Newform orbit 1848.2.v.e

• Label: 1848.2.v.e
• Level: $1848$
• Weight: $2$
• Character orbit: 1848.v
• Analytic conductor: $14.756$
• Analytic rank: $0$
• Dimension: $32$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 1848 = 2^{3} \cdot 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1848.v (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(14.7563542935\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 32 q + 4 q^{7} + 4 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
881.1		0		−1.72051	−	0.199608i		0		3.94119				0		−0.792788	+	2.52418i		0		2.92031	+	0.686854i		0
881.2		0		−1.72051	+	0.199608i		0		3.94119				0		−0.792788	−	2.52418i		0		2.92031	−	0.686854i		0
881.3		0		−1.64966	−	0.527849i		0		−2.50380				0		2.27837	+	1.34501i		0		2.44275	+	1.74154i		0
881.4		0		−1.64966	+	0.527849i		0		−2.50380				0		2.27837	−	1.34501i		0		2.44275	−	1.74154i		0
881.5		0		−1.45288	−	0.942942i		0		−2.14239				0		0.721340	+	2.54552i		0		1.22172	+	2.73996i		0
881.6		0		−1.45288	+	0.942942i		0		−2.14239				0		0.721340	−	2.54552i		0		1.22172	−	2.73996i		0
881.7		0		−1.44336	−	0.957453i		0		0.755862				0		2.49060	+	0.892695i		0		1.16657	+	2.76390i		0
881.8		0		−1.44336	+	0.957453i		0		0.755862				0		2.49060	−	0.892695i		0		1.16657	−	2.76390i		0
881.9		0		−1.12980	−	1.31284i		0		−1.68437				0		−2.40047	+	1.11255i		0		−0.447111	+	2.96649i		0
881.10		0		−1.12980	+	1.31284i		0		−1.68437				0		−2.40047	−	1.11255i		0		−0.447111	−	2.96649i		0
881.11		0		−0.977486	−	1.42987i		0		2.44607				0		−0.368459	−	2.61997i		0		−1.08904	+	2.79535i		0
881.12		0		−0.977486	+	1.42987i		0		2.44607				0		−0.368459	+	2.61997i		0		−1.08904	−	2.79535i		0
881.13		0		−0.583380	−	1.63085i		0		4.22177				0		−1.21528	+	2.35012i		0		−2.31934	+	1.90281i		0
881.14		0		−0.583380	+	1.63085i		0		4.22177				0		−1.21528	−	2.35012i		0		−2.31934	−	1.90281i		0
881.15		0		−0.228186	−	1.71695i		0		1.84204				0		0.286690	−	2.63017i		0		−2.89586	+	0.783571i		0
881.16		0		−0.228186	+	1.71695i		0		1.84204				0		0.286690	+	2.63017i		0		−2.89586	−	0.783571i		0
881.17		0		0.228186	−	1.71695i		0		−1.84204				0		0.286690	−	2.63017i		0		−2.89586	−	0.783571i		0
881.18		0		0.228186	+	1.71695i		0		−1.84204				0		0.286690	+	2.63017i		0		−2.89586	+	0.783571i		0
881.19		0		0.583380	−	1.63085i		0		−4.22177				0		−1.21528	+	2.35012i		0		−2.31934	−	1.90281i		0
881.20		0		0.583380	+	1.63085i		0		−4.22177				0		−1.21528	−	2.35012i		0		−2.31934	+	1.90281i		0

Inner twists

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

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	1848.2.v.e	✓	32
3.b	odd	2	1	inner	1848.2.v.e	✓	32
7.b	odd	2	1	inner	1848.2.v.e	✓	32
21.c	even	2	1	inner	1848.2.v.e	✓	32

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
1848.2.v.e	✓	32	1.a	even	1	1	trivial
1848.2.v.e	✓	32	3.b	odd	2	1	inner
1848.2.v.e	✓	32	7.b	odd	2	1	inner
1848.2.v.e	✓	32	21.c	even	2	1	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T5^16 - 57*T5^14 + 1287*T5^12 - 14971*T5^10 + 98420*T5^8 - 373360*T5^6 + 785920*T5^4 - 802816*T5^2 + 262144