Newform orbit 60.4.e.a

• Label: 60.4.e.a
• Level: $60$
• Weight: $4$
• Character orbit: 60.e
• Analytic conductor: $3.540$
• Analytic rank: $0$
• Dimension: $24$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 60 = 2^{2} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	60.e (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(3.54011460034\)
Analytic rank:	\(0\)
Dimension:	\(24\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 24 q + 6 q^{4} + 30 q^{6} + 20 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
11.1	−2.81775	−	0.245521i	−1.56674	−	4.95432i	7.87944	+	1.38363i		−	5.00000i	3.19829	+	14.3447i		−	5.80602i	−21.8626	−	5.83329i	−22.0907	+	15.5243i	−1.22760	+	14.0888i
11.2	−2.81775	+	0.245521i	−1.56674	+	4.95432i	7.87944	−	1.38363i			5.00000i	3.19829	−	14.3447i			5.80602i	−21.8626	+	5.83329i	−22.0907	−	15.5243i	−1.22760	−	14.0888i
11.3	−2.72356	−	0.763049i	4.56698	+	2.47844i	6.83551	+	4.15641i		−	5.00000i	−10.5473	−	10.2350i			20.9745i	−15.4454	−	16.5360i	14.7146	+	22.6380i	−3.81524	+	13.6178i
11.4	−2.72356	+	0.763049i	4.56698	−	2.47844i	6.83551	−	4.15641i			5.00000i	−10.5473	+	10.2350i		−	20.9745i	−15.4454	+	16.5360i	14.7146	−	22.6380i	−3.81524	−	13.6178i
11.5	−2.29793	−	1.64910i	−5.00938	−	1.38062i	2.56093	+	7.57903i			5.00000i	9.23440	+	11.4335i		−	0.228949i	6.61376	−	21.6393i	23.1878	+	13.8321i	8.24551	−	11.4896i
11.6	−2.29793	+	1.64910i	−5.00938	+	1.38062i	2.56093	−	7.57903i		−	5.00000i	9.23440	−	11.4335i			0.228949i	6.61376	+	21.6393i	23.1878	−	13.8321i	8.24551	+	11.4896i
11.7	−1.91554	−	2.08103i	−2.09257	+	4.75617i	−0.661378	+	7.97261i		−	5.00000i	13.9062	−	4.75594i		−	32.2690i	17.8582	−	13.8955i	−18.2423	−	19.9053i	−10.4052	+	9.57772i
11.8	−1.91554	+	2.08103i	−2.09257	−	4.75617i	−0.661378	−	7.97261i			5.00000i	13.9062	+	4.75594i			32.2690i	17.8582	+	13.8955i	−18.2423	+	19.9053i	−10.4052	−	9.57772i
11.9	−0.622346	−	2.75911i	1.95519	+	4.81427i	−7.22537	+	3.43424i			5.00000i	12.0663	−	8.39074i			20.3642i	13.9721	+	17.7983i	−19.3544	+	18.8257i	13.7955	−	3.11173i
11.10	−0.622346	+	2.75911i	1.95519	−	4.81427i	−7.22537	−	3.43424i		−	5.00000i	12.0663	+	8.39074i		−	20.3642i	13.9721	−	17.7983i	−19.3544	−	18.8257i	13.7955	+	3.11173i
11.11	−0.235442	−	2.81861i	−5.18580	−	0.327893i	−7.88913	+	1.32724i		−	5.00000i	0.296752	+	14.6939i			26.3120i	5.59840	+	21.9239i	26.7850	+	3.40077i	−14.0931	+	1.17721i
11.12	−0.235442	+	2.81861i	−5.18580	+	0.327893i	−7.88913	−	1.32724i			5.00000i	0.296752	−	14.6939i		−	26.3120i	5.59840	−	21.9239i	26.7850	−	3.40077i	−14.0931	−	1.17721i
11.13	0.235442	−	2.81861i	5.18580	+	0.327893i	−7.88913	−	1.32724i		−	5.00000i	2.14516	−	14.5395i		−	26.3120i	−5.59840	+	21.9239i	26.7850	+	3.40077i	−14.0931	−	1.17721i
11.14	0.235442	+	2.81861i	5.18580	−	0.327893i	−7.88913	+	1.32724i			5.00000i	2.14516	+	14.5395i			26.3120i	−5.59840	−	21.9239i	26.7850	−	3.40077i	−14.0931	+	1.17721i
11.15	0.622346	−	2.75911i	−1.95519	−	4.81427i	−7.22537	−	3.43424i			5.00000i	−14.4999	+	2.39845i		−	20.3642i	−13.9721	+	17.7983i	−19.3544	+	18.8257i	13.7955	+	3.11173i
11.16	0.622346	+	2.75911i	−1.95519	+	4.81427i	−7.22537	+	3.43424i		−	5.00000i	−14.4999	−	2.39845i			20.3642i	−13.9721	−	17.7983i	−19.3544	−	18.8257i	13.7955	−	3.11173i
11.17	1.91554	−	2.08103i	2.09257	−	4.75617i	−0.661378	−	7.97261i		−	5.00000i	−5.88931	−	13.4654i			32.2690i	−17.8582	−	13.8955i	−18.2423	−	19.9053i	−10.4052	−	9.57772i
11.18	1.91554	+	2.08103i	2.09257	+	4.75617i	−0.661378	+	7.97261i			5.00000i	−5.88931	+	13.4654i		−	32.2690i	−17.8582	+	13.8955i	−18.2423	+	19.9053i	−10.4052	+	9.57772i
11.19	2.29793	−	1.64910i	5.00938	+	1.38062i	2.56093	−	7.57903i			5.00000i	13.7880	−	5.08841i			0.228949i	−6.61376	−	21.6393i	23.1878	+	13.8321i	8.24551	+	11.4896i
11.20	2.29793	+	1.64910i	5.00938	−	1.38062i	2.56093	+	7.57903i		−	5.00000i	13.7880	+	5.08841i		−	0.228949i	−6.61376	+	21.6393i	23.1878	−	13.8321i	8.24551	−	11.4896i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	inner
4.b	odd	2	1	inner
12.b	even	2	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	60.4.e.a	✓	24
3.b	odd	2	1	inner	60.4.e.a	✓	24
4.b	odd	2	1	inner	60.4.e.a	✓	24
8.b	even	2	1		960.4.h.d		24
8.d	odd	2	1		960.4.h.d		24
12.b	even	2	1	inner	60.4.e.a	✓	24
24.f	even	2	1		960.4.h.d		24
24.h	odd	2	1		960.4.h.d		24

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
60.4.e.a	✓	24	1.a	even	1	1	trivial
60.4.e.a	✓	24	3.b	odd	2	1	inner
60.4.e.a	✓	24	4.b	odd	2	1	inner
60.4.e.a	✓	24	12.b	even	2	1	inner
960.4.h.d		24	8.b	even	2	1
960.4.h.d		24	8.d	odd	2	1
960.4.h.d		24	24.f	even	2	1
960.4.h.d		24	24.h	odd	2	1

Hecke kernels

This newform subspace is the entire newspace \(S_{4}^{\mathrm{new}}(60, [\chi])\).