Newform orbit 900.6.j.c

• Label: 900.6.j.c
• Level: $900$
• Weight: $6$
• Character orbit: 900.j
• Analytic conductor: $144.345$
• Analytic rank: $0$
• Dimension: $24$
• CM: no
• Inner twists: $8$

Newspace parameters

Level:	\( N \)	\(=\)	\( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	900.j (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(144.345437832\)
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 dimension is sufficiently large that we do not compute an algebraic \(q\)-expansion, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 24 q+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
557.1		0			0			0			0			0		−123.937	−	123.937i		0			0			0
557.2		0			0			0			0			0		−123.937	−	123.937i		0			0			0
557.3		0			0			0			0			0		−102.346	−	102.346i		0			0			0
557.4		0			0			0			0			0		−102.346	−	102.346i		0			0			0
557.5		0			0			0			0			0		−35.0625	−	35.0625i		0			0			0
557.6		0			0			0			0			0		−35.0625	−	35.0625i		0			0			0
557.7		0			0			0			0			0		35.0625	+	35.0625i		0			0			0
557.8		0			0			0			0			0		35.0625	+	35.0625i		0			0			0
557.9		0			0			0			0			0		102.346	+	102.346i		0			0			0
557.10		0			0			0			0			0		102.346	+	102.346i		0			0			0
557.11		0			0			0			0			0		123.937	+	123.937i		0			0			0
557.12		0			0			0			0			0		123.937	+	123.937i		0			0			0
593.1		0			0			0			0			0		−123.937	+	123.937i		0			0			0
593.2		0			0			0			0			0		−123.937	+	123.937i		0			0			0
593.3		0			0			0			0			0		−102.346	+	102.346i		0			0			0
593.4		0			0			0			0			0		−102.346	+	102.346i		0			0			0
593.5		0			0			0			0			0		−35.0625	+	35.0625i		0			0			0
593.6		0			0			0			0			0		−35.0625	+	35.0625i		0			0			0
593.7		0			0			0			0			0		35.0625	−	35.0625i		0			0			0
593.8		0			0			0			0			0		35.0625	−	35.0625i		0			0			0

Inner twists

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

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	900.6.j.c	✓	24
3.b	odd	2	1	inner	900.6.j.c	✓	24
5.b	even	2	1	inner	900.6.j.c	✓	24
5.c	odd	4	2	inner	900.6.j.c	✓	24
15.d	odd	2	1	inner	900.6.j.c	✓	24
15.e	even	4	2	inner	900.6.j.c	✓	24

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
900.6.j.c	✓	24	1.a	even	1	1	trivial
900.6.j.c	✓	24	3.b	odd	2	1	inner
900.6.j.c	✓	24	5.b	even	2	1	inner
900.6.j.c	✓	24	5.c	odd	4	2	inner
900.6.j.c	✓	24	15.d	odd	2	1	inner
900.6.j.c	✓	24	15.e	even	4	2	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{7}^{12} + 1388689227T_{7}^{8} + 422560801167320403T_{7}^{4} + 2504044864493700961858569 \) acting on \(S_{6}^{\mathrm{new}}(900, [\chi])\).