Newform orbit 232.2.q.a

• Label: 232.2.q.a
• Level: $232$
• Weight: $2$
• Character orbit: 232.q
• Analytic conductor: $1.853$
• Analytic rank: $0$
• Dimension: $48$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 232 = 2^{3} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	232.q (of order \(14\), degree \(6\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(1.85252932689\)
Analytic rank:	\(0\)
Dimension:	\(48\)
Relative dimension:	\(8\) over \(\Q(\zeta_{14})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 48 q - 2 q^{5} - 4 q^{7} + 6 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
9.1		0		−2.39252	+	1.90797i		0		−1.10330	+	0.531322i		0		−0.889636	−	1.11557i		0		1.41624	−	6.20496i		0
9.2		0		−1.79043	+	1.42782i		0		2.68076	−	1.29099i		0		0.839902	+	1.05320i		0		0.499400	−	2.18801i		0
9.3		0		−0.728009	+	0.580567i		0		−2.19459	+	1.05686i		0		−0.988136	−	1.23908i		0		−0.474625	+	2.07947i		0
9.4		0		−0.212201	+	0.169225i		0		−1.28207	+	0.617411i		0		1.27595	+	1.59999i		0		−0.651170	+	2.85296i		0
9.5		0		0.0131000	−	0.0104469i		0		3.41718	−	1.64563i		0		−3.15424	−	3.95529i		0		−0.667500	+	2.92451i		0
9.6		0		0.884679	−	0.705508i		0		0.449269	−	0.216356i		0		2.01029	+	2.52083i		0		−0.382647	+	1.67649i		0
9.7		0		1.96464	−	1.56675i		0		1.24505	−	0.599586i		0		1.40365	+	1.76012i		0		0.737555	−	3.23144i		0
9.8		0		2.26073	−	1.80288i		0		−0.608430	+	0.293004i		0		−2.74476	−	3.44182i		0		1.19300	−	5.22686i		0
33.1		0		−1.28436	−	2.66699i		0		0.805849	−	3.53066i		0		−1.47444	+	0.710053i		0		−3.59282	+	4.50525i		0
33.2		0		−1.19841	−	2.48852i		0		−0.882074	+	3.86462i		0		−3.53526	+	1.70249i		0		−2.88609	+	3.61904i		0
33.3		0		−0.661075	−	1.37274i		0		−0.510076	+	2.23479i		0		3.30380	−	1.59102i		0		0.423086	−	0.530533i		0
33.4		0		−0.186194	−	0.386637i		0		0.478397	−	2.09600i		0		−1.33207	+	0.641493i		0		1.75565	−	2.20152i		0
33.5		0		0.201238	+	0.417875i		0		−0.296646	+	1.29969i		0		2.78319	−	1.34032i		0		1.73635	−	2.17731i		0
33.6		0		0.846741	+	1.75828i		0		0.850744	−	3.72735i		0		2.85493	−	1.37486i		0		−0.504093	+	0.632112i		0
33.7		0		0.857903	+	1.78145i		0		−0.419644	+	1.83858i		0		−2.09267	+	1.00778i		0		−0.567114	+	0.711138i		0
33.8		0		1.42415	+	2.95728i		0		−0.136467	+	0.597901i		0		0.294470	−	0.141809i		0		−4.84685	+	6.07775i		0
121.1		0		−3.23807	+	0.739069i		0		−1.39730	−	1.75216i		0		0.718779	+	3.14918i		0		7.23599	−	3.48467i		0
121.2		0		−1.64676	+	0.375863i		0		−0.945962	−	1.18620i		0		0.445391	+	1.95139i		0		−0.132354	+	0.0637382i		0
121.3		0		−1.18604	+	0.270705i		0		1.84749	+	2.31668i		0		−0.161250	−	0.706484i		0		−1.36950	+	0.659517i		0
121.4		0		−1.15926	+	0.264594i		0		−0.233976	−	0.293397i		0		−0.933454	−	4.08973i		0		−1.42903	+	0.688186i		0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
29.e	even	14	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	232.2.q.a	✓	48
4.b	odd	2	1		464.2.y.e		48
29.e	even	14	1	inner	232.2.q.a	✓	48
29.f	odd	28	1		6728.2.a.be		24
29.f	odd	28	1		6728.2.a.bf		24
116.h	odd	14	1		464.2.y.e		48

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
232.2.q.a	✓	48	1.a	even	1	1	trivial
232.2.q.a	✓	48	29.e	even	14	1	inner
464.2.y.e		48	4.b	odd	2	1
464.2.y.e		48	116.h	odd	14	1
6728.2.a.be		24	29.f	odd	28	1
6728.2.a.bf		24	29.f	odd	28	1

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(232, [\chi])\).