Newform orbit 1872.4.n.e

• Label: 1872.4.n.e
• Level: $1872$
• Weight: $4$
• Character orbit: 1872.n
• Analytic conductor: $110.452$
• Analytic rank: $0$
• Dimension: $56$
• CM: no
• Inner twists: $8$

Newspace parameters

Level:	\( N \)	\(=\)	\( 1872 = 2^{4} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1872.n (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(110.451575531\)
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.

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

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
1871.1		0			0			0		−21.7144				0		14.3806				0			0			0
1871.2		0			0			0		−21.7144				0		−14.3806				0			0			0
1871.3		0			0			0		−21.7144				0		−14.3806				0			0			0
1871.4		0			0			0		−21.7144				0		14.3806				0			0			0
1871.5		0			0			0		−16.7041				0		5.99827				0			0			0
1871.6		0			0			0		−16.7041				0		−5.99827				0			0			0
1871.7		0			0			0		−16.7041				0		−5.99827				0			0			0
1871.8		0			0			0		−16.7041				0		5.99827				0			0			0
1871.9		0			0			0		−11.7883				0		24.3049				0			0			0
1871.10		0			0			0		−11.7883				0		−24.3049				0			0			0
1871.11		0			0			0		−11.7883				0		−24.3049				0			0			0
1871.12		0			0			0		−11.7883				0		24.3049				0			0			0
1871.13		0			0			0		−9.29743				0		28.6741				0			0			0
1871.14		0			0			0		−9.29743				0		−28.6741				0			0			0
1871.15		0			0			0		−9.29743				0		−28.6741				0			0			0
1871.16		0			0			0		−9.29743				0		28.6741				0			0			0
1871.17		0			0			0		−7.25620				0		11.0448				0			0			0
1871.18		0			0			0		−7.25620				0		−11.0448				0			0			0
1871.19		0			0			0		−7.25620				0		−11.0448				0			0			0
1871.20		0			0			0		−7.25620				0		11.0448				0			0			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
13.b	even	2	1	inner
39.d	odd	2	1	inner
52.b	odd	2	1	inner
156.h	even	2	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	1872.4.n.e	✓	56
3.b	odd	2	1	inner	1872.4.n.e	✓	56
4.b	odd	2	1	inner	1872.4.n.e	✓	56
12.b	even	2	1	inner	1872.4.n.e	✓	56
13.b	even	2	1	inner	1872.4.n.e	✓	56
39.d	odd	2	1	inner	1872.4.n.e	✓	56
52.b	odd	2	1	inner	1872.4.n.e	✓	56
156.h	even	2	1	inner	1872.4.n.e	✓	56

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
1872.4.n.e	✓	56	1.a	even	1	1	trivial
1872.4.n.e	✓	56	3.b	odd	2	1	inner
1872.4.n.e	✓	56	4.b	odd	2	1	inner
1872.4.n.e	✓	56	12.b	even	2	1	inner
1872.4.n.e	✓	56	13.b	even	2	1	inner
1872.4.n.e	✓	56	39.d	odd	2	1	inner
1872.4.n.e	✓	56	52.b	odd	2	1	inner
1872.4.n.e	✓	56	156.h	even	2	1	inner

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{4}^{\mathrm{new}}(1872, [\chi])\):

T5^14 - 1098*T5^12 + 436728*T5^10 - 81647280*T5^8 + 7881188688*T5^6 - 400525982496*T5^4 + 10125223852032*T5^2 - 100095176245248

T7^14 - 2500*T7^12 + 2417688*T7^10 - 1150071744*T7^8 + 284874278544*T7^6 - 36375647910336*T7^4 + 2159900752271616*T7^2 - 42104433244372992