Newform orbit 855.2.bd.b

• Label: 855.2.bd.b
• Level: $855$
• Weight: $2$
• Character orbit: 855.bd
• Analytic conductor: $6.827$
• Analytic rank: $0$
• Dimension: $64$
• CM: no
• Inner twists: $8$

Newspace parameters

Level:	\( N \)	\(=\)	\( 855 = 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	855.bd (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(6.82720937282\)
Analytic rank:	\(0\)
Dimension:	\(64\)
Relative dimension:	\(32\) over \(\Q(\zeta_{6})\)
Twist minimal:	yes
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.

\(\operatorname{Tr}(f)(q) = \) \( 64 q + 32 q^{4}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
179.1	−2.26225	−	1.30611i		0		2.41186	+	4.17746i	−2.09471	−	0.782428i		0			−	5.02675i		−	7.37618i		0		3.71682	+	4.50598i
179.2	−2.26225	−	1.30611i		0		2.41186	+	4.17746i	1.72496	+	1.42286i		0				5.02675i		−	7.37618i		0		−2.04388	−	5.47185i
179.3	−1.94074	−	1.12049i		0		1.51098	+	2.61710i	−2.21695	−	0.291796i		0				3.33650i		−	2.29019i		0		3.97556	+	3.05036i
179.4	−1.94074	−	1.12049i		0		1.51098	+	2.61710i	1.36118	+	1.77403i		0			−	3.33650i		−	2.29019i		0		−0.653908	−	4.96812i
179.5	−1.89356	−	1.09325i		0		1.39038	+	2.40822i	−1.61298	+	1.54864i		0				3.11972i		−	1.70715i		0		4.74733	−	1.16906i
179.6	−1.89356	−	1.09325i		0		1.39038	+	2.40822i	−0.534671	+	2.17120i		0			−	3.11972i		−	1.70715i		0		3.38610	−	3.52678i
179.7	−1.39467	−	0.805210i		0		0.296727	+	0.513947i	−0.118176	−	2.23294i		0				1.53368i			2.26513i		0		−1.63317	+	3.20936i
179.8	−1.39467	−	0.805210i		0		0.296727	+	0.513947i	1.99287	−	1.01413i		0			−	1.53368i			2.26513i		0		−3.59598	−	0.190314i
179.9	−1.28088	−	0.739517i		0		0.0937695	+	0.162414i	−2.08817	−	0.799720i		0			−	1.42659i			2.68069i		0		2.08329	+	2.56858i
179.10	−1.28088	−	0.739517i		0		0.0937695	+	0.162414i	1.73666	+	1.40855i		0				1.42659i			2.68069i		0		−1.18281	−	3.08847i
179.11	−1.16898	−	0.674911i		0		−0.0889909	−	0.154137i	−1.41132	−	1.73441i		0			−	1.42537i			2.93989i		0		0.479226	+	2.98001i
179.12	−1.16898	−	0.674911i		0		−0.0889909	−	0.154137i	2.20770	+	0.355029i		0				1.42537i			2.93989i		0		−2.34115	−	1.90502i
179.13	−0.738238	−	0.426222i		0		−0.636670	−	1.10275i	−1.97340	+	1.05152i		0			−	1.90300i			2.79034i		0		1.90502	+	0.0648331i
179.14	−0.738238	−	0.426222i		0		−0.636670	−	1.10275i	0.0760556	+	2.23477i		0				1.90300i			2.79034i		0		0.896362	−	1.68221i
179.15	−0.181415	−	0.104740i		0		−0.978059	−	1.69405i	0.217972	−	2.22542i		0			−	2.41379i			0.828726i		0		−0.272633	+	0.380893i
179.16	−0.181415	−	0.104740i		0		−0.978059	−	1.69405i	1.81828	−	1.30148i		0				2.41379i			0.828726i		0		−0.466180	+	0.0456606i
179.17	0.181415	+	0.104740i		0		−0.978059	−	1.69405i	−1.81828	+	1.30148i		0				2.41379i		−	0.828726i		0		−0.466180	+	0.0456606i
179.18	0.181415	+	0.104740i		0		−0.978059	−	1.69405i	−0.217972	+	2.22542i		0			−	2.41379i		−	0.828726i		0		−0.272633	+	0.380893i
179.19	0.738238	+	0.426222i		0		−0.636670	−	1.10275i	−0.0760556	−	2.23477i		0				1.90300i		−	2.79034i		0		0.896362	−	1.68221i
179.20	0.738238	+	0.426222i		0		−0.636670	−	1.10275i	1.97340	−	1.05152i		0			−	1.90300i		−	2.79034i		0		1.90502	+	0.0648331i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	inner
5.b	even	2	1	inner
15.d	odd	2	1	inner
19.d	odd	6	1	inner
57.f	even	6	1	inner
95.h	odd	6	1	inner
285.q	even	6	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	855.2.bd.b	✓	64
3.b	odd	2	1	inner	855.2.bd.b	✓	64
5.b	even	2	1	inner	855.2.bd.b	✓	64
15.d	odd	2	1	inner	855.2.bd.b	✓	64
19.d	odd	6	1	inner	855.2.bd.b	✓	64
57.f	even	6	1	inner	855.2.bd.b	✓	64
95.h	odd	6	1	inner	855.2.bd.b	✓	64
285.q	even	6	1	inner	855.2.bd.b	✓	64

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
855.2.bd.b	✓	64	1.a	even	1	1	trivial
855.2.bd.b	✓	64	3.b	odd	2	1	inner
855.2.bd.b	✓	64	5.b	even	2	1	inner
855.2.bd.b	✓	64	15.d	odd	2	1	inner
855.2.bd.b	✓	64	19.d	odd	6	1	inner
855.2.bd.b	✓	64	57.f	even	6	1	inner
855.2.bd.b	✓	64	95.h	odd	6	1	inner
855.2.bd.b	✓	64	285.q	even	6	1	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T2^32 - 24*T2^30 + 343*T2^28 - 3232*T2^26 + 22620*T2^24 - 119490*T2^22 + 493465*T2^20 - 1586058*T2^18 + 4021672*T2^16 - 7902824*T2^14 + 12021633*T2^12 - 13497670*T2^10 + 10962559*T2^8 - 5511534*T2^6 + 1755090*T2^4 - 76140*T2^2 + 2916