Newform orbit 1001.2.b.a

• Label: 1001.2.b.a
• 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.a	✓	48
7.b	odd	2	1		1001.2.b.b	yes	48
11.b	odd	2	1		1001.2.b.b	yes	48
77.b	even	2	1	inner	1001.2.b.a	✓	48

    

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