7.o.c	yes	24	9.d	odd	6	1
144.7.o.c	yes	24	12.b	even	2	1
432.7.o.b		24	4.b	odd	2	1
432.7.o.b		24	9.c	even	3	1
432.7.o.c		24	1.a	even	1	1	trivial
432.7.o.c		24	36.f	odd	6	1	inner