Newform orbit 232.5.j.a

• Label: 232.5.j.a
• Level: $232$
• Weight: $5$
• Character orbit: 232.j
• Analytic conductor: $23.982$
• Analytic rank: $0$
• Dimension: $30$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 232 = 2^{3} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	232.j (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(23.9818314355\)
Analytic rank:	\(0\)
Dimension:	\(30\)
Relative dimension:	\(15\) over \(\Q(i)\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 30 q - 16 q^{3} + 96 q^{7}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
17.1		0		−11.8570	+	11.8570i		0				31.9894i		0		−82.2327				0			−	200.178i		0
17.2		0		−9.56376	+	9.56376i		0				14.0712i		0		45.3270				0			−	101.931i		0
17.3		0		−9.45823	+	9.45823i		0			−	40.7263i		0		−7.09414				0			−	97.9163i		0
17.4		0		−9.37185	+	9.37185i		0			−	12.7836i		0		57.3578				0			−	94.6630i		0
17.5		0		−4.72808	+	4.72808i		0			−	17.4984i		0		−73.2968				0				36.2905i		0
17.6		0		−3.68895	+	3.68895i		0				38.4087i		0		−8.89666				0				53.7832i		0
17.7		0		−2.53877	+	2.53877i		0				1.80324i		0		56.4986				0				68.1093i		0
17.8		0		−1.44306	+	1.44306i		0				19.5814i		0		−11.8564				0				76.8352i		0
17.9		0		2.47186	−	2.47186i		0			−	41.1820i		0		3.27122				0				68.7798i		0
17.10		0		2.58124	−	2.58124i		0			−	27.5547i		0		5.14627				0				67.6744i		0
17.11		0		5.45186	−	5.45186i		0			−	11.1560i		0		94.7001				0				21.5544i		0
17.12		0		7.21500	−	7.21500i		0				40.8231i		0		55.2371				0			−	23.1123i		0
17.13		0		7.45605	−	7.45605i		0			−	3.58644i		0		−83.2067				0			−	30.1855i		0
17.14		0		7.68658	−	7.68658i		0				23.9755i		0		−23.1407				0			−	37.1671i		0
17.15		0		11.7871	−	11.7871i		0			−	20.1650i		0		20.1860				0			−	196.873i		0
41.1		0		−11.8570	−	11.8570i		0			−	31.9894i		0		−82.2327				0				200.178i		0
41.2		0		−9.56376	−	9.56376i		0			−	14.0712i		0		45.3270				0				101.931i		0
41.3		0		−9.45823	−	9.45823i		0				40.7263i		0		−7.09414				0				97.9163i		0
41.4		0		−9.37185	−	9.37185i		0				12.7836i		0		57.3578				0				94.6630i		0
41.5		0		−4.72808	−	4.72808i		0				17.4984i		0		−73.2968				0			−	36.2905i		0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
29.c	odd	4	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	232.5.j.a	✓	30
29.c	odd	4	1	inner	232.5.j.a	✓	30

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
232.5.j.a	✓	30	1.a	even	1	1	trivial
232.5.j.a	✓	30	29.c	odd	4	1	inner