Newform orbit 600.2.v.b

• Label: 600.2.v.b
• Level: $600$
• Weight: $2$
• Character orbit: 600.v
• Analytic conductor: $4.791$
• Analytic rank: $0$
• Dimension: $24$
• CM: no
• Inner twists: $4$

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:	\(24\)
Relative dimension:	\(12\) over \(\Q(i)\)
Twist minimal:	no (minimal twist has level 120)
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.

\(\operatorname{Tr}(f)(q) = \) \( 24 q + 4 q^{6} + 12 q^{8}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
43.1	−1.31581	+	0.518298i	−0.707107	−	0.707107i	1.46273	−	1.36397i		0		1.29691	+	0.563929i	−0.645414	−	0.645414i	−1.21775	+	2.55286i			1.00000i		0
43.2	−1.25738	+	0.647304i	0.707107	+	0.707107i	1.16200	−	1.62781i		0		−1.34681	−	0.431387i	1.45533	+	1.45533i	−0.407381	+	2.79894i			1.00000i		0
43.3	−1.08304	−	0.909406i	−0.707107	−	0.707107i	0.345961	+	1.96985i		0		0.122779	+	1.40887i	2.10796	+	2.10796i	1.41670	−	2.44805i			1.00000i		0
43.4	−0.647304	+	1.25738i	0.707107	+	0.707107i	−1.16200	−	1.62781i		0		−1.34681	+	0.431387i	−1.45533	−	1.45533i	2.79894	−	0.407381i			1.00000i		0
43.5	−0.624608	−	1.26880i	0.707107	+	0.707107i	−1.21973	+	1.58501i		0		0.455516	−	1.33884i	−1.93078	−	1.93078i	2.77292	+	0.557590i			1.00000i		0
43.6	−0.518298	+	1.31581i	−0.707107	−	0.707107i	−1.46273	−	1.36397i		0		1.29691	−	0.563929i	0.645414	+	0.645414i	2.55286	−	1.21775i			1.00000i		0
43.7	−0.109339	−	1.40998i	−0.707107	−	0.707107i	−1.97609	+	0.308331i		0		−0.919693	+	1.07432i	1.21782	+	1.21782i	0.650804	+	2.75254i			1.00000i		0
43.8	0.804501	−	1.16309i	0.707107	+	0.707107i	−0.705556	−	1.87141i		0		1.39130	−	0.253561i	3.43671	+	3.43671i	−2.74424	−	0.684930i			1.00000i		0
43.9	0.909406	+	1.08304i	−0.707107	−	0.707107i	−0.345961	+	1.96985i		0		0.122779	−	1.40887i	−2.10796	−	2.10796i	−2.44805	+	1.41670i			1.00000i		0
43.10	1.16309	−	0.804501i	0.707107	+	0.707107i	0.705556	−	1.87141i		0		1.39130	+	0.253561i	−3.43671	−	3.43671i	−0.684930	−	2.74424i			1.00000i		0
43.11	1.26880	+	0.624608i	0.707107	+	0.707107i	1.21973	+	1.58501i		0		0.455516	+	1.33884i	1.93078	+	1.93078i	0.557590	+	2.77292i			1.00000i		0
43.12	1.40998	+	0.109339i	−0.707107	−	0.707107i	1.97609	+	0.308331i		0		−0.919693	−	1.07432i	−1.21782	−	1.21782i	2.75254	+	0.650804i			1.00000i		0
307.1	−1.31581	−	0.518298i	−0.707107	+	0.707107i	1.46273	+	1.36397i		0		1.29691	−	0.563929i	−0.645414	+	0.645414i	−1.21775	−	2.55286i		−	1.00000i		0
307.2	−1.25738	−	0.647304i	0.707107	−	0.707107i	1.16200	+	1.62781i		0		−1.34681	+	0.431387i	1.45533	−	1.45533i	−0.407381	−	2.79894i		−	1.00000i		0
307.3	−1.08304	+	0.909406i	−0.707107	+	0.707107i	0.345961	−	1.96985i		0		0.122779	−	1.40887i	2.10796	−	2.10796i	1.41670	+	2.44805i		−	1.00000i		0
307.4	−0.647304	−	1.25738i	0.707107	−	0.707107i	−1.16200	+	1.62781i		0		−1.34681	−	0.431387i	−1.45533	+	1.45533i	2.79894	+	0.407381i		−	1.00000i		0
307.5	−0.624608	+	1.26880i	0.707107	−	0.707107i	−1.21973	−	1.58501i		0		0.455516	+	1.33884i	−1.93078	+	1.93078i	2.77292	−	0.557590i		−	1.00000i		0
307.6	−0.518298	−	1.31581i	−0.707107	+	0.707107i	−1.46273	+	1.36397i		0		1.29691	+	0.563929i	0.645414	−	0.645414i	2.55286	+	1.21775i		−	1.00000i		0
307.7	−0.109339	+	1.40998i	−0.707107	+	0.707107i	−1.97609	−	0.308331i		0		−0.919693	−	1.07432i	1.21782	−	1.21782i	0.650804	−	2.75254i		−	1.00000i		0
307.8	0.804501	+	1.16309i	0.707107	−	0.707107i	−0.705556	+	1.87141i		0		1.39130	+	0.253561i	3.43671	−	3.43671i	−2.74424	+	0.684930i		−	1.00000i		0

Inner twists

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

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	600.2.v.b		24
4.b	odd	2	1		2400.2.bh.b		24
5.b	even	2	1		120.2.v.a	✓	24
5.c	odd	4	1		120.2.v.a	✓	24
5.c	odd	4	1	inner	600.2.v.b		24
8.b	even	2	1		2400.2.bh.b		24
8.d	odd	2	1	inner	600.2.v.b		24
15.d	odd	2	1		360.2.w.e		24
15.e	even	4	1		360.2.w.e		24
20.d	odd	2	1		480.2.bh.a		24
20.e	even	4	1		480.2.bh.a		24
20.e	even	4	1		2400.2.bh.b		24
40.e	odd	2	1		120.2.v.a	✓	24
40.f	even	2	1		480.2.bh.a		24
40.i	odd	4	1		480.2.bh.a		24
40.i	odd	4	1		2400.2.bh.b		24
40.k	even	4	1		120.2.v.a	✓	24
40.k	even	4	1	inner	600.2.v.b		24
60.h	even	2	1		1440.2.bi.e		24
60.l	odd	4	1		1440.2.bi.e		24
120.i	odd	2	1		1440.2.bi.e		24
120.m	even	2	1		360.2.w.e		24
120.q	odd	4	1		360.2.w.e		24
120.w	even	4	1		1440.2.bi.e		24

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
120.2.v.a	✓	24	5.b	even	2	1
120.2.v.a	✓	24	5.c	odd	4	1
120.2.v.a	✓	24	40.e	odd	2	1
120.2.v.a	✓	24	40.k	even	4	1
360.2.w.e		24	15.d	odd	2	1
360.2.w.e		24	15.e	even	4	1
360.2.w.e		24	120.m	even	2	1
360.2.w.e		24	120.q	odd	4	1
480.2.bh.a		24	20.d	odd	2	1
480.2.bh.a		24	20.e	even	4	1
480.2.bh.a		24	40.f	even	2	1
480.2.bh.a		24	40.i	odd	4	1
600.2.v.b		24	1.a	even	1	1	trivial
600.2.v.b		24	5.c	odd	4	1	inner
600.2.v.b		24	8.d	odd	2	1	inner
600.2.v.b		24	40.k	even	4	1	inner
1440.2.bi.e		24	60.h	even	2	1
1440.2.bi.e		24	60.l	odd	4	1
1440.2.bi.e		24	120.i	odd	2	1
1440.2.bi.e		24	120.w	even	4	1
2400.2.bh.b		24	4.b	odd	2	1
2400.2.bh.b		24	8.b	even	2	1
2400.2.bh.b		24	20.e	even	4	1
2400.2.bh.b		24	40.i	odd	4	1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{7}^{24} + 720T_{7}^{20} + 98656T_{7}^{16} + 4752640T_{7}^{12} + 81309952T_{7}^{8} + 440926208T_{7}^{4} + 268435456 \) acting on \(S_{2}^{\mathrm{new}}(600, [\chi])\).