Newform orbit 465.2.o.a

• Label: 465.2.o.a
• Level: $465$
• Weight: $2$
• Character orbit: 465.o
• Analytic conductor: $3.713$
• Analytic rank: $0$
• Dimension: $84$
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 465 = 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	465.o (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(3.71304369399\)
Analytic rank:	\(0\)
Dimension:	\(84\)
Relative dimension:	\(42\) 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.

\(\operatorname{Tr}(f)(q) = \) 84 * q - 76 * q^4 + 18 * q^6 + 2 * q^10 - 18 * q^13 + 60 * q^16 + 10 * q^18 + 10 * q^19 - 42 * q^21 - 36 * q^24 + 42 * q^25 - 8 * q^28 - 28 * q^31 - 4 * q^33 - 18 * q^34 + 6 * q^36 + 18 * q^37 + 32 * q^39 + 24 * q^40 - 90 * q^42 + 42 * q^43 + 4 * q^45 + 48 * q^48 - 62 * q^49 - 8 * q^51 + 144 * q^52 - 12 * q^55 - 12 * q^57 - 72 * q^63 - 160 * q^64 - 76 * q^66 - 32 * q^67 + 24 * q^69 - 84 * q^72 - 30 * q^73 - 86 * q^76 + 76 * q^78 + 28 * q^81 - 36 * q^82 + 210 * q^84 - 6 * q^87 - 72 * q^88 + 8 * q^90 - 100 * q^93 + 220 * q^94 + 168 * q^96 + 12 * q^97 + 54 * 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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
26.1		−	2.75560i	0.965315	+	1.43811i	−5.59331			0.866025	−	0.500000i	3.96286	−	2.66002i	−2.20986	+	3.82759i			9.90170i	−1.13633	+	2.77646i	−1.37780	−	2.38642i
26.2		−	2.64726i	−1.47729	+	0.904227i	−5.00797			−0.866025	+	0.500000i	2.39372	+	3.91076i	−0.0311239	+	0.0539082i			7.96287i	1.36475	−	2.67160i	1.32363	+	2.29259i
26.3		−	2.62586i	−0.134987	−	1.72678i	−4.89514			0.866025	−	0.500000i	−4.53429	+	0.354457i	2.14649	−	3.71783i			7.60223i	−2.96356	+	0.466187i	−1.31293	−	2.27406i
26.4		−	2.38701i	0.715863	+	1.57719i	−3.69781			−0.866025	+	0.500000i	3.76478	−	1.70877i	1.50161	−	2.60087i			4.05268i	−1.97508	+	2.25811i	1.19350	+	2.06721i
26.5		−	2.29159i	−1.47595	+	0.906412i	−3.25139			0.866025	−	0.500000i	2.07713	+	3.38227i	0.405889	−	0.703021i			2.86768i	1.35683	−	2.67563i	−1.14580	−	1.98458i
26.6		−	2.07473i	1.45124	−	0.945463i	−2.30452			0.866025	−	0.500000i	−1.96158	−	3.01094i	−0.753936	+	1.30586i			0.631788i	1.21220	−	2.74419i	−1.03737	−	1.79677i
26.7		−	2.01133i	−1.26968	−	1.17810i	−2.04544			−0.866025	+	0.500000i	−2.36955	+	2.55374i	−0.941394	+	1.63054i			0.0913974i	0.224160	+	2.99161i	1.00566	+	1.74186i
26.8		−	1.78703i	−0.483456	+	1.66321i	−1.19348			−0.866025	+	0.500000i	2.97221	+	0.863952i	−1.94940	+	3.37646i		−	1.44127i	−2.53254	−	1.60818i	0.893516	+	1.54761i
26.9		−	1.78039i	−0.284115	−	1.70859i	−1.16979			−0.866025	+	0.500000i	−3.04196	+	0.505835i	1.86834	−	3.23606i		−	1.47810i	−2.83856	+	0.970870i	0.890195	+	1.54186i
26.10		−	1.64741i	1.01103	−	1.40635i	−0.713974			−0.866025	+	0.500000i	−2.31685	−	1.66558i	−0.179912	+	0.311616i		−	2.11862i	−0.955654	−	2.84372i	0.823707	+	1.42670i
26.11		−	1.59574i	−1.69863	−	0.338601i	−0.546377			0.866025	−	0.500000i	−0.540317	+	2.71057i	1.58858	−	2.75151i		−	2.31960i	2.77070	+	1.15032i	−0.797869	−	1.38195i
26.12		−	1.57069i	1.37717	+	1.05043i	−0.467081			0.866025	−	0.500000i	1.64991	−	2.16311i	0.571783	−	0.990357i		−	2.40775i	0.793189	+	2.89324i	−0.785347	−	1.36026i
26.13		−	1.47744i	1.61791	+	0.618351i	−0.182823			−0.866025	+	0.500000i	0.913576	−	2.39037i	−2.25563	+	3.90686i		−	2.68477i	2.23528	+	2.00088i	0.738719	+	1.27950i
26.14		−	0.929497i	1.71887	+	0.213270i	1.13603			−0.866025	+	0.500000i	0.198233	−	1.59769i	2.04756	−	3.54648i		−	2.91494i	2.90903	+	0.733165i	0.464749	+	0.804968i
26.15		−	0.874240i	−1.69245	+	0.368254i	1.23570			0.866025	−	0.500000i	0.321943	+	1.47961i	−2.57080	+	4.45276i		−	2.82878i	2.72878	−	1.24650i	−0.437120	−	0.757114i
26.16		−	0.873617i	−0.976350	+	1.43064i	1.23679			−0.866025	+	0.500000i	1.24984	+	0.852956i	1.44167	−	2.49704i		−	2.82772i	−1.09348	−	2.79362i	0.436809	+	0.756575i
26.17		−	0.831589i	−0.465689	−	1.66827i	1.30846			0.866025	−	0.500000i	−1.38732	+	0.387262i	0.0353422	−	0.0612145i		−	2.75128i	−2.56627	+	1.55379i	−0.415794	−	0.720177i
26.18		−	0.778487i	−1.71064	−	0.271514i	1.39396			−0.866025	+	0.500000i	−0.211370	+	1.33171i	−0.567828	+	0.983507i		−	2.64215i	2.85256	+	0.928925i	0.389244	+	0.674190i
26.19		−	0.459345i	−1.16522	+	1.28150i	1.78900			0.866025	−	0.500000i	0.588653	+	0.535240i	1.20094	−	2.08009i		−	1.74046i	−0.284505	−	2.98648i	−0.229673	−	0.397805i
26.20		−	0.151885i	0.0908737	+	1.72967i	1.97693			0.866025	−	0.500000i	0.262711	−	0.0138024i	−0.275801	+	0.477701i		−	0.604038i	−2.98348	+	0.314362i	−0.0759427	−	0.131537i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	inner
31.e	odd	6	1	inner
93.g	even	6	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	465.2.o.a	✓	84
3.b	odd	2	1	inner	465.2.o.a	✓	84
31.e	odd	6	1	inner	465.2.o.a	✓	84
93.g	even	6	1	inner	465.2.o.a	✓	84

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
465.2.o.a	✓	84	1.a	even	1	1	trivial
465.2.o.a	✓	84	3.b	odd	2	1	inner
465.2.o.a	✓	84	31.e	odd	6	1	inner
465.2.o.a	✓	84	93.g	even	6	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(465, [\chi])\).