Newform orbit 225.6.f.c

• Label: 225.6.f.c
• Level: $225$
• Weight: $6$
• Character orbit: 225.f
• Analytic conductor: $36.086$
• Analytic rank: $0$
• Dimension: $24$
• CM: no
• Inner twists: $8$

Newspace parameters

Level:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	225.f (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(36.0863594579\)
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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
107.1	−6.22732	+	6.22732i		0			−	45.5591i		0			0		83.4434	+	83.4434i	84.4372	+	84.4372i		0			0
107.2	−6.22732	+	6.22732i		0			−	45.5591i		0			0		−83.4434	−	83.4434i	84.4372	+	84.4372i		0			0
107.3	−5.41913	+	5.41913i		0			−	26.7338i		0			0		−10.9755	−	10.9755i	−28.5379	−	28.5379i		0			0
107.4	−5.41913	+	5.41913i		0			−	26.7338i		0			0		10.9755	+	10.9755i	−28.5379	−	28.5379i		0			0
107.5	−0.923852	+	0.923852i		0				30.2930i		0			0		31.9569	+	31.9569i	−57.5495	−	57.5495i		0			0
107.6	−0.923852	+	0.923852i		0				30.2930i		0			0		−31.9569	−	31.9569i	−57.5495	−	57.5495i		0			0
107.7	0.923852	−	0.923852i		0				30.2930i		0			0		31.9569	+	31.9569i	57.5495	+	57.5495i		0			0
107.8	0.923852	−	0.923852i		0				30.2930i		0			0		−31.9569	−	31.9569i	57.5495	+	57.5495i		0			0
107.9	5.41913	−	5.41913i		0			−	26.7338i		0			0		10.9755	+	10.9755i	28.5379	+	28.5379i		0			0
107.10	5.41913	−	5.41913i		0			−	26.7338i		0			0		−10.9755	−	10.9755i	28.5379	+	28.5379i		0			0
107.11	6.22732	−	6.22732i		0			−	45.5591i		0			0		83.4434	+	83.4434i	−84.4372	−	84.4372i		0			0
107.12	6.22732	−	6.22732i		0			−	45.5591i		0			0		−83.4434	−	83.4434i	−84.4372	−	84.4372i		0			0
143.1	−6.22732	−	6.22732i		0				45.5591i		0			0		83.4434	−	83.4434i	84.4372	−	84.4372i		0			0
143.2	−6.22732	−	6.22732i		0				45.5591i		0			0		−83.4434	+	83.4434i	84.4372	−	84.4372i		0			0
143.3	−5.41913	−	5.41913i		0				26.7338i		0			0		−10.9755	+	10.9755i	−28.5379	+	28.5379i		0			0
143.4	−5.41913	−	5.41913i		0				26.7338i		0			0		10.9755	−	10.9755i	−28.5379	+	28.5379i		0			0
143.5	−0.923852	−	0.923852i		0			−	30.2930i		0			0		31.9569	−	31.9569i	−57.5495	+	57.5495i		0			0
143.6	−0.923852	−	0.923852i		0			−	30.2930i		0			0		−31.9569	+	31.9569i	−57.5495	+	57.5495i		0			0
143.7	0.923852	+	0.923852i		0			−	30.2930i		0			0		31.9569	−	31.9569i	57.5495	−	57.5495i		0			0
143.8	0.923852	+	0.923852i		0			−	30.2930i		0			0		−31.9569	+	31.9569i	57.5495	−	57.5495i		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	225.6.f.c	✓	24
3.b	odd	2	1	inner	225.6.f.c	✓	24
5.b	even	2	1	inner	225.6.f.c	✓	24
5.c	odd	4	2	inner	225.6.f.c	✓	24
15.d	odd	2	1	inner	225.6.f.c	✓	24
15.e	even	4	2	inner	225.6.f.c	✓	24

    

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

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{12} + 9468T_{2}^{8} + 20778768T_{2}^{4} + 60466176 \) acting on \(S_{6}^{\mathrm{new}}(225, [\chi])\).