Newform orbit 465.2.be.a

• Label: 465.2.be.a
• Level: $465$
• Weight: $2$
• Character orbit: 465.be
• Analytic conductor: $3.713$
• Analytic rank: $0$
• Dimension: $240$
• CM: no
• Inner twists: $8$

Newspace parameters

Level:	\( N \)	\(=\)	\( 465 = 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	465.be (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(3.71304369399\)
Analytic rank:	\(0\)
Dimension:	\(240\)
Relative dimension:	\(60\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 240 q - 6 q^{3} - 4 q^{6}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
98.1	−1.93622	−	1.93622i	−1.72994	−	0.0855625i			5.49791i	1.23362	−	1.86499i	3.18387	+	3.51521i	−0.576519	−	2.15160i	6.77273	−	6.77273i	2.98536	+	0.296035i	−5.99959	+	1.22248i
98.2	−1.87901	−	1.87901i	−0.840793	+	1.51429i			5.06133i	0.913745	+	2.04085i	4.42521	−	1.26550i	0.793040	+	2.95967i	5.75226	−	5.75226i	−1.58614	−	2.54640i	2.11784	−	5.55170i
98.3	−1.84495	−	1.84495i	1.68449	−	0.403121i			4.80768i	−1.30163	+	1.81817i	−3.85153	−	2.36405i	−0.819803	−	3.05955i	5.18002	−	5.18002i	2.67499	−	1.35810i	5.75588	−	0.952991i
98.4	−1.84242	−	1.84242i	−1.10472	−	1.33402i			4.78904i	−1.47481	+	1.68076i	−0.422471	+	4.49318i	0.651939	+	2.43307i	5.13859	−	5.13859i	−0.559206	+	2.94742i	5.81388	−	0.379441i
98.5	−1.84102	−	1.84102i	0.834923	+	1.51753i			4.77870i	−1.66280	−	1.49502i	1.25670	−	4.33091i	0.308327	+	1.15069i	5.11564	−	5.11564i	−1.60581	+	2.53404i	0.308888	+	5.81361i
98.6	−1.68480	−	1.68480i	0.167725	−	1.72391i			3.67707i	−0.970904	−	2.01429i	−3.18702	+	2.62186i	−1.13309	−	4.22876i	2.82552	−	2.82552i	−2.94374	−	0.578284i	−1.75788	+	5.02943i
98.7	−1.62658	−	1.62658i	1.72162	−	0.189762i			3.29154i	1.58899	−	1.57325i	−3.10903	−	2.49170i	0.419558	+	1.56581i	2.10079	−	2.10079i	2.92798	−	0.653398i	−5.14364	−	0.0256022i
98.8	−1.46359	−	1.46359i	−1.13704	−	1.30657i			2.28419i	2.22776	−	0.192591i	−0.248128	+	3.57645i	0.281899	+	1.05206i	0.415932	−	0.415932i	−0.414276	+	2.97126i	−3.54240	−	2.97865i
98.9	−1.44260	−	1.44260i	−1.11708	+	1.32368i			2.16217i	−2.23322	−	0.112833i	3.52104	−	0.298036i	−0.231092	−	0.862448i	0.233953	−	0.233953i	−0.504254	−	2.95732i	3.05886	+	3.38441i
98.10	−1.40988	−	1.40988i	−0.596389	+	1.62614i			1.97552i	2.23540	−	0.0546927i	3.13349	−	1.45182i	−0.419910	−	1.56713i	−0.0345080	+	0.0345080i	−2.28864	−	1.93962i	−3.22875	−	3.07453i
98.11	−1.38421	−	1.38421i	1.36494	+	1.06628i			1.83208i	0.940181	+	2.02881i	−0.413413	−	3.36531i	0.112718	+	0.420667i	−0.232438	+	0.232438i	0.726114	+	2.91080i	1.50689	−	4.10971i
98.12	−1.37486	−	1.37486i	−1.73040	+	0.0756319i			1.78046i	0.524907	+	2.17359i	2.48303	+	2.27507i	−1.05912	−	3.95270i	−0.301832	+	0.301832i	2.98856	−	0.261747i	2.26670	−	3.71004i
98.13	−1.33275	−	1.33275i	−1.70465	−	0.306863i			1.55244i	−1.43453	−	1.71526i	1.86290	+	2.68084i	0.858496	+	3.20395i	−0.596486	+	0.596486i	2.81167	+	1.04619i	−0.374142	+	4.19788i
98.14	−1.13894	−	1.13894i	0.0753204	−	1.73041i			0.594373i	−1.62755	+	1.53332i	−2.05662	+	1.88505i	−0.0981291	−	0.366223i	−1.60093	+	1.60093i	−2.98865	−	0.260671i	3.60005	+	0.107326i
98.15	−1.07746	−	1.07746i	−0.0990226	−	1.72922i			0.321843i	0.838391	−	2.07294i	−1.75647	+	1.96986i	0.299875	+	1.11915i	−1.80815	+	1.80815i	−2.98039	+	0.342463i	−3.13685	+	1.33018i
98.16	−1.04825	−	1.04825i	1.14484	−	1.29975i			0.197665i	0.693500	+	2.12581i	−2.56254	+	0.162386i	1.04385	+	3.89570i	−1.88930	+	1.88930i	−0.378694	−	2.97600i	1.50142	−	2.95535i
98.17	−1.03032	−	1.03032i	0.741075	+	1.56551i			0.123114i	−2.05042	+	0.892066i	0.849426	−	2.37651i	−0.433832	−	1.61908i	−1.93379	+	1.93379i	−1.90162	+	2.32031i	3.03170	+	1.19347i
98.18	−0.989024	−	0.989024i	0.175826	+	1.72310i		−	0.0436644i	1.18284	−	1.89760i	1.53029	−	1.87809i	1.22619	+	4.57620i	−2.02123	+	2.02123i	−2.93817	+	0.605932i	−3.04663	+	0.706916i
98.19	−0.870093	−	0.870093i	1.66082	−	0.491607i		−	0.485876i	−1.68819	−	1.46629i	−1.87281	−	1.01732i	−0.0904276	−	0.337480i	−2.16294	+	2.16294i	2.51665	−	1.63294i	0.193071	+	2.74469i
98.20	−0.816536	−	0.816536i	1.28127	−	1.16548i		−	0.666538i	2.16826	+	0.546490i	−1.99786	−	0.0945498i	−1.26333	−	4.71479i	−2.17732	+	2.17732i	0.283319	−	2.98659i	−1.32423	−	2.21669i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	inner
5.c	odd	4	1	inner
15.e	even	4	1	inner
31.c	even	3	1	inner
93.h	odd	6	1	inner
155.o	odd	12	1	inner
465.be	even	12	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	465.2.be.a	✓	240
3.b	odd	2	1	inner	465.2.be.a	✓	240
5.c	odd	4	1	inner	465.2.be.a	✓	240
15.e	even	4	1	inner	465.2.be.a	✓	240
31.c	even	3	1	inner	465.2.be.a	✓	240
93.h	odd	6	1	inner	465.2.be.a	✓	240
155.o	odd	12	1	inner	465.2.be.a	✓	240
465.be	even	12	1	inner	465.2.be.a	✓	240

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
465.2.be.a	✓	240	1.a	even	1	1	trivial
465.2.be.a	✓	240	3.b	odd	2	1	inner
465.2.be.a	✓	240	5.c	odd	4	1	inner
465.2.be.a	✓	240	15.e	even	4	1	inner
465.2.be.a	✓	240	31.c	even	3	1	inner
465.2.be.a	✓	240	93.h	odd	6	1	inner
465.2.be.a	✓	240	155.o	odd	12	1	inner
465.2.be.a	✓	240	465.be	even	12	1	inner

Hecke kernels

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