Newform orbit 48.26.c.c

• Label: 48.26.c.c
• Level: $48$
• Weight: $26$
• Character orbit: 48.c
• Analytic conductor: $190.078$
• Analytic rank: $0$
• Dimension: $32$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 48 = 2^{4} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 26 \)
Character orbit:	\([\chi]\)	\(=\)	48.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(190.078454377\)
Analytic rank:	\(0\)
Dimension:	\(32\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 32 q + 3881794291104 q^{9}+O(q^{10}) \)

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		−920353.	−	15454.6i		0			−	3.79737e8i		0				1.78094e10i		0		8.46811e11	+	2.84475e10i		0
47.2		0		−920353.	+	15454.6i		0				3.79737e8i		0			−	1.78094e10i		0		8.46811e11	−	2.84475e10i		0
47.3		0		−874132.	−	288412.i		0				9.52315e8i		0				6.80483e10i		0		6.80925e11	+	5.04221e11i		0
47.4		0		−874132.	+	288412.i		0			−	9.52315e8i		0			−	6.80483e10i		0		6.80925e11	−	5.04221e11i		0
47.5		0		−810717.	−	435921.i		0			−	8.90954e8i		0			−	8.67077e9i		0		4.67235e11	+	7.06817e11i		0
47.6		0		−810717.	+	435921.i		0				8.90954e8i		0				8.67077e9i		0		4.67235e11	−	7.06817e11i		0
47.7		0		−750929.	−	532347.i		0				1.02779e7i		0			−	1.06568e10i		0		2.80501e11	+	7.99511e11i		0
47.8		0		−750929.	+	532347.i		0			−	1.02779e7i		0				1.06568e10i		0		2.80501e11	−	7.99511e11i		0
47.9		0		−716146.	−	578293.i		0			−	2.45023e8i		0				4.55185e10i		0		1.78442e11	+	8.28285e11i		0
47.10		0		−716146.	+	578293.i		0				2.45023e8i		0			−	4.55185e10i		0		1.78442e11	−	8.28285e11i		0
47.11		0		−686084.	−	613659.i		0				5.43780e8i		0			−	5.85379e10i		0		9.41337e10	+	8.42043e11i		0
47.12		0		−686084.	+	613659.i		0			−	5.43780e8i		0				5.85379e10i		0		9.41337e10	−	8.42043e11i		0
47.13		0		−231231.	−	890966.i		0			−	3.41554e8i		0				1.60809e10i		0		−7.40353e11	+	4.12038e11i		0
47.14		0		−231231.	+	890966.i		0				3.41554e8i		0			−	1.60809e10i		0		−7.40353e11	−	4.12038e11i		0
47.15		0		−70862.5	−	917751.i		0				9.79693e8i		0				2.11593e10i		0		−8.37246e11	+	1.30068e11i		0
47.16		0		−70862.5	+	917751.i		0			−	9.79693e8i		0			−	2.11593e10i		0		−8.37246e11	−	1.30068e11i		0
47.17		0		70862.5	−	917751.i		0			−	9.79693e8i		0				2.11593e10i		0		−8.37246e11	−	1.30068e11i		0
47.18		0		70862.5	+	917751.i		0				9.79693e8i		0			−	2.11593e10i		0		−8.37246e11	+	1.30068e11i		0
47.19		0		231231.	−	890966.i		0				3.41554e8i		0				1.60809e10i		0		−7.40353e11	−	4.12038e11i		0
47.20		0		231231.	+	890966.i		0			−	3.41554e8i		0			−	1.60809e10i		0		−7.40353e11	+	4.12038e11i		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	48.26.c.c	✓	32
3.b	odd	2	1	inner	48.26.c.c	✓	32
4.b	odd	2	1	inner	48.26.c.c	✓	32
12.b	even	2	1	inner	48.26.c.c	✓	32

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
48.26.c.c	✓	32	1.a	even	1	1	trivial
48.26.c.c	✓	32	3.b	odd	2	1	inner
48.26.c.c	✓	32	4.b	odd	2	1	inner
48.26.c.c	✓	32	12.b	even	2	1	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T5^16 + 3277199779259855616*T5^14 + 4120394522262466039671327991927142400*T5^12 + 2491248478870825275990620086134694826707845605376000000*T5^10 + 754449634898077186180942199963145397325070447150554185263482880000000000*T5^8 + 113851661851589604601098827434824629231759169904969662353707242198740599603200000000000000*T5^6 + 8049113753109336059528105041751494324794150705732714618202720406750507520041178086227968000000000000000000*T5^4 + 207195215230983546859390975555943210226434698867691435211023939806537637664479699826275195334391234560000000000000000000000*T5^2 + 21797410951896195899512531178223852562604327481100793548854161767142336088441575492259316673942560065164043878400000000000000000000000000