Newform orbit 2002.2.c.a

• Label: 2002.2.c.a
• Level: $2002$
• Weight: $2$
• Character orbit: 2002.c
• Analytic conductor: $15.986$
• Analytic rank: $0$
• Dimension: $48$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 2002 = 2 \cdot 7 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2002.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(15.9860504847\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 48 q - 48 q^{4} - 8 q^{7} - 48 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
1847.1		−	1.00000i		−	3.36221i	−1.00000					3.29278i	−3.36221			−2.47244	+	0.941817i			1.00000i	−8.30444			3.29278
1847.2		−	1.00000i		−	2.92551i	−1.00000				−	4.07131i	−2.92551			0.0600807	+	2.64507i			1.00000i	−5.55863			−4.07131
1847.3		−	1.00000i		−	2.80296i	−1.00000				−	3.66969i	−2.80296			−1.34713	−	2.27711i			1.00000i	−4.85657			−3.66969
1847.4		−	1.00000i		−	2.29113i	−1.00000					3.41801i	−2.29113			2.07947	−	1.63579i			1.00000i	−2.24929			3.41801
1847.5		−	1.00000i		−	2.13268i	−1.00000					0.413386i	−2.13268			−0.100968	+	2.64382i			1.00000i	−1.54835			0.413386
1847.6		−	1.00000i		−	1.85438i	−1.00000					0.245055i	−1.85438			1.80002	+	1.93906i			1.00000i	−0.438736			0.245055
1847.7		−	1.00000i		−	1.76908i	−1.00000					1.20526i	−1.76908			−2.47342	−	0.939240i			1.00000i	−0.129628			1.20526
1847.8		−	1.00000i		−	1.25179i	−1.00000					0.655152i	−1.25179			−1.25426	−	2.32955i			1.00000i	1.43303			0.655152
1847.9		−	1.00000i		−	0.955484i	−1.00000				−	1.38977i	−0.955484			1.00844	−	2.44603i			1.00000i	2.08705			−1.38977
1847.10		−	1.00000i		−	0.636695i	−1.00000					3.96116i	−0.636695			−1.19783	+	2.35907i			1.00000i	2.59462			3.96116
1847.11		−	1.00000i		−	0.424566i	−1.00000				−	2.84129i	−0.424566			−2.16302	+	1.52360i			1.00000i	2.81974			−2.84129
1847.12		−	1.00000i		−	0.389687i	−1.00000					2.49031i	−0.389687			1.95763	−	1.77979i			1.00000i	2.84814			2.49031
1847.13		−	1.00000i		−	0.0955312i	−1.00000				−	0.882493i	−0.0955312			2.29173	+	1.32210i			1.00000i	2.99087			−0.882493
1847.14		−	1.00000i			0.0326469i	−1.00000				−	3.56973i	0.0326469			1.21421	−	2.35068i			1.00000i	2.99893			−3.56973
1847.15		−	1.00000i			0.802461i	−1.00000				−	0.569964i	0.802461			−2.62786	−	0.307150i			1.00000i	2.35606			−0.569964
1847.16		−	1.00000i			1.14174i	−1.00000					1.32439i	1.14174			0.668437	+	2.55992i			1.00000i	1.69644			1.32439
1847.17		−	1.00000i			1.51546i	−1.00000					2.93695i	1.51546			−2.33688	+	1.24055i			1.00000i	0.703367			2.93695
1847.18		−	1.00000i			1.80527i	−1.00000					3.01589i	1.80527			−2.24712	−	1.39658i			1.00000i	−0.258987			3.01589
1847.19		−	1.00000i			2.11185i	−1.00000				−	2.45312i	2.11185			1.53733	−	2.15328i			1.00000i	−1.45992			−2.45312
1847.20		−	1.00000i			2.45714i	−1.00000				−	2.27629i	2.45714			−1.65770	−	2.06205i			1.00000i	−3.03752			−2.27629

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	2002.2.c.a	✓	48
7.b	odd	2	1		2002.2.c.b	yes	48
11.b	odd	2	1		2002.2.c.b	yes	48
77.b	even	2	1	inner	2002.2.c.a	✓	48

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
2002.2.c.a	✓	48	1.a	even	1	1	trivial
2002.2.c.a	✓	48	77.b	even	2	1	inner
2002.2.c.b	yes	48	7.b	odd	2	1
2002.2.c.b	yes	48	11.b	odd	2	1