Newform orbit 270.3.l.a

• Label: 270.3.l.a
• Level: $270$
• Weight: $3$
• Character orbit: 270.l
• Analytic conductor: $7.357$
• Analytic rank: $0$
• Dimension: $24$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 270 = 2 \cdot 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	270.l (of order \(12\), degree \(4\), not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(7.35696713773\)
Analytic rank:	\(0\)
Dimension:	\(24\)
Relative dimension:	\(6\) over \(\Q(\zeta_{12})\)
Twist minimal:	no (minimal twist has level 90)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 24 q - 12 q^{2} + 6 q^{7} - 48 q^{8}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
37.1	0.366025	−	1.36603i		0		−1.73205	−	1.00000i	−3.60463	−	3.46506i		0		−3.02677	+	11.2960i	−2.00000	+	2.00000i		0		−6.05274	+	3.65572i
37.2	0.366025	−	1.36603i		0		−1.73205	−	1.00000i	−3.04798	+	3.96356i		0		0.227789	−	0.850119i	−2.00000	+	2.00000i		0		4.29869	+	5.61438i
37.3	0.366025	−	1.36603i		0		−1.73205	−	1.00000i	−1.44906	+	4.78542i		0		1.61267	−	6.01857i	−2.00000	+	2.00000i		0		6.00661	+	3.73103i
37.4	0.366025	−	1.36603i		0		−1.73205	−	1.00000i	1.38594	−	4.80408i		0		−0.473946	+	1.76879i	−2.00000	+	2.00000i		0		−6.05520	−	3.65165i
37.5	0.366025	−	1.36603i		0		−1.73205	−	1.00000i	4.46665	+	2.24700i		0		−2.16011	+	8.06163i	−2.00000	+	2.00000i		0		4.70437	−	5.27910i
37.6	0.366025	−	1.36603i		0		−1.73205	−	1.00000i	4.84715	−	1.22685i		0		2.72228	−	10.1597i	−2.00000	+	2.00000i		0		0.0982721	−	7.07038i
73.1	0.366025	+	1.36603i		0		−1.73205	+	1.00000i	−3.60463	+	3.46506i		0		−3.02677	−	11.2960i	−2.00000	−	2.00000i		0		−6.05274	−	3.65572i
73.2	0.366025	+	1.36603i		0		−1.73205	+	1.00000i	−3.04798	−	3.96356i		0		0.227789	+	0.850119i	−2.00000	−	2.00000i		0		4.29869	−	5.61438i
73.3	0.366025	+	1.36603i		0		−1.73205	+	1.00000i	−1.44906	−	4.78542i		0		1.61267	+	6.01857i	−2.00000	−	2.00000i		0		6.00661	−	3.73103i
73.4	0.366025	+	1.36603i		0		−1.73205	+	1.00000i	1.38594	+	4.80408i		0		−0.473946	−	1.76879i	−2.00000	−	2.00000i		0		−6.05520	+	3.65165i
73.5	0.366025	+	1.36603i		0		−1.73205	+	1.00000i	4.46665	−	2.24700i		0		−2.16011	−	8.06163i	−2.00000	−	2.00000i		0		4.70437	+	5.27910i
73.6	0.366025	+	1.36603i		0		−1.73205	+	1.00000i	4.84715	+	1.22685i		0		2.72228	+	10.1597i	−2.00000	−	2.00000i		0		0.0982721	+	7.07038i
127.1	−1.36603	+	0.366025i		0		1.73205	−	1.00000i	−4.17929	+	2.74473i		0		8.06163	−	2.16011i	−2.00000	+	2.00000i		0		4.70437	−	5.27910i
127.2	−1.36603	+	0.366025i		0		1.73205	−	1.00000i	−3.41977	−	3.64763i		0		−6.01857	+	1.61267i	−2.00000	+	2.00000i		0		6.00661	+	3.73103i
127.3	−1.36603	+	0.366025i		0		1.73205	−	1.00000i	−1.90856	−	4.62141i		0		−0.850119	+	0.227789i	−2.00000	+	2.00000i		0		4.29869	+	5.61438i
127.4	−1.36603	+	0.366025i		0		1.73205	−	1.00000i	−1.36109	+	4.81118i		0		−10.1597	+	2.72228i	−2.00000	+	2.00000i		0		0.0982721	−	7.07038i
127.5	−1.36603	+	0.366025i		0		1.73205	−	1.00000i	3.46748	+	3.60230i		0		1.76879	−	0.473946i	−2.00000	+	2.00000i		0		−6.05520	−	3.65165i
127.6	−1.36603	+	0.366025i		0		1.73205	−	1.00000i	4.80314	−	1.38918i		0		11.2960	−	3.02677i	−2.00000	+	2.00000i		0		−6.05274	+	3.65572i
253.1	−1.36603	−	0.366025i		0		1.73205	+	1.00000i	−4.17929	−	2.74473i		0		8.06163	+	2.16011i	−2.00000	−	2.00000i		0		4.70437	+	5.27910i
253.2	−1.36603	−	0.366025i		0		1.73205	+	1.00000i	−3.41977	+	3.64763i		0		−6.01857	−	1.61267i	−2.00000	−	2.00000i		0		6.00661	−	3.73103i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
5.c	odd	4	1	inner
9.c	even	3	1	inner
45.k	odd	12	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	270.3.l.a		24
3.b	odd	2	1		90.3.k.b	✓	24
5.c	odd	4	1	inner	270.3.l.a		24
9.c	even	3	1	inner	270.3.l.a		24
9.c	even	3	1		810.3.g.j		12
9.d	odd	6	1		90.3.k.b	✓	24
9.d	odd	6	1		810.3.g.h		12
15.e	even	4	1		90.3.k.b	✓	24
45.k	odd	12	1	inner	270.3.l.a		24
45.k	odd	12	1		810.3.g.j		12
45.l	even	12	1		90.3.k.b	✓	24
45.l	even	12	1		810.3.g.h		12

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
90.3.k.b	✓	24	3.b	odd	2	1
90.3.k.b	✓	24	9.d	odd	6	1
90.3.k.b	✓	24	15.e	even	4	1
90.3.k.b	✓	24	45.l	even	12	1
270.3.l.a		24	1.a	even	1	1	trivial
270.3.l.a		24	5.c	odd	4	1	inner
270.3.l.a		24	9.c	even	3	1	inner
270.3.l.a		24	45.k	odd	12	1	inner
810.3.g.h		12	9.d	odd	6	1
810.3.g.h		12	45.l	even	12	1
810.3.g.j		12	9.c	even	3	1
810.3.g.j		12	45.k	odd	12	1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T7^24 - 6*T7^23 + 18*T7^22 - 772*T7^21 - 14187*T7^20 + 132888*T7^19 - 243970*T7^18 + 9692424*T7^17 + 222455946*T7^16 - 1364373754*T7^15 + 2067892050*T7^14 - 92324567232*T7^13 - 415391718911*T7^12 + 4926183303708*T7^11 - 1533079243440*T7^10 + 120042844724296*T7^9 + 1492809912294186*T7^8 - 2167846190558946*T7^7 + 895293432997160*T7^6 - 9115557841678752*T7^5 + 2997206395404693*T7^4 + 15312197518390708*T7^3 + 4631533073395488*T7^2 + 10228464964360344*T7 + 11294477861781361