Newform orbit 700.2.bv.a

• Label: 700.2.bv.a
• Level: $700$
• Weight: $2$
• Character orbit: 700.bv
• Analytic conductor: $5.590$
• Analytic rank: $0$
• Dimension: $320$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 700 = 2^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	700.bv (of order \(60\), degree \(16\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(5.58952814149\)
Analytic rank:	\(0\)
Dimension:	\(320\)
Relative dimension:	\(20\) over \(\Q(\zeta_{60})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

$q$-expansion

The dimension is sufficiently large that we do not compute an algebraic \(q\)-expansion, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 320 q - 6 q^{5} - 2 q^{7}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
17.1		0		−2.05448	+	2.53708i		0		0.960872	−	2.01909i		0		1.96637	+	1.77014i		0		−1.59212	−	7.49032i		0
17.2		0		−1.78176	+	2.20029i		0		−2.23526	−	0.0600796i		0		−0.424504	−	2.61147i		0		−1.04288	−	4.90636i		0
17.3		0		−1.45635	+	1.79844i		0		2.23561	−	0.0451077i		0		−2.64489	−	0.0673922i		0		−0.489705	−	2.30388i		0
17.4		0		−1.33151	+	1.64428i		0		−2.17631	+	0.513496i		0		0.369328	+	2.61985i		0		−0.306995	−	1.44430i		0
17.5		0		−1.08236	+	1.33660i		0		0.307790	−	2.21478i		0		0.439012	−	2.60907i		0		0.00873051	+	0.0410738i		0
17.6		0		−1.07573	+	1.32842i		0		0.365618	+	2.20597i		0		2.49118	+	0.891066i		0		0.0162379	+	0.0763933i		0
17.7		0		−0.771786	+	0.953076i		0		2.18412	+	0.479201i		0		−1.10209	+	2.40529i		0		0.311034	+	1.46330i		0
17.8		0		−0.724186	+	0.894296i		0		−0.318491	+	2.21327i		0		−2.19573	−	1.47607i		0		0.348416	+	1.63917i		0
17.9		0		−0.711934	+	0.879165i		0		−0.162815	−	2.23013i		0		−2.43873	−	1.02596i		0		0.357654	+	1.68263i		0
17.10		0		0.0395755	−	0.0488716i		0		−1.26424	−	1.84437i		0		−0.745960	+	2.53841i		0		0.622913	+	2.93057i		0
17.11		0		0.0705744	−	0.0871521i		0		−1.35823	+	1.77629i		0		1.63501	−	2.08008i		0		0.621120	+	2.92214i		0
17.12		0		0.199076	−	0.245838i		0		1.72318	−	1.42501i		0		2.60074	+	0.485932i		0		0.602930	+	2.83656i		0
17.13		0		0.406320	−	0.501764i		0		−2.11330	−	0.730722i		0		2.28795	−	1.32863i		0		0.537064	+	2.52669i		0
17.14		0		0.827844	−	1.02230i		0		1.93417	+	1.12204i		0		−0.526591	−	2.59282i		0		0.263959	+	1.24183i		0
17.15		0		1.02151	−	1.26145i		0		1.07217	+	1.96226i		0		−1.45757	+	2.20805i		0		0.0759413	+	0.357276i		0
17.16		0		1.37654	−	1.69988i		0		−2.09116	+	0.791855i		0		−2.62544	−	0.327247i		0		−0.371011	−	1.74547i		0
17.17		0		1.44017	−	1.77846i		0		1.06630	−	1.96545i		0		−2.63336	+	0.255746i		0		−0.465095	−	2.18810i		0
17.18		0		1.71786	−	2.12139i		0		−1.68158	+	1.47387i		0		1.58019	+	2.12203i		0		−0.925486	−	4.35407i		0
17.19		0		1.87526	−	2.31575i		0		−1.02585	−	1.98686i		0		0.641610	−	2.56678i		0		−1.22237	−	5.75082i		0
17.20		0		2.01538	−	2.48879i		0		2.21729	+	0.289149i		0		2.64026	−	0.170325i		0		−1.50857	−	7.09727i		0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
7.d	odd	6	1	inner
25.f	odd	20	1	inner
175.x	even	60	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	700.2.bv.a	✓	320
7.d	odd	6	1	inner	700.2.bv.a	✓	320
25.f	odd	20	1	inner	700.2.bv.a	✓	320
175.x	even	60	1	inner	700.2.bv.a	✓	320

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
700.2.bv.a	✓	320	1.a	even	1	1	trivial
700.2.bv.a	✓	320	7.d	odd	6	1	inner
700.2.bv.a	✓	320	25.f	odd	20	1	inner
700.2.bv.a	✓	320	175.x	even	60	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(700, [\chi])\).