Newform orbit 1503.2.c.a

• Label: 1503.2.c.a
• Level: $1503$
• Weight: $2$
• Character orbit: 1503.c
• Analytic conductor: $12.002$
• Analytic rank: $0$
• Dimension: $56$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 1503 = 3^{2} \cdot 167 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1503.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(12.0015154238\)
Analytic rank:	\(0\)
Dimension:	\(56\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 56 q - 48 q^{4}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
1502.1		−	1.18160i		0		0.603817			−4.40626				0		−3.48779				−	3.07668i		0				5.20644i
1502.2			1.18160i		0		0.603817			−4.40626				0		−3.48779					3.07668i		0			−	5.20644i
1502.3		−	2.66906i		0		−5.12388			−3.16492				0		−0.263490					8.33782i		0				8.44736i
1502.4			2.66906i		0		−5.12388			−3.16492				0		−0.263490				−	8.33782i		0			−	8.44736i
1502.5		−	1.78744i		0		−1.19494			3.10541				0		3.91211				−	1.43899i		0			−	5.55073i
1502.6			1.78744i		0		−1.19494			3.10541				0		3.91211					1.43899i		0				5.55073i
1502.7		−	2.52227i		0		−4.36184			2.54201				0		2.74873					5.95720i		0			−	6.41163i
1502.8			2.52227i		0		−4.36184			2.54201				0		2.74873				−	5.95720i		0				6.41163i
1502.9		−	1.78653i		0		−1.19168			3.08210				0		4.41569				−	1.44408i		0			−	5.50625i
1502.10			1.78653i		0		−1.19168			3.08210				0		4.41569					1.44408i		0				5.50625i
1502.11		−	0.118553i		0		1.98595			3.37331				0		2.05489				−	0.472544i		0			−	0.399915i
1502.12			0.118553i		0		1.98595			3.37331				0		2.05489					0.472544i		0				0.399915i
1502.13		−	2.46644i		0		−4.08332			1.88017				0		−1.78260					5.13837i		0			−	4.63731i
1502.14			2.46644i		0		−4.08332			1.88017				0		−1.78260				−	5.13837i		0				4.63731i
1502.15		−	2.16730i		0		−2.69717			−1.88079				0		−3.73517					1.51098i		0				4.07624i
1502.16			2.16730i		0		−2.69717			−1.88079				0		−3.73517				−	1.51098i		0			−	4.07624i
1502.17		−	0.799957i		0		1.36007			−2.53587				0		−2.19364				−	2.68791i		0				2.02859i
1502.18			0.799957i		0		1.36007			−2.53587				0		−2.19364					2.68791i		0			−	2.02859i
1502.19		−	1.84274i		0		−1.39570			−1.15735				0		0.906437				−	1.11357i		0				2.13270i
1502.20			1.84274i		0		−1.39570			−1.15735				0		0.906437					1.11357i		0			−	2.13270i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	inner
167.b	odd	2	1	inner
501.c	even	2	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	1503.2.c.a	✓	56
3.b	odd	2	1	inner	1503.2.c.a	✓	56
167.b	odd	2	1	inner	1503.2.c.a	✓	56
501.c	even	2	1	inner	1503.2.c.a	✓	56

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
1503.2.c.a	✓	56	1.a	even	1	1	trivial
1503.2.c.a	✓	56	3.b	odd	2	1	inner
1503.2.c.a	✓	56	167.b	odd	2	1	inner
1503.2.c.a	✓	56	501.c	even	2	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(1503, [\chi])\).