Newform orbit 495.2.p.a

• Label: 495.2.p.a
• Level: $495$
• Weight: $2$
• Character orbit: 495.p
• Analytic conductor: $3.953$
• Analytic rank: $0$
• Dimension: $96$
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 495 = 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	495.p (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(3.95259490005\)
Analytic rank:	\(0\)
Dimension:	\(96\)
Relative dimension:	\(48\) over \(\Q(\zeta_{6})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

$q$-expansion

The algebraic \(q\)-expansion of this newform has not been computed, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) 96 * q + 4 * q^3 - 48 * q^4 - 20 * q^9 + 12 * q^11 - 24 * q^12 + 4 * q^15 - 48 * q^16 - 6 * q^22 - 36 * q^23 + 48 * q^25 + 4 * q^27 + 20 * q^33 - 12 * q^34 - 36 * q^36 - 48 * q^38 + 8 * q^42 - 80 * q^48 + 48 * q^49 + 84 * q^56 + 48 * q^59 - 12 * q^60 + 96 * q^64 - 24 * q^66 + 12 * q^67 - 164 * q^69 - 4 * q^75 - 54 * q^77 + 20 * q^78 - 52 * q^81 - 24 * q^82 + 60 * q^86 - 18 * q^88 - 24 * q^91 + 204 * q^92 + 116 * q^93 - 36 * q^97 + 52 * q^99

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
131.1	−1.38813	−	2.40431i	0.630545	+	1.61320i	−2.85382	+	4.94295i	−0.866025	−	0.500000i	3.00336	−	3.75536i	−0.786806	+	0.454263i	10.2934			−2.20483	+	2.03439i			2.77626i
131.2	−1.36254	−	2.35998i	1.60165	−	0.659342i	−2.71301	+	4.69908i	0.866025	+	0.500000i	−3.73834	−	2.88148i	−1.96970	+	1.13721i	9.33617			2.13053	−	2.11207i		−	2.72507i
131.3	−1.25650	−	2.17632i	−1.47357	−	0.910275i	−2.15759	+	3.73706i	−0.866025	−	0.500000i	−0.129515	+	4.35072i	2.81641	−	1.62605i	5.81807			1.34280	+	2.68270i			2.51300i
131.4	−1.24238	−	2.15187i	−0.161011	−	1.72455i	−2.08704	+	3.61485i	0.866025	+	0.500000i	−3.51098	+	2.48903i	4.12719	−	2.38284i	5.40207			−2.94815	+	0.555343i		−	2.48477i
131.5	−1.19006	−	2.06124i	−0.361941	+	1.69381i	−1.83247	+	3.17394i	0.866025	+	0.500000i	3.92208	−	1.26969i	0.517586	−	0.298829i	3.96276			−2.73800	−	1.22612i		−	2.38011i
131.6	−1.12141	−	1.94234i	−0.880636	−	1.49147i	−1.51512	+	2.62426i	0.866025	+	0.500000i	−1.90938	+	3.38304i	−2.88407	+	1.66512i	2.31062			−1.44896	+	2.62688i		−	2.24282i
131.7	−1.10444	−	1.91294i	−0.863075	+	1.50170i	−1.43955	+	2.49338i	−0.866025	−	0.500000i	3.82587	−	0.00752193i	0.958765	−	0.553543i	1.94183			−1.51020	−	2.59216i			2.20887i
131.8	−1.09687	−	1.89984i	1.41080	+	1.00482i	−1.40626	+	2.43571i	0.866025	+	0.500000i	0.361525	−	3.78244i	1.52319	−	0.879414i	1.78245			0.980691	+	2.83518i		−	2.19374i
131.9	−0.999282	−	1.73081i	1.55315	+	0.766638i	−0.997129	+	1.72708i	−0.866025	−	0.500000i	−0.225130	−	3.45429i	−3.65753	+	2.11168i	−0.0114739			1.82453	+	2.38140i			1.99856i
131.10	−0.993620	−	1.72100i	0.830918	−	1.51973i	−0.974561	+	1.68799i	−0.866025	−	0.500000i	−3.44107	+	0.0800229i	−0.349912	+	0.202022i	−0.101107			−1.61915	−	2.52554i			1.98724i
131.11	−0.833416	−	1.44352i	−1.72533	+	0.152438i	−0.389163	+	0.674050i	0.866025	+	0.500000i	1.65796	+	2.36350i	0.135146	−	0.0780264i	−2.03632			2.95353	−	0.526012i		−	1.66683i
131.12	−0.806273	−	1.39651i	−1.42574	+	0.983501i	−0.300153	+	0.519880i	−0.866025	−	0.500000i	2.52300	+	1.19808i	−3.42896	+	1.97971i	−2.25707			1.06545	−	2.80443i			1.61255i
131.13	−0.757430	−	1.31191i	1.05327	+	1.37500i	−0.147399	+	0.255303i	−0.866025	−	0.500000i	1.00609	−	2.42326i	4.31548	−	2.49154i	−2.58314			−0.781250	+	2.89649i			1.51486i
131.14	−0.717408	−	1.24259i	−1.61675	−	0.621387i	−0.0293497	+	0.0508352i	−0.866025	−	0.500000i	0.387742	+	2.45474i	2.19669	−	1.26826i	−2.78541			2.22776	+	2.00925i			1.43482i
131.15	−0.709731	−	1.22929i	0.0339627	+	1.73172i	−0.00743576	+	0.0128791i	0.866025	+	0.500000i	2.10468	−	1.27080i	−1.79029	+	1.03363i	−2.81781			−2.99769	+	0.117628i		−	1.41946i
131.16	−0.565518	−	0.979507i	−0.721938	−	1.57442i	0.360378	−	0.624193i	−0.866025	−	0.500000i	−1.13389	+	1.59751i	−1.97291	+	1.13906i	−3.07727			−1.95761	+	2.27327i			1.13104i
131.17	−0.458138	−	0.793518i	1.70787	−	0.288434i	0.580220	−	1.00497i	0.866025	+	0.500000i	−1.01132	−	1.22308i	1.94199	−	1.12121i	−2.89583			2.83361	−	0.985213i		−	0.916276i
131.18	−0.414796	−	0.718448i	1.73102	−	0.0597968i	0.655888	−	1.13603i	−0.866025	−	0.500000i	−0.760981	−	1.21884i	0.350251	−	0.202217i	−2.74743			2.99285	−	0.207019i			0.829593i
131.19	−0.388436	−	0.672791i	0.612983	−	1.61995i	0.698235	−	1.20938i	0.866025	+	0.500000i	−1.32800	+	0.216839i	0.931864	−	0.538012i	−2.63862			−2.24850	−	1.98601i		−	0.776872i
131.20	−0.350651	−	0.607346i	1.04496	+	1.38132i	0.754088	−	1.30612i	0.866025	+	0.500000i	0.472524	−	1.11902i	−2.21245	+	1.27736i	−2.46029			−0.816113	+	2.88686i		−	0.701302i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
9.d	odd	6	1	inner
11.b	odd	2	1	inner
99.g	even	6	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	495.2.p.a	✓	96
3.b	odd	2	1		1485.2.p.a		96
9.c	even	3	1		1485.2.p.a		96
9.d	odd	6	1	inner	495.2.p.a	✓	96
11.b	odd	2	1	inner	495.2.p.a	✓	96
33.d	even	2	1		1485.2.p.a		96
99.g	even	6	1	inner	495.2.p.a	✓	96
99.h	odd	6	1		1485.2.p.a		96

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
495.2.p.a	✓	96	1.a	even	1	1	trivial
495.2.p.a	✓	96	9.d	odd	6	1	inner
495.2.p.a	✓	96	11.b	odd	2	1	inner
495.2.p.a	✓	96	99.g	even	6	1	inner
1485.2.p.a		96	3.b	odd	2	1
1485.2.p.a		96	9.c	even	3	1
1485.2.p.a		96	33.d	even	2	1
1485.2.p.a		96	99.h	odd	6	1

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(495, [\chi])\).