Newform orbit 400.6.n.h

• Label: 400.6.n.h
• Level: $400$
• Weight: $6$
• Character orbit: 400.n
• Analytic conductor: $64.154$
• Analytic rank: $0$
• Dimension: $24$
• Inner twists: $8$

Newspace parameters

Level:	$N$	$=$	$400 = 2^{4} \cdot 5^{2}$
Weight:	$k$	$=$	$6$
Character orbit:	$[\chi]$	$=$	400.n (of order $4$, degree $2$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$64.1535279252$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

$q$-expansion

The algebraic $q$-expansion of this newform has not been computed, but we have computed the trace expansion.

$\operatorname{Tr}(f)(q) =$ $24 q + 19936 q^{21} + 32568 q^{41} + 454944 q^{61} + 1059176 q^{81}+O(q^{100})$

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	$a_{2}$			$a_{3}$			$a_{4}$			$a_{5}$			$a_{6}$			$a_{7}$			$a_{8}$			$a_{9}$			$a_{10}$
143.1		0		−13.8504	+	13.8504i		0			0			0		−156.283	−	156.283i		0			−	140.668i		0
143.2		0		−13.8504	+	13.8504i		0			0			0		−156.283	−	156.283i		0			−	140.668i		0
143.3		0		−13.2732	+	13.2732i		0			0			0		25.6490	+	25.6490i		0			−	109.358i		0
143.4		0		−13.2732	+	13.2732i		0			0			0		25.6490	+	25.6490i		0			−	109.358i		0
143.5		0		−5.78678	+	5.78678i		0			0			0		99.9080	+	99.9080i		0				176.026i		0
143.6		0		−5.78678	+	5.78678i		0			0			0		99.9080	+	99.9080i		0				176.026i		0
143.7		0		5.78678	−	5.78678i		0			0			0		−99.9080	−	99.9080i		0				176.026i		0
143.8		0		5.78678	−	5.78678i		0			0			0		−99.9080	−	99.9080i		0				176.026i		0
143.9		0		13.2732	−	13.2732i		0			0			0		−25.6490	−	25.6490i		0			−	109.358i		0
143.10		0		13.2732	−	13.2732i		0			0			0		−25.6490	−	25.6490i		0			−	109.358i		0
143.11		0		13.8504	−	13.8504i		0			0			0		156.283	+	156.283i		0			−	140.668i		0
143.12		0		13.8504	−	13.8504i		0			0			0		156.283	+	156.283i		0			−	140.668i		0
207.1		0		−13.8504	−	13.8504i		0			0			0		−156.283	+	156.283i		0				140.668i		0
207.2		0		−13.8504	−	13.8504i		0			0			0		−156.283	+	156.283i		0				140.668i		0
207.3		0		−13.2732	−	13.2732i		0			0			0		25.6490	−	25.6490i		0				109.358i		0
207.4		0		−13.2732	−	13.2732i		0			0			0		25.6490	−	25.6490i		0				109.358i		0
207.5		0		−5.78678	−	5.78678i		0			0			0		99.9080	−	99.9080i		0			−	176.026i		0
207.6		0		−5.78678	−	5.78678i		0			0			0		99.9080	−	99.9080i		0			−	176.026i		0
207.7		0		5.78678	+	5.78678i		0			0			0		−99.9080	+	99.9080i		0			−	176.026i		0
207.8		0		5.78678	+	5.78678i		0			0			0		−99.9080	+	99.9080i		0			−	176.026i		0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
4.b	odd	2	1	inner
5.b	even	2	1	inner
5.c	odd	4	2	inner
20.d	odd	2	1	inner
20.e	even	4	2	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	400.6.n.h	✓	24
4.b	odd	2	1	inner	400.6.n.h	✓	24
5.b	even	2	1	inner	400.6.n.h	✓	24
5.c	odd	4	2	inner	400.6.n.h	✓	24
20.d	odd	2	1	inner	400.6.n.h	✓	24
20.e	even	4	2	inner	400.6.n.h	✓	24

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
400.6.n.h	✓	24	1.a	even	1	1	trivial
400.6.n.h	✓	24	4.b	odd	2	1	inner
400.6.n.h	✓	24	5.b	even	2	1	inner
400.6.n.h	✓	24	5.c	odd	4	2	inner
400.6.n.h	✓	24	20.d	odd	2	1	inner
400.6.n.h	✓	24	20.e	even	4	2	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator $T_{3}^{12} + 275843T_{3}^{8} + 19493123203T_{3}^{4} + 81976382754561$ acting on $S_{6}^{\mathrm{new}}(400, [\chi])$.