Newform orbit 380.2.bh.a

• Label: 380.2.bh.a
• Level: $380$
• Weight: $2$
• Character orbit: 380.bh
• Analytic conductor: $3.034$
• Analytic rank: $0$
• Dimension: $120$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	380.bh (of order \(36\), degree \(12\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(3.03431527681\)
Analytic rank:	\(0\)
Dimension:	\(120\)
Relative dimension:	\(10\) over \(\Q(\zeta_{36})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 120 q + 6 q^{7}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
13.1		0		−2.74765	+	1.28125i		0		−1.16017	−	1.91154i		0		−0.370262	−	1.38184i		0		3.97961	−	4.74272i		0
13.2		0		−2.38123	+	1.11039i		0		1.56340	+	1.59868i		0		0.558906	+	2.08587i		0		2.50894	−	2.99004i		0
13.3		0		−1.41596	+	0.660272i		0		−0.949889	+	2.02428i		0		−1.12143	−	4.18524i		0		−0.359387	+	0.428300i		0
13.4		0		−0.927188	+	0.432355i		0		0.140904	−	2.23162i		0		−0.231730	−	0.864827i		0		−1.25562	+	1.49639i		0
13.5		0		−0.362674	+	0.169118i		0		1.57660	−	1.58566i		0		1.00773	+	3.76091i		0		−1.82543	+	2.17546i		0
13.6		0		0.224420	−	0.104649i		0		−2.15088	+	0.611320i		0		0.357605	+	1.33460i		0		−1.88895	+	2.25116i		0
13.7		0		0.959290	−	0.447324i		0		1.57989	+	1.58239i		0		0.204631	+	0.763694i		0		−1.20823	+	1.43991i		0
13.8		0		1.80092	−	0.839782i		0		−1.74340	−	1.40020i		0		−0.755503	−	2.81958i		0		0.609708	−	0.726622i		0
13.9		0		1.84872	−	0.862074i		0		2.22179	+	0.252247i		0		−1.05366	−	3.93231i		0		0.746246	−	0.889341i		0
13.10		0		3.00135	−	1.39955i		0		−0.904597	+	2.04492i		0		1.03769	+	3.87270i		0		5.12098	−	6.10295i		0
33.1		0		−1.61138	−	2.30128i		0		1.99179	−	1.01625i		0		4.91485	+	1.31693i		0		−1.67331	+	4.59739i		0
33.2		0		−1.41957	−	2.02735i		0		0.187939	−	2.22816i		0		−3.90736	−	1.04697i		0		−1.06893	+	2.93686i		0
33.3		0		−1.02333	−	1.46147i		0		0.710865	+	2.12006i		0		−2.65380	−	0.711084i		0		−0.0626300	+	0.172074i		0
33.4		0		−0.886233	−	1.26567i		0		−2.22818	−	0.187668i		0		0.477272	+	0.127885i		0		0.209544	−	0.575718i		0
33.5		0		0.0411373	+	0.0587502i		0		−2.20598	+	0.365568i		0		0.553309	+	0.148259i		0		1.02430	−	2.81424i		0
33.6		0		0.230238	+	0.328814i		0		−0.244120	−	2.22270i		0		1.71755	+	0.460216i		0		0.970951	−	2.66767i		0
33.7		0		0.377219	+	0.538725i		0		2.02714	+	0.943776i		0		1.97160	+	0.528288i		0		0.878130	−	2.41264i		0
33.8		0		0.935220	+	1.33563i		0		−0.351064	+	2.20834i		0		−4.10912	−	1.10104i		0		0.116783	−	0.320859i		0
33.9		0		1.60791	+	2.29633i		0		1.74139	−	1.40270i		0		−0.546238	−	0.146364i		0		−1.66171	+	4.56550i		0
33.10		0		1.74879	+	2.49753i		0		−0.863736	+	2.06251i		0		2.94797	+	0.789905i		0		−2.15333	+	5.91624i		0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
5.c	odd	4	1	inner
19.f	odd	18	1	inner
95.r	even	36	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	380.2.bh.a	✓	120
5.c	odd	4	1	inner	380.2.bh.a	✓	120
19.f	odd	18	1	inner	380.2.bh.a	✓	120
95.r	even	36	1	inner	380.2.bh.a	✓	120

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
380.2.bh.a	✓	120	1.a	even	1	1	trivial
380.2.bh.a	✓	120	5.c	odd	4	1	inner
380.2.bh.a	✓	120	19.f	odd	18	1	inner
380.2.bh.a	✓	120	95.r	even	36	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(380, [\chi])\).