Newform orbit 300.3.q.a

• Label: 300.3.q.a
• Level: $300$
• Weight: $3$
• Character orbit: 300.q
• Analytic conductor: $8.174$
• Analytic rank: $0$
• Dimension: $80$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	300.q (of order \(10\), degree \(4\), minimal)

Newform invariants

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

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 80 q - 10 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
29.1		0		−2.98816	+	0.266235i		0		0.198536	+	4.99606i		0			−	7.61642i		0		8.85824	−	1.59111i		0
29.2		0		−2.98508	−	0.298850i		0		−4.92635	+	0.855043i		0				4.01685i		0		8.82138	+	1.78418i		0
29.3		0		−2.47618	−	1.69367i		0		4.50149	−	2.17636i		0				3.80146i		0		3.26296	+	8.38768i		0
29.4		0		−2.45062	+	1.73045i		0		0.429865	−	4.98149i		0				8.53756i		0		3.01109	−	8.48135i		0
29.5		0		−2.30928	+	1.91500i		0		4.93780	+	0.786213i		0			−	6.91961i		0		1.66552	−	8.84455i		0
29.6		0		−1.63226	−	2.51709i		0		−3.32839	−	3.73119i		0			−	9.95709i		0		−3.67146	+	8.21708i		0
29.7		0		−1.62504	−	2.52175i		0		2.37369	+	4.40064i		0				0.329259i		0		−3.71849	+	8.19590i		0
29.8		0		−1.10767	+	2.78802i		0		−4.93780	−	0.786213i		0			−	6.91961i		0		−6.54613	−	6.17642i		0
29.9		0		−0.888471	+	2.86542i		0		−0.429865	+	4.98149i		0				8.53756i		0		−7.42124	−	5.09168i		0
29.10		0		0.131296	−	2.99713i		0		−3.41233	−	3.65459i		0				12.0594i		0		−8.96552	−	0.787022i		0
29.11		0		0.518617	−	2.95483i		0		−1.93263	+	4.61139i		0				2.08277i		0		−8.46207	−	3.06485i		0
29.12		0		0.670189	+	2.92418i		0		−0.198536	−	4.99606i		0			−	7.61642i		0		−8.10169	+	3.91951i		0
29.13		0		1.11578	−	2.78478i		0		4.34405	−	2.47573i		0			−	8.68529i		0		−6.51005	−	6.21443i		0
29.14		0		1.20666	+	2.74663i		0		4.92635	−	0.855043i		0				4.01685i		0		−6.08793	+	6.62851i		0
29.15		0		2.30369	−	1.92172i		0		−4.34405	+	2.47573i		0			−	8.68529i		0		1.61399	−	8.85410i		0
29.16		0		2.37596	+	1.83162i		0		−4.50149	+	2.17636i		0				3.80146i		0		2.29037	+	8.70369i		0
29.17		0		2.64995	−	1.40633i		0		1.93263	−	4.61139i		0				2.08277i		0		5.04449	−	7.45340i		0
29.18		0		2.80986	−	1.05103i		0		3.41233	+	3.65459i		0				12.0594i		0		6.79066	−	5.90652i		0
29.19		0		2.89829	+	0.774548i		0		3.32839	+	3.73119i		0			−	9.95709i		0		7.80015	+	4.48973i		0
29.20		0		2.90050	+	0.766240i		0		−2.37369	−	4.40064i		0				0.329259i		0		7.82575	+	4.44495i		0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	inner
25.e	even	10	1	inner
75.h	odd	10	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	300.3.q.a	✓	80
3.b	odd	2	1	inner	300.3.q.a	✓	80
25.e	even	10	1	inner	300.3.q.a	✓	80
75.h	odd	10	1	inner	300.3.q.a	✓	80

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
300.3.q.a	✓	80	1.a	even	1	1	trivial
300.3.q.a	✓	80	3.b	odd	2	1	inner
300.3.q.a	✓	80	25.e	even	10	1	inner
300.3.q.a	✓	80	75.h	odd	10	1	inner

Hecke kernels

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