Newform orbit 48.22.c.c

• Label: 48.22.c.c
• Level: $48$
• Weight: $22$
• Character orbit: 48.c
• Analytic conductor: $134.149$
• Analytic rank: $0$
• Dimension: $28$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 48 = 2^{4} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 22 \)
Character orbit:	\([\chi]\)	\(=\)	48.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(134.149125258\)
Analytic rank:	\(0\)
Dimension:	\(28\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 28 q + 109254828 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
47.1		0		−102247.	−	2435.85i		0			−	1.44607e7i		0				1.26694e9i		0		1.04485e10	+	4.98117e8i		0
47.2		0		−102247.	+	2435.85i		0				1.44607e7i		0			−	1.26694e9i		0		1.04485e10	−	4.98117e8i		0
47.3		0		−102214.	−	3563.40i		0				3.58965e7i		0			−	2.03455e8i		0		1.04350e10	+	7.28456e8i		0
47.4		0		−102214.	+	3563.40i		0			−	3.58965e7i		0				2.03455e8i		0		1.04350e10	−	7.28456e8i		0
47.5		0		−87580.8	−	52820.0i		0				2.44170e7i		0				1.13340e9i		0		4.88046e9	+	9.25203e9i		0
47.6		0		−87580.8	+	52820.0i		0			−	2.44170e7i		0			−	1.13340e9i		0		4.88046e9	−	9.25203e9i		0
47.7		0		−66724.2	−	77512.8i		0			−	3.35931e6i		0			−	5.38569e8i		0		−1.55613e9	+	1.03440e10i		0
47.8		0		−66724.2	+	77512.8i		0				3.35931e6i		0				5.38569e8i		0		−1.55613e9	−	1.03440e10i		0
47.9		0		−51369.6	−	88439.3i		0			−	1.40544e6i		0			−	5.11154e8i		0		−5.18267e9	+	9.08619e9i		0
47.10		0		−51369.6	+	88439.3i		0				1.40544e6i		0				5.11154e8i		0		−5.18267e9	−	9.08619e9i		0
47.11		0		−31002.5	−	97463.8i		0			−	2.82711e7i		0				1.02999e8i		0		−8.53805e9	+	6.04324e9i		0
47.12		0		−31002.5	+	97463.8i		0				2.82711e7i		0			−	1.02999e8i		0		−8.53805e9	−	6.04324e9i		0
47.13		0		−554.307	−	102274.i		0				3.49802e7i		0				7.47725e8i		0		−1.04597e10	+	1.13383e8i		0
47.14		0		−554.307	+	102274.i		0			−	3.49802e7i		0			−	7.47725e8i		0		−1.04597e10	−	1.13383e8i		0
47.15		0		554.307	−	102274.i		0			−	3.49802e7i		0				7.47725e8i		0		−1.04597e10	−	1.13383e8i		0
47.16		0		554.307	+	102274.i		0				3.49802e7i		0			−	7.47725e8i		0		−1.04597e10	+	1.13383e8i		0
47.17		0		31002.5	−	97463.8i		0				2.82711e7i		0				1.02999e8i		0		−8.53805e9	−	6.04324e9i		0
47.18		0		31002.5	+	97463.8i		0			−	2.82711e7i		0			−	1.02999e8i		0		−8.53805e9	+	6.04324e9i		0
47.19		0		51369.6	−	88439.3i		0				1.40544e6i		0			−	5.11154e8i		0		−5.18267e9	−	9.08619e9i		0
47.20		0		51369.6	+	88439.3i		0			−	1.40544e6i		0				5.11154e8i		0		−5.18267e9	+	9.08619e9i		0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	inner
4.b	odd	2	1	inner
12.b	even	2	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	48.22.c.c	✓	28
3.b	odd	2	1	inner	48.22.c.c	✓	28
4.b	odd	2	1	inner	48.22.c.c	✓	28
12.b	even	2	1	inner	48.22.c.c	✓	28

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
48.22.c.c	✓	28	1.a	even	1	1	trivial
48.22.c.c	✓	28	3.b	odd	2	1	inner
48.22.c.c	✓	28	4.b	odd	2	1	inner
48.22.c.c	✓	28	12.b	even	2	1	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T5^14 + 4129992029107296*T5^12 + 6430550742981469053997846686720*T5^10 + 4644320034870755751942495044012886947057664000*T5^8 + 1522323129560335693749907221420552195832567987540131840000000*T5^6 + 176591975808541278280303754764778128993886481995011737031940505600000000000*T5^4 + 2115866952056740817319392262702919908168665701797145861187071379281281024000000000000000*T5^2 + 3502047175395813142970832655803184740064568197469238539474108934281469622977822720000000000000000000