Newform orbit 855.2.bx.a

• Label: 855.2.bx.a
• Level: $855$
• Weight: $2$
• Character orbit: 855.bx
• Analytic conductor: $6.827$
• Analytic rank: $0$
• Dimension: $464$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 855 = 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	855.bx (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(6.82720937282\)
Analytic rank:	\(0\)
Dimension:	\(464\)
Relative dimension:	\(116\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 464 q - 2 q^{3} - 6 q^{5} - 4 q^{6} - 4 q^{7}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
68.1	−1.98315	−	1.98315i	1.22786	−	1.22162i			5.86578i	−2.14188	+	0.642130i	−4.85769	−	0.0123644i	−3.35240	−	0.898272i	7.66642	−	7.66642i	0.0152719	−	2.99996i	5.52112	+	2.97424i
68.2	−1.93273	−	1.93273i	−0.457222	+	1.67061i			5.47091i	1.47027	−	1.68473i	4.11254	−	2.34516i	2.45245	+	0.657131i	6.70834	−	6.70834i	−2.58190	−	1.52768i	−6.09777	+	0.414491i
68.3	−1.91836	−	1.91836i	−1.57207	−	0.727045i			5.36023i	1.70623	−	1.44526i	1.62106	+	4.41054i	−2.89189	−	0.774879i	6.44613	−	6.44613i	1.94281	+	2.28593i	−6.04570	−	0.500625i
68.4	−1.90526	−	1.90526i	0.967548	−	1.43661i			5.26004i	1.93830	+	1.11489i	−4.58055	+	0.893686i	3.52893	+	0.945574i	6.21122	−	6.21122i	−1.12770	−	2.77998i	−1.56880	−	5.81713i
68.5	−1.83229	−	1.83229i	−1.31573	+	1.12643i			4.71456i	0.593080	+	2.15598i	4.47475	+	0.346861i	−3.11425	−	0.834459i	4.97385	−	4.97385i	0.462313	−	2.96416i	2.86368	−	5.03707i
68.6	−1.82972	−	1.82972i	1.16954	+	1.27756i			4.69575i	−1.53851	+	1.62265i	0.197650	−	4.47752i	0.0610090	+	0.0163473i	4.93247	−	4.93247i	−0.264341	+	2.98833i	5.78403	−	0.153953i
68.7	−1.80641	−	1.80641i	1.65319	+	0.516670i			4.52625i	−0.397276	−	2.20049i	−2.05303	−	3.91967i	0.530881	+	0.142249i	4.56346	−	4.56346i	2.46610	+	1.70831i	−3.25735	+	4.69264i
68.8	−1.76525	−	1.76525i	1.60584	+	0.649064i			4.23220i	1.69893	+	1.45384i	−1.68894	−	3.98046i	2.19928	+	0.589295i	3.94038	−	3.94038i	2.15743	+	2.08458i	−0.432635	−	5.56541i
68.9	−1.75379	−	1.75379i	−1.67679	+	0.434030i			4.15154i	−1.52255	+	1.63763i	3.70193	+	2.17953i	4.56622	+	1.22351i	3.77334	−	3.77334i	2.62324	−	1.45555i	5.54229	−	0.201835i
68.10	−1.72878	−	1.72878i	−0.596167	+	1.62622i			3.97736i	−2.15959	−	0.579784i	3.84201	−	1.78073i	−0.563084	−	0.150878i	3.41842	−	3.41842i	−2.28917	−	1.93900i	2.73114	+	4.73578i
68.11	−1.64234	−	1.64234i	0.222594	−	1.71769i			3.39459i	2.05924	−	0.871522i	−3.18661	+	2.45546i	−1.72506	−	0.462229i	2.29040	−	2.29040i	−2.90090	−	0.764693i	−4.81331	−	1.95063i
68.12	−1.64116	−	1.64116i	−1.02226	−	1.39821i			3.38678i	−2.14386	−	0.635487i	−0.617001	+	3.97236i	−0.295580	−	0.0792005i	2.27592	−	2.27592i	−0.909988	+	2.85866i	2.47548	+	4.56135i
68.13	−1.62066	−	1.62066i	−1.59069	−	0.685360i			3.25310i	1.71155	+	1.43895i	1.46723	+	3.68871i	1.11894	+	0.299818i	2.03086	−	2.03086i	2.06056	+	2.18039i	−0.441788	−	5.10591i
68.14	−1.61546	−	1.61546i	0.126631	−	1.72742i			3.21945i	−0.781034	−	2.09523i	−2.99515	+	2.58601i	−2.08873	−	0.559673i	1.96998	−	1.96998i	−2.96793	−	0.437490i	−2.12304	+	4.64650i
68.15	−1.57188	−	1.57188i	0.480129	+	1.66417i			2.94159i	2.15009	+	0.614083i	1.86117	−	3.37058i	−0.800204	−	0.214414i	1.48006	−	1.48006i	−2.53895	+	1.59804i	−2.41442	−	4.34494i
68.16	−1.55363	−	1.55363i	1.70748	−	0.290733i			2.82751i	1.85686	−	1.24583i	−3.10447	−	2.20109i	−2.86631	−	0.768026i	1.28565	−	1.28565i	2.83095	−	0.992838i	−4.82041	−	0.949311i
68.17	−1.50834	−	1.50834i	−1.72316	+	0.175291i			2.55018i	−1.39261	−	1.74947i	2.86351	+	2.33471i	−1.03953	−	0.278542i	0.829852	−	0.829852i	2.93855	−	0.604110i	−0.538274	+	4.73932i
68.18	−1.49100	−	1.49100i	−1.69537	+	0.354591i			2.44617i	0.629601	−	2.14560i	3.05649	+	1.99910i	2.38168	+	0.638169i	0.665237	−	0.665237i	2.74853	−	1.20232i	−4.13783	+	2.26036i
68.19	−1.49097	−	1.49097i	1.50814	−	0.851779i			2.44596i	−2.17152	−	0.533390i	−3.51855	−	0.978607i	3.89151	+	1.04273i	0.664917	−	0.664917i	1.54895	−	2.56920i	2.44240	+	4.03293i
68.20	−1.44468	−	1.44468i	1.57030	−	0.730864i			2.17420i	1.12591	+	1.93192i	−3.32444	−	1.21272i	−4.44643	−	1.19142i	0.251669	−	0.251669i	1.93168	−	2.29535i	1.16443	−	4.41759i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
5.c	odd	4	1	inner
171.j	odd	6	1	inner
855.bx	even	12	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	855.2.bx.a	✓	464
5.c	odd	4	1	inner	855.2.bx.a	✓	464
9.d	odd	6	1		855.2.ci.a	yes	464
19.c	even	3	1		855.2.ci.a	yes	464
45.l	even	12	1		855.2.ci.a	yes	464
95.m	odd	12	1		855.2.ci.a	yes	464
171.j	odd	6	1	inner	855.2.bx.a	✓	464
855.bx	even	12	1	inner	855.2.bx.a	✓	464

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
855.2.bx.a	✓	464	1.a	even	1	1	trivial
855.2.bx.a	✓	464	5.c	odd	4	1	inner
855.2.bx.a	✓	464	171.j	odd	6	1	inner
855.2.bx.a	✓	464	855.bx	even	12	1	inner
855.2.ci.a	yes	464	9.d	odd	6	1
855.2.ci.a	yes	464	19.c	even	3	1
855.2.ci.a	yes	464	45.l	even	12	1
855.2.ci.a	yes	464	95.m	odd	12	1

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(855, [\chi])\).