Newform orbit 763.2.c.b

• Label: 763.2.c.b
• Level: $763$
• Weight: $2$
• Character orbit: 763.c
• Analytic conductor: $6.093$
• Analytic rank: $0$
• Dimension: $28$
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 763 = 7 \cdot 109 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	763.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(6.09258567422\)
Analytic rank:	\(0\)
Dimension:	\(28\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

$q$-expansion

The algebraic \(q\)-expansion of this newform has not been computed, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 28 q - 18 q^{4} + 2 q^{5} - 28 q^{7} + 28 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
435.1		−	2.72335i	−2.24541			−5.41663			−0.508233					6.11503i	−1.00000					9.30468i	2.04186					1.38410i
435.2		−	2.60208i	1.74623			−4.77080			−2.83819				−	4.54382i	−1.00000					7.20983i	0.0493198					7.38520i
435.3		−	2.03111i	1.16381			−2.12542			−0.790334				−	2.36383i	−1.00000					0.254743i	−1.64555					1.60526i
435.4		−	2.03010i	−0.527316			−2.12129			1.66866					1.07050i	−1.00000					0.246225i	−2.72194				−	3.38754i
435.5		−	2.01326i	2.92249			−2.05321			2.30449				−	5.88374i	−1.00000					0.107119i	5.54098				−	4.63954i
435.6		−	1.74938i	−1.50489			−1.06034			−3.61345					2.63263i	−1.00000				−	1.64382i	−0.735304					6.32131i
435.7		−	1.69948i	−3.20546			−0.888226			3.89077					5.44761i	−1.00000				−	1.88944i	7.27497				−	6.61227i
435.8		−	1.40921i	1.77451			0.0141177			1.75083				−	2.50066i	−1.00000				−	2.83832i	0.148878				−	2.46729i
435.9		−	1.13244i	−0.497369			0.717586			−1.01001					0.563239i	−1.00000				−	3.07750i	−2.75262					1.14377i
435.10		−	0.626400i	0.950191			1.60762			−3.22959				−	0.595200i	−1.00000				−	2.25982i	−2.09714					2.02301i
435.11		−	0.602737i	3.01902			1.63671			−0.478153				−	1.81967i	−1.00000				−	2.19198i	6.11448					0.288201i
435.12		−	0.524750i	−1.68921			1.72464			1.57634					0.886415i	−1.00000				−	1.95450i	−0.146554				−	0.827182i
435.13		−	0.493199i	−2.83891			1.75675			−1.68559					1.40015i	−1.00000				−	1.85283i	5.05941					0.831329i
435.14		−	0.146670i	0.932315			1.97849			3.96246				−	0.136743i	−1.00000				−	0.583524i	−2.13079				−	0.581174i
435.15			0.146670i	0.932315			1.97849			3.96246					0.136743i	−1.00000					0.583524i	−2.13079					0.581174i
435.16			0.493199i	−2.83891			1.75675			−1.68559				−	1.40015i	−1.00000					1.85283i	5.05941				−	0.831329i
435.17			0.524750i	−1.68921			1.72464			1.57634				−	0.886415i	−1.00000					1.95450i	−0.146554					0.827182i
435.18			0.602737i	3.01902			1.63671			−0.478153					1.81967i	−1.00000					2.19198i	6.11448				−	0.288201i
435.19			0.626400i	0.950191			1.60762			−3.22959					0.595200i	−1.00000					2.25982i	−2.09714				−	2.02301i
435.20			1.13244i	−0.497369			0.717586			−1.01001				−	0.563239i	−1.00000					3.07750i	−2.75262				−	1.14377i

Inner twists

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

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	763.2.c.b	✓	28
109.b	even	2	1	inner	763.2.c.b	✓	28

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
763.2.c.b	✓	28	1.a	even	1	1	trivial
763.2.c.b	✓	28	109.b	even	2	1	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T2^28 + 37*T2^26 + 597*T2^24 + 5534*T2^22 + 32672*T2^20 + 128663*T2^18 + 343998*T2^16 + 623721*T2^14 + 754582*T2^12 + 591611*T2^10 + 289275*T2^8 + 84422*T2^6 + 13599*T2^4 + 1000*T2^2 + 16