Newform orbit 300.3.v.a

• Label: 300.3.v.a
• Level: $300$
• Weight: $3$
• Character orbit: 300.v
• Analytic conductor: $8.174$
• Analytic rank: $0$
• Dimension: $80$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	300.v (of order \(20\), degree \(8\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(8.17440793081\)
Analytic rank:	\(0\)
Dimension:	\(80\)
Relative dimension:	\(10\) over \(\Q(\zeta_{20})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 80 q - 12 q^{5} - 20 q^{7}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
13.1		0		−0.786335	+	1.54327i		0		−4.55777	+	2.05590i		0		0.171657	−	0.171657i		0		−1.76336	−	2.42705i		0
13.2		0		−0.786335	+	1.54327i		0		−0.450640	−	4.97965i		0		−4.19715	+	4.19715i		0		−1.76336	−	2.42705i		0
13.3		0		−0.786335	+	1.54327i		0		2.10641	+	4.53465i		0		5.39673	−	5.39673i		0		−1.76336	−	2.42705i		0
13.4		0		−0.786335	+	1.54327i		0		3.56274	−	3.50812i		0		6.23072	−	6.23072i		0		−1.76336	−	2.42705i		0
13.5		0		−0.786335	+	1.54327i		0		4.74554	+	1.57475i		0		−9.54973	+	9.54973i		0		−1.76336	−	2.42705i		0
13.6		0		0.786335	−	1.54327i		0		−4.94031	+	0.770276i		0		−3.78617	+	3.78617i		0		−1.76336	−	2.42705i		0
13.7		0		0.786335	−	1.54327i		0		−1.98584	−	4.58873i		0		5.52939	−	5.52939i		0		−1.76336	−	2.42705i		0
13.8		0		0.786335	−	1.54327i		0		−1.31241	+	4.82468i		0		−4.66774	+	4.66774i		0		−1.76336	−	2.42705i		0
13.9		0		0.786335	−	1.54327i		0		−0.0846108	−	4.99928i		0		−3.62206	+	3.62206i		0		−1.76336	−	2.42705i		0
13.10		0		0.786335	−	1.54327i		0		4.43705	+	2.30490i		0		4.59881	−	4.59881i		0		−1.76336	−	2.42705i		0
37.1		0		−1.54327	−	0.786335i		0		−4.49742	+	2.18476i		0		−2.00492	−	2.00492i		0		1.76336	+	2.42705i		0
37.2		0		−1.54327	−	0.786335i		0		−3.16854	−	3.86786i		0		5.74378	+	5.74378i		0		1.76336	+	2.42705i		0
37.3		0		−1.54327	−	0.786335i		0		−1.08429	−	4.88102i		0		−8.84116	−	8.84116i		0		1.76336	+	2.42705i		0
37.4		0		−1.54327	−	0.786335i		0		1.29694	+	4.82887i		0		−0.204955	−	0.204955i		0		1.76336	+	2.42705i		0
37.5		0		−1.54327	−	0.786335i		0		4.54462	−	2.08480i		0		3.63701	+	3.63701i		0		1.76336	+	2.42705i		0
37.6		0		1.54327	+	0.786335i		0		−4.33028	−	2.49974i		0		5.03354	+	5.03354i		0		1.76336	+	2.42705i		0
37.7		0		1.54327	+	0.786335i		0		−4.07935	+	2.89118i		0		−6.25125	−	6.25125i		0		1.76336	+	2.42705i		0
37.8		0		1.54327	+	0.786335i		0		0.492133	−	4.97572i		0		−2.87386	−	2.87386i		0		1.76336	+	2.42705i		0
37.9		0		1.54327	+	0.786335i		0		4.10134	+	2.85989i		0		−5.04208	−	5.04208i		0		1.76336	+	2.42705i		0
37.10		0		1.54327	+	0.786335i		0		4.44076	+	2.29775i		0		7.46339	+	7.46339i		0		1.76336	+	2.42705i		0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
25.f	odd	20	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	300.3.v.a	✓	80
25.f	odd	20	1	inner	300.3.v.a	✓	80

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
300.3.v.a	✓	80	1.a	even	1	1	trivial
300.3.v.a	✓	80	25.f	odd	20	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(300, [\chi])\).