Newform orbit 921.2.x.a

• Label: 921.2.x.a
• Level: $921$
• Weight: $2$
• Character orbit: 921.x
• Analytic conductor: $7.354$
• Analytic rank: $0$
• Dimension: $96$
• CM discriminant: -3
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 921 = 3 \cdot 307 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	921.x (of order \(306\), degree \(96\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(7.35422202616\)
Analytic rank:	\(0\)
Dimension:	\(96\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{U}(1)[D_{306}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 96 q - 6 q^{4} + 18 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
5.1		0		−1.16688	−	1.28000i	−0.664710	+	1.88631i		0			0		−1.93722	−	4.85205i		0		−0.276805	+	2.98720i		0
14.1		0		−0.911807	−	1.47262i	−1.98484	−	0.245777i		0			0		−3.74933	−	3.27957i		0		−1.33722	+	2.68549i		0
23.1		0		0.625689	+	1.61509i	−1.63239	+	1.15555i		0			0		−3.98250	+	1.93228i		0		−2.21703	+	2.02109i		0
29.1		0		−0.625689	+	1.61509i	1.81693	−	0.835921i		0			0		1.31128	−	1.81264i		0		−2.21703	−	2.02109i		0
47.1		0		−1.72466	+	0.159813i	0.306783	+	1.97633i		0			0		−3.92744	+	2.90303i		0		2.94892	−	0.551249i		0
50.1		0		1.55047	+	0.772041i	1.39227	−	1.43582i		0			0		5.28533	+	0.217172i		0		1.80790	+	2.39405i		0
56.1		0		0.318264	−	1.70256i	1.90588	+	0.606305i		0			0		−3.52542	+	3.78834i		0		−2.79742	−	1.08372i		0
59.1		0		1.66593	−	0.473998i	−1.10473	+	1.66720i		0			0		3.97961	−	2.24347i		0		2.55065	−	1.57930i		0
74.1		0		0.911807	+	1.47262i	0.779572	+	1.84181i		0			0		−2.47799	−	0.0508884i		0		−1.33722	+	2.68549i		0
80.1		0		1.16688	−	1.28000i	−1.30124	+	1.51881i		0			0		0.493554	+	1.49804i		0		−0.276805	−	2.98720i		0
92.1		0		−0.625689	+	1.61509i	1.81693	−	0.835921i		0			0		0.914150	+	2.04192i		0		−2.21703	−	2.02109i		0
95.1		0		1.16688	−	1.28000i	−1.30124	+	1.51881i		0			0		−1.54412	−	0.321591i		0		−0.276805	−	2.98720i		0
98.1		0		−1.72466	−	0.159813i	0.306783	−	1.97633i		0			0		−3.92744	−	2.90303i		0		2.94892	+	0.551249i		0
116.1		0		−1.55047	+	0.772041i	−1.93959	+	0.487827i		0			0		0.492718	+	0.380089i		0		1.80790	−	2.39405i		0
131.1		0		−1.72466	−	0.159813i	0.306783	−	1.97633i		0			0		−0.550381	+	4.85278i		0		2.94892	+	0.551249i		0
137.1		0		−0.625689	−	1.61509i	1.81693	+	0.835921i		0			0		−2.22543	+	0.229283i		0		−2.21703	+	2.02109i		0
143.1		0		1.72466	+	0.159813i	1.55816	+	1.25385i		0			0		0.308335	+	1.28141i		0		2.94892	+	0.551249i		0
161.1		0		1.66593	+	0.473998i	−1.10473	−	1.66720i		0			0		−3.93271	+	2.32471i		0		2.55065	+	1.57930i		0
173.1		0		−1.38221	+	1.04379i	0.0615901	+	1.99905i		0			0		1.31608	+	2.78494i		0		0.820989	−	2.88548i		0
185.1		0		−1.72466	+	0.159813i	0.306783	+	1.97633i		0			0		4.47782	+	1.94975i		0		2.94892	−	0.551249i		0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	CM by \(\Q(\sqrt{-3}) \)
307.l	odd	306	1	inner
921.x	even	306	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	921.2.x.a	✓	96
3.b	odd	2	1	CM	921.2.x.a	✓	96
307.l	odd	306	1	inner	921.2.x.a	✓	96
921.x	even	306	1	inner	921.2.x.a	✓	96

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
921.2.x.a	✓	96	1.a	even	1	1	trivial
921.2.x.a	✓	96	3.b	odd	2	1	CM
921.2.x.a	✓	96	307.l	odd	306	1	inner
921.2.x.a	✓	96	921.x	even	306	1	inner