Newform orbit 465.2.q.b

• Label: 465.2.q.b
• Level: $465$
• Weight: $2$
• Character orbit: 465.q
• Analytic conductor: $3.713$
• Analytic rank: $0$
• Dimension: $60$
• Inner twists: $4$

Newspace parameters

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

Newform invariants

Self dual:	no
Analytic conductor:	\(3.71304369399\)
Analytic rank:	\(0\)
Dimension:	\(60\)
Relative dimension:	\(30\) 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.

\(\operatorname{Tr}(f)(q) = \) 60 * q - 68 * q^4 - 2 * q^5 + 6 * q^6 + 30 * q^9 + 2 * q^10 - 6 * q^11 + 4 * q^14 + 16 * q^15 + 20 * q^16 - 18 * q^20 + 16 * q^21 - 12 * q^24 + 18 * q^25 - 36 * q^26 - 12 * q^29 - 8 * q^30 - 2 * q^31 - 26 * q^34 - 4 * q^35 - 34 * q^36 - 40 * q^39 - 4 * q^40 + 2 * q^41 - 76 * q^44 + 2 * q^45 - 32 * q^46 + 54 * q^49 + 62 * q^50 - 8 * q^51 + 12 * q^54 + 2 * q^55 - 36 * q^56 - 22 * q^59 - 8 * q^60 - 76 * q^61 - 24 * q^64 + 18 * q^65 - 8 * q^66 + 20 * q^69 + 184 * q^70 + 2 * q^71 - 88 * q^74 + 16 * q^75 + 30 * q^76 - 14 * q^79 + 8 * q^80 - 30 * q^81 - 32 * q^84 - 40 * q^85 - 8 * q^86 + 44 * q^89 - 2 * q^90 + 24 * q^91 + 4 * q^94 + 84 * q^95 + 50 * q^96 + 6 * 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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
304.1		−	2.71530i	−0.866025	+	0.500000i	−5.37283			−0.793165	−	2.09067i	1.35765	+	2.35152i	−3.52866	+	2.03727i			9.15824i	0.500000	−	0.866025i	−5.67678	+	2.15368i
304.2		−	2.52175i	−0.866025	+	0.500000i	−4.35921			1.40815	+	1.73698i	1.26087	+	2.18390i	1.27653	−	0.737003i			5.94933i	0.500000	−	0.866025i	4.38022	−	3.55101i
304.3		−	2.42055i	0.866025	−	0.500000i	−3.85906			0.0792470	+	2.23466i	−1.21027	−	2.09626i	3.48532	−	2.01225i			4.49995i	0.500000	−	0.866025i	5.40911	−	0.191821i
304.4		−	2.24754i	0.866025	−	0.500000i	−3.05145			1.89729	−	1.18334i	−1.12377	−	1.94643i	−2.11510	+	1.22115i			2.36317i	0.500000	−	0.866025i	−2.65961	−	4.26423i
304.5		−	2.16012i	0.866025	−	0.500000i	−2.66614			−1.31012	−	1.81206i	−1.08006	−	1.87072i	−1.09424	+	0.631758i			1.43894i	0.500000	−	0.866025i	−3.91428	+	2.83003i
304.6		−	2.11581i	−0.866025	+	0.500000i	−2.47665			−1.82252	−	1.29553i	1.05790	+	1.83234i	4.27194	−	2.46641i			1.00850i	0.500000	−	0.866025i	−2.74110	+	3.85611i
304.7		−	1.97266i	−0.866025	+	0.500000i	−1.89140			1.71541	+	1.43435i	0.986332	+	1.70838i	−3.55080	+	2.05006i		−	0.214231i	0.500000	−	0.866025i	2.82949	−	3.38393i
304.8		−	1.56738i	0.866025	−	0.500000i	−0.456691			2.09283	+	0.787438i	−0.783692	−	1.35739i	0.751020	−	0.433602i		−	2.41896i	0.500000	−	0.866025i	1.23422	−	3.28027i
304.9		−	1.40377i	−0.866025	+	0.500000i	0.0294315			0.833968	−	2.07473i	0.701885	+	1.21570i	−0.717444	+	0.414216i		−	2.84885i	0.500000	−	0.866025i	−2.91244	−	1.17070i
304.10		−	1.29837i	−0.866025	+	0.500000i	0.314240			−1.59440	+	1.56777i	0.649184	+	1.12442i	−2.02725	+	1.17043i		−	3.00474i	0.500000	−	0.866025i	2.03554	+	2.07012i
304.11		−	1.09870i	0.866025	−	0.500000i	0.792852			−2.14855	+	0.619461i	−0.549351	−	0.951505i	2.60166	−	1.50207i		−	3.06851i	0.500000	−	0.866025i	0.680604	+	2.36062i
304.12		−	0.884829i	−0.866025	+	0.500000i	1.21708			−2.18219	−	0.487898i	0.442414	+	0.766284i	−2.44399	+	1.41104i		−	2.84656i	0.500000	−	0.866025i	−0.431706	+	1.93086i
304.13		−	0.725626i	−0.866025	+	0.500000i	1.47347			−0.00238698	+	2.23607i	0.362813	+	0.628410i	3.46926	−	2.00298i		−	2.52044i	0.500000	−	0.866025i	1.62255	+	0.00173205i
304.14		−	0.712440i	0.866025	−	0.500000i	1.49243			0.623543	−	2.14737i	−0.356220	−	0.616991i	1.79597	−	1.03690i		−	2.48815i	0.500000	−	0.866025i	−1.52987	−	0.444237i
304.15		−	0.431366i	0.866025	−	0.500000i	1.81392			1.40014	+	1.74345i	−0.215683	−	0.373574i	−1.74686	+	1.00855i		−	1.64520i	0.500000	−	0.866025i	0.752064	−	0.603970i
304.16			0.431366i	−0.866025	+	0.500000i	1.81392			−2.20994	−	0.340828i	−0.215683	−	0.373574i	1.74686	−	1.00855i			1.64520i	0.500000	−	0.866025i	0.147022	−	0.953292i
304.17			0.712440i	−0.866025	+	0.500000i	1.49243			1.54790	−	1.61369i	−0.356220	−	0.616991i	−1.79597	+	1.03690i			2.48815i	0.500000	−	0.866025i	1.14966	+	1.10279i
304.18			0.725626i	0.866025	−	0.500000i	1.47347			−1.93530	+	1.12010i	0.362813	+	0.628410i	−3.46926	+	2.00298i			2.52044i	0.500000	−	0.866025i	−0.812774	−	1.40430i
304.19			0.884829i	0.866025	−	0.500000i	1.21708			1.51363	+	1.64588i	0.442414	+	0.766284i	2.44399	−	1.41104i			2.84656i	0.500000	−	0.866025i	−1.45632	+	1.33930i
304.20			1.09870i	−0.866025	+	0.500000i	0.792852			0.537806	+	2.17043i	−0.549351	−	0.951505i	−2.60166	+	1.50207i			3.06851i	0.500000	−	0.866025i	−2.38466	+	0.590889i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
5.b	even	2	1	inner
31.c	even	3	1	inner
155.j	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.q.b	✓	60
5.b	even	2	1	inner	465.2.q.b	✓	60
31.c	even	3	1	inner	465.2.q.b	✓	60
155.j	even	6	1	inner	465.2.q.b	✓	60

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
465.2.q.b	✓	60	1.a	even	1	1	trivial
465.2.q.b	✓	60	5.b	even	2	1	inner
465.2.q.b	✓	60	31.c	even	3	1	inner
465.2.q.b	✓	60	155.j	even	6	1	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T2^30 + 47*T2^28 + 991*T2^26 + 12392*T2^24 + 102369*T2^22 + 589155*T2^20 + 2428248*T2^18 + 7258425*T2^16 + 15769809*T2^14 + 24740676*T2^12 + 27603812*T2^10 + 21344704*T2^8 + 10978676*T2^6 + 3510364*T2^4 + 614916*T2^2 + 43264