Newform orbit 555.2.bm.a

• Label: 555.2.bm.a
• Level: $555$
• Weight: $2$
• Character orbit: 555.bm
• Analytic conductor: $4.432$
• Analytic rank: $0$
• Dimension: $288$
• CM: no
• Inner twists: $8$

Newspace parameters

Level:	\( N \)	\(=\)	\( 555 = 3 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	555.bm (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(4.43169731218\)
Analytic rank:	\(0\)
Dimension:	\(288\)
Relative dimension:	\(72\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 288 q - 24 q^{4} - 16 q^{6}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
14.1	−2.51036	+	0.672650i	1.17720	−	1.27051i	4.11741	−	2.37719i	−1.25457	+	1.85096i	−2.10059	+	3.98129i	−2.69334	+	1.55500i	−5.06175	+	5.06175i	−0.228404	−	2.99129i	1.90438	−	5.49047i
14.2	−2.51036	+	0.672650i	1.68890	−	0.384228i	4.11741	−	2.37719i	−0.161010	−	2.23026i	−3.98129	+	2.10059i	2.69334	−	1.55500i	−5.06175	+	5.06175i	2.70474	−	1.29784i	1.90438	+	5.49047i
14.3	−2.47244	+	0.662488i	−1.58144	−	0.706434i	3.94201	−	2.27592i	2.10967	+	0.741153i	4.37801	+	0.698931i	−0.914186	+	0.527806i	−4.61870	+	4.61870i	2.00190	+	2.23437i	−5.70702	−	0.434826i
14.4	−2.47244	+	0.662488i	−0.178930	+	1.72278i	3.94201	−	2.27592i	2.19760	+	0.412976i	−0.698931	−	4.37801i	0.914186	−	0.527806i	−4.61870	+	4.61870i	−2.93597	−	0.616514i	−5.70702	+	0.434826i
14.5	−2.42690	+	0.650286i	−0.589846	−	1.62852i	3.73492	−	2.15636i	−1.31206	−	1.81066i	2.49050	+	3.56869i	0.483430	−	0.279108i	−4.10881	+	4.10881i	−2.30416	+	1.92115i	4.36170	+	3.54107i
14.6	−2.42690	+	0.650286i	1.11542	+	1.32508i	3.73492	−	2.15636i	−2.04161	+	0.912045i	−3.56869	−	2.49050i	−0.483430	+	0.279108i	−4.10881	+	4.10881i	−0.511686	+	2.95604i	4.36170	−	3.54107i
14.7	−2.36889	+	0.634743i	−0.496912	−	1.65924i	3.47671	−	2.00728i	−0.509964	+	2.17714i	2.23032	+	3.61515i	3.10032	−	1.78997i	−3.49355	+	3.49355i	−2.50616	+	1.64899i	−0.173873	−	5.48111i
14.8	−2.36889	+	0.634743i	1.18849	+	1.25996i	3.47671	−	2.00728i	0.646928	−	2.14044i	−3.61515	−	2.23032i	−3.10032	+	1.78997i	−3.49355	+	3.49355i	−0.174990	+	2.99489i	−0.173873	+	5.48111i
14.9	−2.10178	+	0.563171i	−1.65091	+	0.523929i	2.36827	−	1.36732i	0.846314	−	2.06972i	3.17479	−	2.03093i	2.46989	−	1.42599i	−1.13033	+	1.13033i	2.45100	−	1.72992i	−0.613159	+	4.82672i
14.10	−2.10178	+	0.563171i	−1.27919	+	1.16776i	2.36827	−	1.36732i	−0.301932	+	2.21559i	2.03093	−	3.17479i	−2.46989	+	1.42599i	−1.13033	+	1.13033i	0.272654	−	2.98758i	−0.613159	−	4.82672i
14.11	−2.03267	+	0.544653i	1.10763	−	1.33160i	2.10306	−	1.21420i	2.12678	+	0.690520i	−1.52619	+	3.30998i	3.21898	−	1.85848i	−0.637478	+	0.637478i	−0.546319	−	2.94984i	−4.69914	−	0.245246i
14.12	−2.03267	+	0.544653i	1.70701	−	0.293434i	2.10306	−	1.21420i	2.18710	+	0.465380i	−3.30998	+	1.52619i	−3.21898	+	1.85848i	−0.637478	+	0.637478i	2.82779	−	1.00179i	−4.69914	+	0.245246i
14.13	−1.74827	+	0.468447i	−0.883442	−	1.48981i	1.10495	−	0.637944i	1.44748	−	1.70435i	2.24239	+	2.19074i	−2.07761	+	1.19951i	0.926734	−	0.926734i	−1.43906	+	2.63232i	−1.73218	+	3.65773i
14.14	−1.74827	+	0.468447i	0.848492	+	1.50999i	1.10495	−	0.637944i	0.401377	+	2.19975i	−2.19074	−	2.24239i	2.07761	−	1.19951i	0.926734	−	0.926734i	−1.56012	+	2.56242i	−1.73218	−	3.65773i
14.15	−1.72090	+	0.461115i	0.973506	−	1.43258i	1.01683	−	0.587068i	−1.69790	−	1.45504i	−1.01473	+	2.91423i	−2.54246	+	1.46789i	1.04042	−	1.04042i	−1.10457	−	2.78925i	3.59286	+	1.72106i
14.16	−1.72090	+	0.461115i	1.72740	−	0.126791i	1.01683	−	0.587068i	−2.19794	+	0.411155i	−2.91423	+	1.01473i	2.54246	−	1.46789i	1.04042	−	1.04042i	2.96785	−	0.438039i	3.59286	−	1.72106i
14.17	−1.71773	+	0.460265i	−1.72706	−	0.131429i	1.00671	−	0.581224i	−2.22726	+	0.198274i	3.02711	−	0.569144i	1.54457	−	0.891756i	1.05320	−	1.05320i	2.96545	+	0.453971i	3.73458	−	1.36571i
14.18	−1.71773	+	0.460265i	−0.749708	+	1.56139i	1.00671	−	0.581224i	−1.82973	−	1.28534i	0.569144	−	3.02711i	−1.54457	+	0.891756i	1.05320	−	1.05320i	−1.87588	−	2.34117i	3.73458	+	1.36571i
14.19	−1.33351	+	0.357313i	−0.0211729	−	1.73192i	−0.0814707	+	0.0470371i	1.09159	+	1.95152i	0.647073	+	2.30197i	−1.62126	+	0.936037i	2.04423	−	2.04423i	−2.99910	+	0.0733396i	−2.15295	−	2.21234i
14.20	−1.33351	+	0.357313i	1.48930	+	0.884297i	−0.0814707	+	0.0470371i	1.92110	−	1.14427i	−2.30197	−	0.647073i	1.62126	−	0.936037i	2.04423	−	2.04423i	1.43604	+	2.63397i	−2.15295	+	2.21234i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	inner
5.b	even	2	1	inner
15.d	odd	2	1	inner
37.g	odd	12	1	inner
111.m	even	12	1	inner
185.q	odd	12	1	inner
555.bm	even	12	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	555.2.bm.a	✓	288
3.b	odd	2	1	inner	555.2.bm.a	✓	288
5.b	even	2	1	inner	555.2.bm.a	✓	288
15.d	odd	2	1	inner	555.2.bm.a	✓	288
37.g	odd	12	1	inner	555.2.bm.a	✓	288
111.m	even	12	1	inner	555.2.bm.a	✓	288
185.q	odd	12	1	inner	555.2.bm.a	✓	288
555.bm	even	12	1	inner	555.2.bm.a	✓	288

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
555.2.bm.a	✓	288	1.a	even	1	1	trivial
555.2.bm.a	✓	288	3.b	odd	2	1	inner
555.2.bm.a	✓	288	5.b	even	2	1	inner
555.2.bm.a	✓	288	15.d	odd	2	1	inner
555.2.bm.a	✓	288	37.g	odd	12	1	inner
555.2.bm.a	✓	288	111.m	even	12	1	inner
555.2.bm.a	✓	288	185.q	odd	12	1	inner
555.2.bm.a	✓	288	555.bm	even	12	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(555, [\chi])\).