Newform orbit 600.2.v.c

• Label: 600.2.v.c
• Level: $600$
• Weight: $2$
• Character orbit: 600.v
• Analytic conductor: $4.791$
• Analytic rank: $0$
• Dimension: $32$
• Inner twists: $8$

Newspace parameters

Level:	\( N \)	\(=\)	\( 600 = 2^{3} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	600.v (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(4.79102412128\)
Analytic rank:	\(0\)
Dimension:	\(32\)
Relative dimension:	\(16\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 32 q - 8 q^{6} - 32 q^{11} + 32 q^{16} - 8 q^{26} - 16 q^{36} - 16 q^{46} + 32 q^{51} - 112 q^{56} + 80 q^{66} - 80 q^{76} - 32 q^{81} + 104 q^{86} - 224 q^{91} + 48 q^{96}+O(q^{100}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
43.1	−1.41358	+	0.0423240i	−0.707107	−	0.707107i	1.99642	−	0.119657i		0		1.02948	+	0.969624i	−0.337834	−	0.337834i	−2.81703	+	0.253641i			1.00000i		0
43.2	−1.37067	+	0.348245i	0.707107	+	0.707107i	1.75745	−	0.954656i		0		−1.21545	−	0.722960i	2.37271	+	2.37271i	−2.07642	+	1.92054i			1.00000i		0
43.3	−1.35226	−	0.413994i	0.707107	+	0.707107i	1.65722	+	1.11966i		0		−0.663454	−	1.24893i	−2.62409	−	2.62409i	−1.77746	−	2.20015i			1.00000i		0
43.4	−1.10079	−	0.887846i	0.707107	+	0.707107i	0.423460	+	1.95466i		0		−0.150571	−	1.40618i	−1.17057	−	1.17057i	1.26929	−	2.52763i			1.00000i		0
43.5	−0.887846	−	1.10079i	−0.707107	−	0.707107i	−0.423460	+	1.95466i		0		−0.150571	+	1.40618i	−1.17057	−	1.17057i	2.52763	−	1.26929i			1.00000i		0
43.6	−0.413994	−	1.35226i	−0.707107	−	0.707107i	−1.65722	+	1.11966i		0		−0.663454	+	1.24893i	−2.62409	−	2.62409i	2.20015	+	1.77746i			1.00000i		0
43.7	−0.348245	+	1.37067i	0.707107	+	0.707107i	−1.75745	−	0.954656i		0		−1.21545	+	0.722960i	−2.37271	−	2.37271i	1.92054	−	2.07642i			1.00000i		0
43.8	−0.0423240	+	1.41358i	−0.707107	−	0.707107i	−1.99642	−	0.119657i		0		1.02948	−	0.969624i	0.337834	+	0.337834i	0.253641	−	2.81703i			1.00000i		0
43.9	0.0423240	−	1.41358i	0.707107	+	0.707107i	−1.99642	−	0.119657i		0		1.02948	−	0.969624i	−0.337834	−	0.337834i	−0.253641	+	2.81703i			1.00000i		0
43.10	0.348245	−	1.37067i	−0.707107	−	0.707107i	−1.75745	−	0.954656i		0		−1.21545	+	0.722960i	2.37271	+	2.37271i	−1.92054	+	2.07642i			1.00000i		0
43.11	0.413994	+	1.35226i	0.707107	+	0.707107i	−1.65722	+	1.11966i		0		−0.663454	+	1.24893i	2.62409	+	2.62409i	−2.20015	−	1.77746i			1.00000i		0
43.12	0.887846	+	1.10079i	0.707107	+	0.707107i	−0.423460	+	1.95466i		0		−0.150571	+	1.40618i	1.17057	+	1.17057i	−2.52763	+	1.26929i			1.00000i		0
43.13	1.10079	+	0.887846i	−0.707107	−	0.707107i	0.423460	+	1.95466i		0		−0.150571	−	1.40618i	1.17057	+	1.17057i	−1.26929	+	2.52763i			1.00000i		0
43.14	1.35226	+	0.413994i	−0.707107	−	0.707107i	1.65722	+	1.11966i		0		−0.663454	−	1.24893i	2.62409	+	2.62409i	1.77746	+	2.20015i			1.00000i		0
43.15	1.37067	−	0.348245i	−0.707107	−	0.707107i	1.75745	−	0.954656i		0		−1.21545	−	0.722960i	−2.37271	−	2.37271i	2.07642	−	1.92054i			1.00000i		0
43.16	1.41358	−	0.0423240i	0.707107	+	0.707107i	1.99642	−	0.119657i		0		1.02948	+	0.969624i	0.337834	+	0.337834i	2.81703	−	0.253641i			1.00000i		0
307.1	−1.41358	−	0.0423240i	−0.707107	+	0.707107i	1.99642	+	0.119657i		0		1.02948	−	0.969624i	−0.337834	+	0.337834i	−2.81703	−	0.253641i		−	1.00000i		0
307.2	−1.37067	−	0.348245i	0.707107	−	0.707107i	1.75745	+	0.954656i		0		−1.21545	+	0.722960i	2.37271	−	2.37271i	−2.07642	−	1.92054i		−	1.00000i		0
307.3	−1.35226	+	0.413994i	0.707107	−	0.707107i	1.65722	−	1.11966i		0		−0.663454	+	1.24893i	−2.62409	+	2.62409i	−1.77746	+	2.20015i		−	1.00000i		0
307.4	−1.10079	+	0.887846i	0.707107	−	0.707107i	0.423460	−	1.95466i		0		−0.150571	+	1.40618i	−1.17057	+	1.17057i	1.26929	+	2.52763i		−	1.00000i		0

Inner twists

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

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	600.2.v.c	✓	32
4.b	odd	2	1		2400.2.bh.c		32
5.b	even	2	1	inner	600.2.v.c	✓	32
5.c	odd	4	2	inner	600.2.v.c	✓	32
8.b	even	2	1		2400.2.bh.c		32
8.d	odd	2	1	inner	600.2.v.c	✓	32
20.d	odd	2	1		2400.2.bh.c		32
20.e	even	4	2		2400.2.bh.c		32
40.e	odd	2	1	inner	600.2.v.c	✓	32
40.f	even	2	1		2400.2.bh.c		32
40.i	odd	4	2		2400.2.bh.c		32
40.k	even	4	2	inner	600.2.v.c	✓	32

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
600.2.v.c	✓	32	1.a	even	1	1	trivial
600.2.v.c	✓	32	5.b	even	2	1	inner
600.2.v.c	✓	32	5.c	odd	4	2	inner
600.2.v.c	✓	32	8.d	odd	2	1	inner
600.2.v.c	✓	32	40.e	odd	2	1	inner
600.2.v.c	✓	32	40.k	even	4	2	inner
2400.2.bh.c		32	4.b	odd	2	1
2400.2.bh.c		32	8.b	even	2	1
2400.2.bh.c		32	20.d	odd	2	1
2400.2.bh.c		32	20.e	even	4	2
2400.2.bh.c		32	40.f	even	2	1
2400.2.bh.c		32	40.i	odd	4	2

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{7}^{16} + 324T_{7}^{12} + 26438T_{7}^{8} + 181956T_{7}^{4} + 9409 \) acting on \(S_{2}^{\mathrm{new}}(600, [\chi])\).