Newform orbit 504.2.bm.c

• Label: 504.2.bm.c
• Level: $504$
• Weight: $2$
• Character orbit: 504.bm
• Analytic conductor: $4.024$
• Analytic rank: $0$
• Dimension: $48$
• CM: no
• Inner twists: $8$

Newspace parameters

Level:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.bm (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(4.02446026187\)
Analytic rank:	\(0\)
Dimension:	\(48\)
Relative dimension:	\(24\) over \(\Q(\zeta_{6})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 48 q+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
107.1	−1.41266	+	0.0663565i		0		1.99119	−	0.187478i	1.02787	−	1.78033i		0		−1.24680	+	2.33356i	−2.80043	+	0.396971i		0		−1.33390	+	2.58320i
107.2	−1.33462	−	0.467740i		0		1.56244	+	1.24851i	−0.316953	+	0.548978i		0		2.06297	−	1.65655i	−1.50129	−	2.39711i		0		0.679792	−	0.584428i
107.3	−1.31291	−	0.525613i		0		1.44746	+	1.38016i	−1.51483	+	2.62375i		0		1.48957	+	2.18659i	−1.17496	−	2.57283i		0		3.36791	−	2.64854i
107.4	−1.23551	+	0.688125i		0		1.05297	−	1.70037i	0.317795	−	0.550436i		0		−2.11900	−	1.58425i	−0.130884	+	2.82540i		0		−0.0138692	+	0.898752i
107.5	−1.11165	−	0.874207i		0		0.471526	+	1.94362i	1.51483	−	2.62375i		0		−1.48957	−	2.18659i	1.17496	−	2.57283i		0		−3.97766	+	1.59242i
107.6	−1.07239	−	0.921948i		0		0.300025	+	1.97737i	0.316953	−	0.548978i		0		−2.06297	+	1.65655i	1.50129	−	2.39711i		0		−0.846025	+	0.296503i
107.7	−1.00991	+	0.989990i		0		0.0398381	−	1.99960i	0.635051	−	1.09994i		0		2.64362	+	0.106220i	1.93936	+	2.05886i		0		0.447586	+	1.73954i
107.8	−0.830529	+	1.14465i		0		−0.620442	−	1.90133i	−1.88256	+	3.26069i		0		2.23426	−	1.41706i	2.69165	+	0.868922i		0		−2.16882	−	4.86297i
107.9	−0.648862	−	1.25657i		0		−1.15796	+	1.63069i	−1.02787	+	1.78033i		0		1.24680	−	2.33356i	2.80043	+	0.396971i		0		2.90407	+	0.136412i
107.10	−0.576030	+	1.29158i		0		−1.33638	−	1.48798i	−1.88256	+	3.26069i		0		−2.23426	+	1.41706i	2.69165	−	0.868922i		0		−3.12704	−	4.30974i
107.11	−0.352402	+	1.36960i		0		−1.75163	−	0.965301i	0.635051	−	1.09994i		0		−2.64362	−	0.106220i	1.93936	−	2.05886i		0		1.28269	+	1.25739i
107.12	−0.0218210	−	1.41405i		0		−1.99905	+	0.0617118i	−0.317795	+	0.550436i		0		2.11900	+	1.58425i	0.130884	+	2.82540i		0		0.785276	+	0.437365i
107.13	0.0218210	+	1.41405i		0		−1.99905	+	0.0617118i	0.317795	−	0.550436i		0		2.11900	+	1.58425i	−0.130884	−	2.82540i		0		0.785276	+	0.437365i
107.14	0.352402	−	1.36960i		0		−1.75163	−	0.965301i	−0.635051	+	1.09994i		0		−2.64362	−	0.106220i	−1.93936	+	2.05886i		0		1.28269	+	1.25739i
107.15	0.576030	−	1.29158i		0		−1.33638	−	1.48798i	1.88256	−	3.26069i		0		−2.23426	+	1.41706i	−2.69165	+	0.868922i		0		−3.12704	−	4.30974i
107.16	0.648862	+	1.25657i		0		−1.15796	+	1.63069i	1.02787	−	1.78033i		0		1.24680	−	2.33356i	−2.80043	−	0.396971i		0		2.90407	+	0.136412i
107.17	0.830529	−	1.14465i		0		−0.620442	−	1.90133i	1.88256	−	3.26069i		0		2.23426	−	1.41706i	−2.69165	−	0.868922i		0		−2.16882	−	4.86297i
107.18	1.00991	−	0.989990i		0		0.0398381	−	1.99960i	−0.635051	+	1.09994i		0		2.64362	+	0.106220i	−1.93936	−	2.05886i		0		0.447586	+	1.73954i
107.19	1.07239	+	0.921948i		0		0.300025	+	1.97737i	−0.316953	+	0.548978i		0		−2.06297	+	1.65655i	−1.50129	+	2.39711i		0		−0.846025	+	0.296503i
107.20	1.11165	+	0.874207i		0		0.471526	+	1.94362i	−1.51483	+	2.62375i		0		−1.48957	−	2.18659i	−1.17496	+	2.57283i		0		−3.97766	+	1.59242i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	inner
7.c	even	3	1	inner
8.d	odd	2	1	inner
21.h	odd	6	1	inner
24.f	even	2	1	inner
56.k	odd	6	1	inner
168.v	even	6	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	504.2.bm.c	✓	48
3.b	odd	2	1	inner	504.2.bm.c	✓	48
4.b	odd	2	1		2016.2.bu.c		48
7.c	even	3	1	inner	504.2.bm.c	✓	48
8.b	even	2	1		2016.2.bu.c		48
8.d	odd	2	1	inner	504.2.bm.c	✓	48
12.b	even	2	1		2016.2.bu.c		48
21.h	odd	6	1	inner	504.2.bm.c	✓	48
24.f	even	2	1	inner	504.2.bm.c	✓	48
24.h	odd	2	1		2016.2.bu.c		48
28.g	odd	6	1		2016.2.bu.c		48
56.k	odd	6	1	inner	504.2.bm.c	✓	48
56.p	even	6	1		2016.2.bu.c		48
84.n	even	6	1		2016.2.bu.c		48
168.s	odd	6	1		2016.2.bu.c		48
168.v	even	6	1	inner	504.2.bm.c	✓	48

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
504.2.bm.c	✓	48	1.a	even	1	1	trivial
504.2.bm.c	✓	48	3.b	odd	2	1	inner
504.2.bm.c	✓	48	7.c	even	3	1	inner
504.2.bm.c	✓	48	8.d	odd	2	1	inner
504.2.bm.c	✓	48	21.h	odd	6	1	inner
504.2.bm.c	✓	48	24.f	even	2	1	inner
504.2.bm.c	✓	48	56.k	odd	6	1	inner
504.2.bm.c	✓	48	168.v	even	6	1	inner
2016.2.bu.c		48	4.b	odd	2	1
2016.2.bu.c		48	8.b	even	2	1
2016.2.bu.c		48	12.b	even	2	1
2016.2.bu.c		48	24.h	odd	2	1
2016.2.bu.c		48	28.g	odd	6	1
2016.2.bu.c		48	56.p	even	6	1
2016.2.bu.c		48	84.n	even	6	1
2016.2.bu.c		48	168.s	odd	6	1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T5^24 + 30*T5^22 + 603*T5^20 + 6622*T5^18 + 52217*T5^16 + 240312*T5^14 + 786520*T5^12 + 1403872*T5^10 + 1764400*T5^8 + 1115136*T5^6 + 505728*T5^4 + 124416*T5^2 + 20736