Newform orbit 546.2.bw.a

• Label: 546.2.bw.a
• Level: $546$
• Weight: $2$
• Character orbit: 546.bw
• Analytic conductor: $4.360$
• Analytic rank: $0$
• Dimension: $152$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.bw (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(4.35983195036\)
Analytic rank:	\(0\)
Dimension:	\(152\)
Relative dimension:	\(38\) over \(\Q(\zeta_{12})\)
Twist minimal:	yes
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.

\(\operatorname{Tr}(f)(q) = \) \( 152 q + 12 q^{7}+O(q^{10}) \)

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	−0.258819	−	0.965926i	−1.73001	−	0.0839781i	−0.866025	+	0.500000i	−2.83225	−	0.758898i	0.366644	+	1.69280i	−2.04314	+	1.68095i	0.707107	+	0.707107i	2.98590	+	0.290567i			2.93216i
11.2	−0.258819	−	0.965926i	−1.61660	−	0.621783i	−0.866025	+	0.500000i	−0.475031	−	0.127284i	−0.182190	+	1.72244i	2.42388	−	1.06056i	0.707107	+	0.707107i	2.22677	+	2.01034i			0.491788i
11.3	−0.258819	−	0.965926i	−1.45291	−	0.942896i	−0.866025	+	0.500000i	0.0616403	+	0.0165165i	−0.534727	+	1.64744i	−1.95035	−	1.78777i	0.707107	+	0.707107i	1.22189	+	2.73989i		−	0.0638147i
11.4	−0.258819	−	0.965926i	−1.41158	+	1.00372i	−0.866025	+	0.500000i	−0.854914	−	0.229074i	1.33486	+	1.10370i	0.275303	−	2.63139i	0.707107	+	0.707107i	0.985106	−	2.83365i			0.885072i
11.5	−0.258819	−	0.965926i	−1.37659	+	1.05119i	−0.866025	+	0.500000i	3.72584	+	0.998336i	1.37166	+	1.05761i	−1.75384	−	1.98092i	0.707107	+	0.707107i	0.789991	−	2.89412i		−	3.85727i
11.6	−0.258819	−	0.965926i	−0.980845	+	1.42757i	−0.866025	+	0.500000i	−3.87106	−	1.03725i	1.63278	+	0.577943i	2.44614	+	1.00817i	0.707107	+	0.707107i	−1.07589	−	2.80044i			4.00762i
11.7	−0.258819	−	0.965926i	−0.773747	−	1.54962i	−0.866025	+	0.500000i	2.25164	+	0.603326i	−1.29656	+	1.14845i	−1.19264	+	2.36170i	0.707107	+	0.707107i	−1.80263	+	2.39802i		−	2.33107i
11.8	−0.258819	−	0.965926i	−0.328251	+	1.70066i	−0.866025	+	0.500000i	1.75073	+	0.469106i	1.72767	−	0.123098i	1.22850	+	2.34324i	0.707107	+	0.707107i	−2.78450	−	1.11649i		−	1.81249i
11.9	−0.258819	−	0.965926i	−0.229196	+	1.71682i	−0.866025	+	0.500000i	0.0852751	+	0.0228494i	1.71764	−	0.222959i	−2.48393	+	0.911101i	0.707107	+	0.707107i	−2.89494	−	0.786976i		−	0.0882833i
11.10	−0.258819	−	0.965926i	0.0687143	−	1.73069i	−0.866025	+	0.500000i	0.682162	+	0.182785i	−1.68950	+	0.381562i	1.42099	+	2.23177i	0.707107	+	0.707107i	−2.99056	−	0.237846i		−	0.706226i
11.11	−0.258819	−	0.965926i	0.131905	−	1.72702i	−0.866025	+	0.500000i	−3.76426	−	1.00863i	−1.70231	+	0.319575i	1.07453	−	2.41772i	0.707107	+	0.707107i	−2.96520	−	0.455606i			3.89704i
11.12	−0.258819	−	0.965926i	0.472866	−	1.66625i	−0.866025	+	0.500000i	2.76510	+	0.740906i	−1.73186	−	0.0254954i	0.700808	−	2.55125i	0.707107	+	0.707107i	−2.55280	−	1.57583i		−	2.86264i
11.13	−0.258819	−	0.965926i	0.770566	+	1.55120i	−0.866025	+	0.500000i	−1.57124	−	0.421014i	1.29891	−	1.14579i	0.222219	−	2.63640i	0.707107	+	0.707107i	−1.81246	+	2.39061i			1.62667i
11.14	−0.258819	−	0.965926i	0.868227	−	1.49873i	−0.866025	+	0.500000i	−3.18146	−	0.852470i	−1.67237	−	0.450743i	−1.87409	+	1.86756i	0.707107	+	0.707107i	−1.49237	−	2.60247i			3.29369i
11.15	−0.258819	−	0.965926i	1.00636	+	1.40969i	−0.866025	+	0.500000i	3.29330	+	0.882438i	1.10119	−	1.33693i	2.64105	−	0.157578i	0.707107	+	0.707107i	−0.974462	+	2.83733i		−	3.40948i
11.16	−0.258819	−	0.965926i	1.57960	+	0.710547i	−0.866025	+	0.500000i	2.90525	+	0.778459i	0.277506	−	1.70968i	−2.63535	−	0.234373i	0.707107	+	0.707107i	1.99025	+	2.24475i		−	3.00773i
11.17	−0.258819	−	0.965926i	1.63257	−	0.578534i	−0.866025	+	0.500000i	−0.965749	−	0.258772i	−0.981362	−	1.42721i	1.68839	+	2.03700i	0.707107	+	0.707107i	2.33060	−	1.88900i			0.999817i
11.18	−0.258819	−	0.965926i	1.66438	−	0.479415i	−0.866025	+	0.500000i	1.88802	+	0.505894i	−0.893853	−	1.48359i	2.05975	−	1.66055i	0.707107	+	0.707107i	2.54032	−	1.59586i		−	1.95463i
11.19	−0.258819	−	0.965926i	1.70453	+	0.307515i	−0.866025	+	0.500000i	−1.89300	−	0.507228i	−0.144129	−	1.72604i	−2.48026	−	0.921033i	0.707107	+	0.707107i	2.81087	+	1.04834i			1.95978i
11.20	0.258819	+	0.965926i	−1.73001	+	0.0839781i	−0.866025	+	0.500000i	2.83225	+	0.758898i	−0.528877	−	1.64933i	−2.04314	+	1.68095i	−0.707107	−	0.707107i	2.98590	−	0.290567i			2.93216i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	inner
91.bd	odd	12	1	inner
273.bw	even	12	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	546.2.bw.a	✓	152
3.b	odd	2	1	inner	546.2.bw.a	✓	152
7.c	even	3	1		546.2.ch.a	yes	152
13.f	odd	12	1		546.2.ch.a	yes	152
21.h	odd	6	1		546.2.ch.a	yes	152
39.k	even	12	1		546.2.ch.a	yes	152
91.bd	odd	12	1	inner	546.2.bw.a	✓	152
273.bw	even	12	1	inner	546.2.bw.a	✓	152

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
546.2.bw.a	✓	152	1.a	even	1	1	trivial
546.2.bw.a	✓	152	3.b	odd	2	1	inner
546.2.bw.a	✓	152	91.bd	odd	12	1	inner
546.2.bw.a	✓	152	273.bw	even	12	1	inner
546.2.ch.a	yes	152	7.c	even	3	1
546.2.ch.a	yes	152	13.f	odd	12	1
546.2.ch.a	yes	152	21.h	odd	6	1
546.2.ch.a	yes	152	39.k	even	12	1

Hecke kernels

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