Newform orbit 546.2.bb.a

• Label: 546.2.bb.a
• Level: $546$
• Weight: $2$
• Character orbit: 546.bb
• Analytic conductor: $4.360$
• Analytic rank: $0$
• Dimension: $76$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.bb (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(4.35983195036\)
Analytic rank:	\(0\)
Dimension:	\(76\)
Relative dimension:	\(38\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 76 q - 76 q^{4} + 10 q^{7} + 4 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
269.1		−	1.00000i	−1.68782	−	0.388948i	−1.00000			−0.386492	−	0.669424i	−0.388948	+	1.68782i	1.88739	+	1.85412i			1.00000i	2.69744	+	1.31294i	−0.669424	+	0.386492i
269.2		−	1.00000i	−1.59766	+	0.668950i	−1.00000			−0.356048	−	0.616693i	0.668950	+	1.59766i	2.34738	−	1.22057i			1.00000i	2.10501	−	2.13750i	−0.616693	+	0.356048i
269.3		−	1.00000i	−1.54137	+	0.790045i	−1.00000			0.886718	+	1.53584i	0.790045	+	1.54137i	−1.67305	+	2.04961i			1.00000i	1.75166	−	2.43551i	1.53584	−	0.886718i
269.4		−	1.00000i	−1.48241	−	0.895807i	−1.00000			0.699535	+	1.21163i	−0.895807	+	1.48241i	−2.51159	+	0.831830i			1.00000i	1.39506	+	2.65590i	1.21163	−	0.699535i
269.5		−	1.00000i	−1.42260	−	0.988029i	−1.00000			1.41378	+	2.44875i	−0.988029	+	1.42260i	0.383892	−	2.61775i			1.00000i	1.04760	+	2.81115i	2.44875	−	1.41378i
269.6		−	1.00000i	−0.926039	+	1.46371i	−1.00000			−2.14723	−	3.71911i	1.46371	+	0.926039i	−0.786623	+	2.52611i			1.00000i	−1.28490	−	2.71091i	−3.71911	+	2.14723i
269.7		−	1.00000i	−0.834971	+	1.51751i	−1.00000			0.277881	+	0.481304i	1.51751	+	0.834971i	−1.71510	−	2.01455i			1.00000i	−1.60565	−	2.53415i	0.481304	−	0.277881i
269.8		−	1.00000i	−0.592023	+	1.62773i	−1.00000			2.12998	+	3.68924i	1.62773	+	0.592023i	2.63074	+	0.281454i			1.00000i	−2.29902	−	1.92731i	3.68924	−	2.12998i
269.9		−	1.00000i	−0.459307	−	1.67004i	−1.00000			−1.40279	−	2.42970i	−1.67004	+	0.459307i	1.21733	+	2.34907i			1.00000i	−2.57807	+	1.53412i	−2.42970	+	1.40279i
269.10		−	1.00000i	−0.215340	−	1.71861i	−1.00000			−1.07511	−	1.86215i	−1.71861	+	0.215340i	−2.48199	−	0.916357i			1.00000i	−2.90726	+	0.740172i	−1.86215	+	1.07511i
269.11		−	1.00000i	0.201730	−	1.72026i	−1.00000			1.75377	+	3.03762i	−1.72026	−	0.201730i	1.27169	+	2.32009i			1.00000i	−2.91861	−	0.694059i	3.03762	−	1.75377i
269.12		−	1.00000i	0.691481	+	1.58803i	−1.00000			−0.349437	−	0.605242i	1.58803	−	0.691481i	2.58515	−	0.563029i			1.00000i	−2.04371	+	2.19619i	−0.605242	+	0.349437i
269.13		−	1.00000i	1.03468	−	1.38904i	−1.00000			0.587127	+	1.01693i	−1.38904	−	1.03468i	−0.859975	−	2.50209i			1.00000i	−0.858887	−	2.87442i	1.01693	−	0.587127i
269.14		−	1.00000i	1.15993	+	1.28630i	−1.00000			−0.0272832	−	0.0472559i	1.28630	−	1.15993i	0.114956	+	2.64325i			1.00000i	−0.309116	+	2.98403i	−0.0472559	+	0.0272832i
269.15		−	1.00000i	1.32763	+	1.11238i	−1.00000			−1.76347	−	3.05441i	1.11238	−	1.32763i	−2.64100	+	0.158422i			1.00000i	0.525225	+	2.95367i	−3.05441	+	1.76347i
269.16		−	1.00000i	1.34890	−	1.08650i	−1.00000			−0.279399	−	0.483934i	−1.08650	−	1.34890i	2.15416	+	1.53609i			1.00000i	0.639049	−	2.93115i	−0.483934	+	0.279399i
269.17		−	1.00000i	1.63536	−	0.570612i	−1.00000			−1.99252	−	3.45115i	−0.570612	−	1.63536i	2.09752	−	1.61258i			1.00000i	2.34880	−	1.86631i	−3.45115	+	1.99252i
269.18		−	1.00000i	1.63815	+	0.562548i	−1.00000			0.604752	+	1.04746i	0.562548	−	1.63815i	0.374319	−	2.61914i			1.00000i	2.36708	+	1.84308i	1.04746	−	0.604752i
269.19		−	1.00000i	1.72167	−	0.189348i	−1.00000			1.42622	+	2.47029i	−0.189348	−	1.72167i	−1.89518	+	1.84615i			1.00000i	2.92829	−	0.651988i	2.47029	−	1.42622i
269.20			1.00000i	−1.73168	−	0.0356471i	−1.00000			−0.277881	−	0.481304i	0.0356471	−	1.73168i	−1.71510	−	2.01455i		−	1.00000i	2.99746	+	0.123459i	0.481304	−	0.277881i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	inner
91.v	odd	6	1	inner
273.r	even	6	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	546.2.bb.a	yes	76
3.b	odd	2	1	inner	546.2.bb.a	yes	76
7.d	odd	6	1		546.2.u.a	✓	76
13.c	even	3	1		546.2.u.a	✓	76
21.g	even	6	1		546.2.u.a	✓	76
39.i	odd	6	1		546.2.u.a	✓	76
91.v	odd	6	1	inner	546.2.bb.a	yes	76
273.r	even	6	1	inner	546.2.bb.a	yes	76

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
546.2.u.a	✓	76	7.d	odd	6	1
546.2.u.a	✓	76	13.c	even	3	1
546.2.u.a	✓	76	21.g	even	6	1
546.2.u.a	✓	76	39.i	odd	6	1
546.2.bb.a	yes	76	1.a	even	1	1	trivial
546.2.bb.a	yes	76	3.b	odd	2	1	inner
546.2.bb.a	yes	76	91.v	odd	6	1	inner
546.2.bb.a	yes	76	273.r	even	6	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(546, [\chi])\).