Newform orbit 270.3.l.b

• Label: 270.3.l.b
• 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	−4.34994	+	2.46536i		0		−0.882779	+	3.29458i	2.00000	−	2.00000i		0		−1.77556	−	6.84452i
37.2	−0.366025	+	1.36603i		0		−1.73205	−	1.00000i	−3.85499	−	3.18419i		0		0.348547	−	1.30080i	2.00000	−	2.00000i		0		5.76070	−	4.10052i
37.3	−0.366025	+	1.36603i		0		−1.73205	−	1.00000i	0.477275	+	4.97717i		0		2.62197	−	9.78534i	2.00000	−	2.00000i		0		−6.97363	−	1.16980i
37.4	−0.366025	+	1.36603i		0		−1.73205	−	1.00000i	0.591182	−	4.96493i		0		−1.80392	+	6.73232i	2.00000	−	2.00000i		0		6.56583	+	2.62486i
37.5	−0.366025	+	1.36603i		0		−1.73205	−	1.00000i	4.80008	+	1.39971i		0		2.39851	−	8.95134i	2.00000	−	2.00000i		0		−3.66899	+	6.04471i
37.6	−0.366025	+	1.36603i		0		−1.73205	−	1.00000i	4.93447	+	0.806874i		0		−1.58425	+	5.91251i	2.00000	−	2.00000i		0		−2.90835	+	6.44527i
73.1	−0.366025	−	1.36603i		0		−1.73205	+	1.00000i	−4.34994	−	2.46536i		0		−0.882779	−	3.29458i	2.00000	+	2.00000i		0		−1.77556	+	6.84452i
73.2	−0.366025	−	1.36603i		0		−1.73205	+	1.00000i	−3.85499	+	3.18419i		0		0.348547	+	1.30080i	2.00000	+	2.00000i		0		5.76070	+	4.10052i
73.3	−0.366025	−	1.36603i		0		−1.73205	+	1.00000i	0.477275	−	4.97717i		0		2.62197	+	9.78534i	2.00000	+	2.00000i		0		−6.97363	+	1.16980i
73.4	−0.366025	−	1.36603i		0		−1.73205	+	1.00000i	0.591182	+	4.96493i		0		−1.80392	−	6.73232i	2.00000	+	2.00000i		0		6.56583	−	2.62486i
73.5	−0.366025	−	1.36603i		0		−1.73205	+	1.00000i	4.80008	−	1.39971i		0		2.39851	+	8.95134i	2.00000	+	2.00000i		0		−3.66899	−	6.04471i
73.6	−0.366025	−	1.36603i		0		−1.73205	+	1.00000i	4.93447	−	0.806874i		0		−1.58425	−	5.91251i	2.00000	+	2.00000i		0		−2.90835	−	6.44527i
127.1	1.36603	−	0.366025i		0		1.73205	−	1.00000i	−4.54899	−	2.07525i		0		−9.78534	+	2.62197i	2.00000	−	2.00000i		0		−6.97363	−	1.16980i
127.2	1.36603	−	0.366025i		0		1.73205	−	1.00000i	−3.61223	+	3.45714i		0		−8.95134	+	2.39851i	2.00000	−	2.00000i		0		−3.66899	+	6.04471i
127.3	1.36603	−	0.366025i		0		1.73205	−	1.00000i	−3.16601	+	3.86994i		0		5.91251	−	1.58425i	2.00000	−	2.00000i		0		−2.90835	+	6.44527i
127.4	1.36603	−	0.366025i		0		1.73205	−	1.00000i	0.0399035	−	4.99984i		0		3.29458	−	0.882779i	2.00000	−	2.00000i		0		−1.77556	−	6.84452i
127.5	1.36603	−	0.366025i		0		1.73205	−	1.00000i	4.00416	+	2.99444i		0		6.73232	−	1.80392i	2.00000	−	2.00000i		0		6.56583	+	2.62486i
127.6	1.36603	−	0.366025i		0		1.73205	−	1.00000i	4.68508	−	1.74643i		0		−1.30080	+	0.348547i	2.00000	−	2.00000i		0		5.76070	−	4.10052i
253.1	1.36603	+	0.366025i		0		1.73205	+	1.00000i	−4.54899	+	2.07525i		0		−9.78534	−	2.62197i	2.00000	+	2.00000i		0		−6.97363	+	1.16980i
253.2	1.36603	+	0.366025i		0		1.73205	+	1.00000i	−3.61223	−	3.45714i		0		−8.95134	−	2.39851i	2.00000	+	2.00000i		0		−3.66899	−	6.04471i

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.b		24
3.b	odd	2	1		90.3.k.a	✓	24
5.c	odd	4	1	inner	270.3.l.b		24
9.c	even	3	1	inner	270.3.l.b		24
9.c	even	3	1		810.3.g.i		12
9.d	odd	6	1		90.3.k.a	✓	24
9.d	odd	6	1		810.3.g.k		12
15.e	even	4	1		90.3.k.a	✓	24
45.k	odd	12	1	inner	270.3.l.b		24
45.k	odd	12	1		810.3.g.i		12
45.l	even	12	1		90.3.k.a	✓	24
45.l	even	12	1		810.3.g.k		12

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
90.3.k.a	✓	24	3.b	odd	2	1
90.3.k.a	✓	24	9.d	odd	6	1
90.3.k.a	✓	24	15.e	even	4	1
90.3.k.a	✓	24	45.l	even	12	1
270.3.l.b		24	1.a	even	1	1	trivial
270.3.l.b		24	5.c	odd	4	1	inner
270.3.l.b		24	9.c	even	3	1	inner
270.3.l.b		24	45.k	odd	12	1	inner
810.3.g.i		12	9.c	even	3	1
810.3.g.i		12	45.k	odd	12	1
810.3.g.k		12	9.d	odd	6	1
810.3.g.k		12	45.l	even	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 + 1196*T7^21 - 3891*T7^20 - 86784*T7^19 + 264542*T7^18 - 6533676*T7^17 + 6812778*T7^16 + 398196074*T7^15 - 752665806*T7^14 + 24919991784*T7^13 - 80858340983*T7^12 - 1266619287492*T7^11 + 5716568968056*T7^10 - 49036549194236*T7^9 + 432645584162106*T7^8 - 1054216635208830*T7^7 + 2383901657917088*T7^6 - 11066035390916880*T7^5 + 2587325236375965*T7^4 + 43246021288307356*T7^3 + 13964271119124552*T7^2 + 56561139537325932*T7 + 114548137832252881