Newform orbit 671.2.c.a

• Label: 671.2.c.a
• Level: $671$
• Weight: $2$
• Character orbit: 671.c
• Analytic conductor: $5.358$
• Analytic rank: $0$
• Dimension: $52$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 671 = 11 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	671.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(5.35796197563\)
Analytic rank:	\(0\)
Dimension:	\(52\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 52 q + 4 q^{3} - 46 q^{4} + 44 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
243.1		−	2.63297i	−2.36979			−4.93252			−2.17160					6.23957i			0.610382i			7.72123i	2.61589					5.71774i
243.2		−	2.62169i	2.11987			−4.87326			−3.20754				−	5.55765i			3.91928i			7.53280i	1.49386					8.40917i
243.3		−	2.61102i	0.235196			−4.81744			1.96208				−	0.614102i		−	1.03120i			7.35640i	−2.94468				−	5.12303i
243.4		−	2.59649i	−0.654344			−4.74178			3.42486					1.69900i			3.69426i			7.11902i	−2.57183				−	8.89263i
243.5		−	2.55622i	3.17337			−4.53424			2.75037				−	8.11182i		−	1.58272i			6.47805i	7.07029				−	7.03053i
243.6		−	2.25711i	0.492207			−3.09455			−0.807025				−	1.11097i		−	3.09615i			2.47053i	−2.75773					1.82155i
243.7		−	2.24927i	2.53871			−3.05919			0.673508				−	5.71023i			2.16122i			2.38241i	3.44505				−	1.51490i
243.8		−	2.11254i	−0.282536			−2.46283			−0.276653					0.596869i			3.62481i			0.977749i	−2.92017					0.584442i
243.9		−	1.99163i	2.57151			−1.96657			−3.32751				−	5.12149i		−	2.02836i		−	0.0665784i	3.61268					6.62716i
243.10		−	1.91000i	−2.76324			−1.64808			−1.89976					5.27777i			4.14984i		−	0.672161i	4.63547					3.62854i
243.11		−	1.84971i	−2.33988			−1.42141			1.46414					4.32808i			0.831776i		−	1.07022i	2.47502				−	2.70823i
243.12		−	1.79229i	−0.857853			−1.21231			−4.20126					1.53752i		−	2.69374i		−	1.41177i	−2.26409					7.52988i
243.13		−	1.45158i	2.14579			−0.107079			1.18384				−	3.11478i		−	1.24262i		−	2.74772i	1.60440				−	1.71843i
243.14		−	1.40832i	−1.33929			0.0166459			0.666179					1.88614i			1.13912i		−	2.84007i	−1.20632				−	0.938191i
243.15		−	1.36842i	−0.881379			0.127429			4.27697					1.20610i		−	1.78127i		−	2.91121i	−2.22317				−	5.85269i
243.16		−	1.26529i	1.92995			0.399048			4.00045				−	2.44194i			4.74746i		−	3.03548i	0.724700				−	5.06172i
243.17		−	1.15791i	−0.124357			0.659243			0.927728					0.143994i		−	4.45290i		−	3.07917i	−2.98454				−	1.07423i
243.18		−	0.992653i	−3.29818			1.01464			−2.08442					3.27394i		−	2.40684i		−	2.99249i	7.87797					2.06910i
243.19		−	0.915688i	0.547336			1.16152			−3.25559				−	0.501189i			1.57444i		−	2.89496i	−2.70042					2.98110i
243.20		−	0.765140i	3.12278			1.41456			−0.808157				−	2.38936i		−	0.856237i		−	2.61262i	6.75173					0.618354i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
61.b	even	2	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	671.2.c.a	✓	52
61.b	even	2	1	inner	671.2.c.a	✓	52

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
671.2.c.a	✓	52	1.a	even	1	1	trivial
671.2.c.a	✓	52	61.b	even	2	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(671, [\chi])\).