Newform orbit 224.7.c.b

• Label: 224.7.c.b
• Level: $224$
• Weight: $7$
• Character orbit: 224.c
• Analytic conductor: $51.532$
• Analytic rank: $0$
• Dimension: $24$
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 224 = 2^{5} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	224.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(51.5321147308\)
Analytic rank:	\(0\)
Dimension:	\(24\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 24 q - 3368 q^{9} - 4448 q^{21} - 34152 q^{25} + 68656 q^{29} - 8976 q^{37} + 291096 q^{49} + 44976 q^{53} + 28224 q^{57} - 371456 q^{65} - 383088 q^{77} + 46936 q^{81} - 1042368 q^{85} + 4054720 q^{93}+O(q^{100}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
97.1		0			−	47.4327i		0			−	83.9816i		0		−320.533	+	122.095i		0		−1520.86				0
97.2		0			−	47.4327i		0				83.9816i		0		320.533	+	122.095i		0		−1520.86				0
97.3		0			−	38.3305i		0			−	148.008i		0		−126.534	−	318.807i		0		−740.230				0
97.4		0			−	38.3305i		0				148.008i		0		126.534	−	318.807i		0		−740.230				0
97.5		0			−	28.2668i		0			−	199.648i		0		342.054	+	25.4558i		0		−70.0140				0
97.6		0			−	28.2668i		0				199.648i		0		−342.054	+	25.4558i		0		−70.0140				0
97.7		0			−	24.6156i		0			−	63.1824i		0		−187.541	+	287.189i		0		123.070				0
97.8		0			−	24.6156i		0				63.1824i		0		187.541	+	287.189i		0		123.070				0
97.9		0			−	7.42258i		0			−	62.8792i		0		−29.5293	−	341.727i		0		673.905				0
97.10		0			−	7.42258i		0				62.8792i		0		29.5293	−	341.727i		0		673.905				0
97.11		0			−	6.07212i		0			−	159.761i		0		342.836	+	10.5965i		0		692.129				0
97.12		0			−	6.07212i		0				159.761i		0		−342.836	+	10.5965i		0		692.129				0
97.13		0				6.07212i		0			−	159.761i		0		−342.836	−	10.5965i		0		692.129				0
97.14		0				6.07212i		0				159.761i		0		342.836	−	10.5965i		0		692.129				0
97.15		0				7.42258i		0			−	62.8792i		0		29.5293	+	341.727i		0		673.905				0
97.16		0				7.42258i		0				62.8792i		0		−29.5293	+	341.727i		0		673.905				0
97.17		0				24.6156i		0			−	63.1824i		0		187.541	−	287.189i		0		123.070				0
97.18		0				24.6156i		0				63.1824i		0		−187.541	−	287.189i		0		123.070				0
97.19		0				28.2668i		0			−	199.648i		0		−342.054	−	25.4558i		0		−70.0140				0
97.20		0				28.2668i		0				199.648i		0		342.054	−	25.4558i		0		−70.0140				0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
4.b	odd	2	1	inner
7.b	odd	2	1	inner
28.d	even	2	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	224.7.c.b	✓	24
4.b	odd	2	1	inner	224.7.c.b	✓	24
7.b	odd	2	1	inner	224.7.c.b	✓	24
8.b	even	2	1		448.7.c.l		24
8.d	odd	2	1		448.7.c.l		24
28.d	even	2	1	inner	224.7.c.b	✓	24
56.e	even	2	1		448.7.c.l		24
56.h	odd	2	1		448.7.c.l		24

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
224.7.c.b	✓	24	1.a	even	1	1	trivial
224.7.c.b	✓	24	4.b	odd	2	1	inner
224.7.c.b	✓	24	7.b	odd	2	1	inner
224.7.c.b	✓	24	28.d	even	2	1	inner
448.7.c.l		24	8.b	even	2	1
448.7.c.l		24	8.d	odd	2	1
448.7.c.l		24	56.e	even	2	1
448.7.c.l		24	56.h	odd	2	1