Newform orbit 1407.2.e.b

• Label: 1407.2.e.b
• Level: $1407$
• Weight: $2$
• Character orbit: 1407.e
• Analytic conductor: $11.235$
• Analytic rank: $0$
• Dimension: $46$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 1407 = 3 \cdot 7 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1407.e (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(11.2349515644\)
Analytic rank:	\(0\)
Dimension:	\(46\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 46 q + 46 q^{3} - 46 q^{4} - 6 q^{7} + 46 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
937.1		−	2.78884i	1.00000			−5.77764			−2.13647				−	2.78884i	−0.813425	−	2.51761i			10.5352i	1.00000					5.95827i
937.2		−	2.67366i	1.00000			−5.14844			4.03783				−	2.67366i	−2.47046	+	0.947001i			8.41783i	1.00000				−	10.7958i
937.3		−	2.56749i	1.00000			−4.59198			−2.13450				−	2.56749i	2.08243	+	1.63202i			6.65488i	1.00000					5.48030i
937.4		−	2.42738i	1.00000			−3.89216			0.379936				−	2.42738i	−2.37494	+	1.16604i			4.59299i	1.00000				−	0.922249i
937.5		−	2.33804i	1.00000			−3.46641			2.08152				−	2.33804i	−1.41631	−	2.23474i			3.42853i	1.00000				−	4.86668i
937.6		−	2.25748i	1.00000			−3.09620			−2.44886				−	2.25748i	2.13257	−	1.56593i			2.47466i	1.00000					5.52824i
937.7		−	2.19211i	1.00000			−2.80536			2.89043				−	2.19211i	0.673476	−	2.55860i			1.76544i	1.00000				−	6.33615i
937.8		−	2.14247i	1.00000			−2.59019			−2.51236				−	2.14247i	−2.48942	+	0.895981i			1.26447i	1.00000					5.38267i
937.9		−	2.11449i	1.00000			−2.47105			−0.183439				−	2.11449i	0.727204	+	2.54385i			0.996022i	1.00000					0.387879i
937.10		−	1.75744i	1.00000			−1.08859			3.53779				−	1.75744i	2.54755	+	0.714129i		−	1.60175i	1.00000				−	6.21744i
937.11		−	1.64010i	1.00000			−0.689932			1.28389				−	1.64010i	0.0425916	+	2.64541i		−	2.14864i	1.00000				−	2.10571i
937.12		−	1.60463i	1.00000			−0.574822			−1.12942				−	1.60463i	2.40455	−	1.10369i		−	2.28688i	1.00000					1.81229i
937.13		−	1.53470i	1.00000			−0.355318			−2.95745				−	1.53470i	−2.23847	−	1.41041i		−	2.52410i	1.00000					4.53881i
937.14		−	1.49509i	1.00000			−0.235308			1.47577				−	1.49509i	−0.341265	−	2.62365i		−	2.63838i	1.00000				−	2.20642i
937.15		−	1.15787i	1.00000			0.659342			−3.28697				−	1.15787i	0.238698	+	2.63496i		−	3.07917i	1.00000					3.80588i
937.16		−	0.845327i	1.00000			1.28542			2.35263				−	0.845327i	−2.63686	+	0.216699i		−	2.77726i	1.00000				−	1.98874i
937.17		−	0.714652i	1.00000			1.48927			2.52700				−	0.714652i	−2.05794	+	1.66279i		−	2.49362i	1.00000				−	1.80592i
937.18		−	0.697032i	1.00000			1.51415			0.989357				−	0.697032i	2.63355	+	0.253816i		−	2.44947i	1.00000				−	0.689614i
937.19		−	0.684769i	1.00000			1.53109			−4.07721				−	0.684769i	2.36728	−	1.18151i		−	2.41798i	1.00000					2.79195i
937.20		−	0.676356i	1.00000			1.54254			−1.23812				−	0.676356i	−2.06634	−	1.65235i		−	2.39602i	1.00000					0.837412i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
469.c	even	2	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	1407.2.e.b	yes	46
7.b	odd	2	1		1407.2.e.a	✓	46
67.b	odd	2	1		1407.2.e.a	✓	46
469.c	even	2	1	inner	1407.2.e.b	yes	46

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
1407.2.e.a	✓	46	7.b	odd	2	1
1407.2.e.a	✓	46	67.b	odd	2	1
1407.2.e.b	yes	46	1.a	even	1	1	trivial
1407.2.e.b	yes	46	469.c	even	2	1	inner