Newform orbit 211.3.b.b

• Label: 211.3.b.b
• Level: $211$
• Weight: $3$
• Character orbit: 211.b
• Analytic conductor: $5.749$
• Analytic rank: $0$
• Dimension: $32$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 211 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	211.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(5.74933357800\)
Analytic rank:	\(0\)
Dimension:	\(32\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 32 q - 84 q^{4} - 2 q^{5} - 20 q^{6} - 118 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
210.1		−	3.91059i		−	1.76044i	−11.2927			−0.831508			−6.88437					7.56472i			28.5189i	5.90085					3.25169i
210.2		−	3.46445i		−	4.68340i	−8.00240			−3.73589			−16.2254				−	6.67151i			13.8661i	−12.9343					12.9428i
210.3		−	3.46099i		−	0.744038i	−7.97846			7.43782			−2.57511				−	12.7309i			13.7694i	8.44641				−	25.7422i
210.4		−	3.41292i			5.38725i	−7.64800			−0.732162			18.3862				−	3.58844i			12.4503i	−20.0225					2.49881i
210.5		−	3.26686i			2.08897i	−6.67236			4.85118			6.82438					3.18428i			8.73022i	4.63619				−	15.8481i
210.6		−	3.21518i			2.30873i	−6.33740			−6.14014			7.42298					7.27634i			7.51516i	3.66978					19.7417i
210.7		−	2.83262i		−	5.60721i	−4.02376			8.47065			−15.8831					4.54838i			0.0673085i	−22.4408				−	23.9942i
210.8		−	2.67925i		−	2.48703i	−3.17838			−6.26495			−6.66338				−	2.23696i		−	2.20133i	2.81467					16.7854i
210.9		−	2.22707i			2.16463i	−0.959848			−5.78042			4.82079				−	6.78348i		−	6.77064i	4.31437					12.8734i
210.10		−	1.98819i		−	1.95057i	0.0470850			2.20605			−3.87811				−	2.26767i		−	8.04639i	5.19528				−	4.38605i
210.11		−	1.78936i		−	1.08406i	0.798176			3.93878			−1.93978					12.7502i		−	8.58568i	7.82481				−	7.04791i
210.12		−	1.61542i			4.58375i	1.39043			7.19021			7.40467					0.110417i		−	8.70779i	−12.0108				−	11.6152i
210.13		−	1.22244i			3.54198i	2.50564			−4.86203			4.32986					11.8298i		−	7.95275i	−3.54564					5.94353i
210.14		−	1.06734i			3.07492i	2.86079			0.524792			3.28199				−	11.7812i		−	7.32279i	−0.455158				−	0.560131i
210.15		−	1.06480i		−	5.35653i	2.86620			−8.34820			−5.70363					9.41942i		−	7.31112i	−19.6925					8.88915i
210.16		−	0.612358i		−	4.43855i	3.62502			1.07582			−2.71798				−	5.13183i		−	4.66924i	−10.7007				−	0.658787i
210.17			0.612358i			4.43855i	3.62502			1.07582			−2.71798					5.13183i			4.66924i	−10.7007					0.658787i
210.18			1.06480i			5.35653i	2.86620			−8.34820			−5.70363				−	9.41942i			7.31112i	−19.6925				−	8.88915i
210.19			1.06734i		−	3.07492i	2.86079			0.524792			3.28199					11.7812i			7.32279i	−0.455158					0.560131i
210.20			1.22244i		−	3.54198i	2.50564			−4.86203			4.32986				−	11.8298i			7.95275i	−3.54564				−	5.94353i

Inner twists

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

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	211.3.b.b	✓	32
211.b	odd	2	1	inner	211.3.b.b	✓	32

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
211.3.b.b	✓	32	1.a	even	1	1	trivial
211.3.b.b	✓	32	211.b	odd	2	1	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T2^32 + 106*T2^30 + 5090*T2^28 + 146552*T2^26 + 2822585*T2^24 + 38419059*T2^22 + 380730009*T2^20 + 2789430385*T2^18 + 15193410970*T2^16 + 61389434472*T2^14 + 182295516884*T2^12 + 391065529578*T2^10 + 589797912561*T2^8 + 599485250747*T2^6 + 383202172465*T2^4 + 135416252461*T2^2 + 19294710075