Newform orbit 1001.2.b.b

• Label: 1001.2.b.b
• Level: $1001$
• Weight: $2$
• Character orbit: 1001.b
• Analytic conductor: $7.993$
• Analytic rank: $0$
• Dimension: $48$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 1001 = 7 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1001.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(7.99302524233\)
Analytic rank:	\(0\)
Dimension:	\(48\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 48 q - 46 q^{4} + 10 q^{6} - 4 q^{7} - 48 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
846.1		−	2.70677i			2.58444i	−5.32659					1.30127i	6.99548			−1.07726	−	2.41651i			9.00429i	−3.67933			3.52222
846.2		−	2.69435i		−	2.53899i	−5.25954					3.47887i	−6.84093			2.35943	+	1.19712i			8.78235i	−3.44646			9.37331
846.3		−	2.57349i		−	0.560659i	−4.62286					2.03999i	−1.44285			−2.50029	+	0.865194i			6.74991i	2.68566			5.24990
846.4		−	2.51095i			0.909245i	−4.30489				−	1.83189i	2.28307			0.00479527	+	2.64575i			5.78748i	2.17327			−4.59979
846.5		−	2.44531i		−	1.68626i	−3.97953				−	3.12189i	−4.12343			−2.62952	−	0.292574i			4.84056i	0.156514			−7.63399
846.6		−	2.30974i			3.07769i	−3.33489				−	0.269592i	7.10866			2.58007	+	0.585847i			3.08323i	−6.47218			−0.622687
846.7		−	2.10525i			1.36777i	−2.43210				−	4.19528i	2.87950			1.74298	−	1.99048i			0.909675i	1.12921			−8.83213
846.8		−	2.10226i			1.85504i	−2.41948					3.88247i	3.89978			−2.63907	+	0.187916i			0.881864i	−0.441182			8.16194
846.9		−	1.94253i		−	0.746295i	−1.77344				−	0.112572i	−1.44970			1.93976	+	1.79925i		−	0.440102i	2.44304			−0.218675
846.10		−	1.91786i		−	3.25959i	−1.67819				−	1.27273i	−6.25143			1.75707	+	1.97806i		−	0.617192i	−7.62492			−2.44092
846.11		−	1.81802i		−	1.66965i	−1.30519				−	1.63764i	−3.03546			−0.622604	−	2.57145i		−	1.26318i	0.212253			−2.97726
846.12		−	1.69518i			2.41423i	−0.873632				−	2.80865i	4.09254			−2.58885	−	0.545744i		−	1.90940i	−2.82848			−4.76117
846.13		−	1.65052i		−	0.153160i	−0.724206					1.39691i	−0.252793			1.78685	−	1.95120i		−	2.10572i	2.97654			2.30562
846.14		−	1.55498i			1.25244i	−0.417977					3.17718i	1.94753			1.17992	+	2.36808i		−	2.46002i	1.43139			4.94046
846.15		−	1.15019i			2.65253i	0.677059					0.315967i	3.05091			−1.21967	−	2.34785i		−	3.07913i	−4.03590			0.363423
846.16		−	0.904586i		−	0.336627i	1.18172					0.961688i	−0.304508			−2.63015	−	0.286875i		−	2.87814i	2.88668			0.869929
846.17		−	0.779676i			1.22435i	1.39211				−	2.03440i	0.954595			2.59885	−	0.495975i		−	2.64474i	1.50097			−1.58617
846.18		−	0.676381i		−	3.11479i	1.54251				−	3.73437i	−2.10679			−2.62062	+	0.363804i		−	2.39609i	−6.70195			−2.52586
846.19		−	0.595725i			1.95016i	1.64511				−	2.08347i	1.16176			−2.26900	+	1.36074i		−	2.17148i	−0.803122			−1.24117
846.20		−	0.595489i		−	0.528706i	1.64539					4.42121i	−0.314839			1.34849	−	2.27631i		−	2.17079i	2.72047			2.63278

Inner twists

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

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	1001.2.b.b	yes	48
7.b	odd	2	1		1001.2.b.a	✓	48
11.b	odd	2	1		1001.2.b.a	✓	48
77.b	even	2	1	inner	1001.2.b.b	yes	48

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
1001.2.b.a	✓	48	7.b	odd	2	1
1001.2.b.a	✓	48	11.b	odd	2	1
1001.2.b.b	yes	48	1.a	even	1	1	trivial
1001.2.b.b	yes	48	77.b	even	2	1	inner