Newform orbit 605.2.e.c

• Label: 605.2.e.c
• Level: $605$
• Weight: $2$
• Character orbit: 605.e
• Analytic conductor: $4.831$
• Analytic rank: $0$
• Dimension: $40$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 605 = 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	605.e (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(4.83094932229\)
Analytic rank:	\(0\)
Dimension:	\(40\)
Relative dimension:	\(20\) over \(\Q(i)\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

$q$-expansion

The dimension is sufficiently large that we do not compute an algebraic \(q\)-expansion, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 40 q + 8 q^{3} - 4 q^{5}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
362.1	−1.91757	+	1.91757i	0.831561	−	0.831561i		−	5.35415i	1.62695	+	1.53396i			3.18915i	−0.383282	+	0.383282i	6.43181	+	6.43181i			1.61701i	−6.06127	+	0.178306i
362.2	−1.64949	+	1.64949i	1.43990	−	1.43990i		−	3.44167i	1.13534	−	1.92640i			4.75021i	3.25511	−	3.25511i	2.37802	+	2.37802i		−	1.14662i	1.30484	+	5.05032i
362.3	−1.63660	+	1.63660i	−0.722598	+	0.722598i		−	3.35690i	0.360665	+	2.20679i		−	2.36520i	2.14665	−	2.14665i	2.22069	+	2.22069i			1.95570i	−4.20189	−	3.02136i
362.4	−1.38689	+	1.38689i	−2.07537	+	2.07537i		−	1.84694i	−2.03181	−	0.933683i		−	5.75663i	−1.48652	+	1.48652i	−0.212274	−	0.212274i		−	5.61432i	4.11281	−	1.52298i
362.5	−1.29704	+	1.29704i	2.21032	−	2.21032i		−	1.36464i	0.668547	+	2.13379i			5.73375i	0.351575	−	0.351575i	−0.824089	−	0.824089i		−	6.77099i	−3.63475	−	1.90048i
362.6	−1.05784	+	1.05784i	1.53861	−	1.53861i		−	0.238041i	−1.92587	−	1.13622i			3.25521i	−1.66576	+	1.66576i	−1.86387	−	1.86387i		−	1.73467i	3.23920	−	0.835322i
362.7	−0.848475	+	0.848475i	−0.258670	+	0.258670i			0.560180i	−0.152228	−	2.23088i		−	0.438950i	1.06376	−	1.06376i	−2.17225	−	2.17225i			2.86618i	2.02201	+	1.76368i
362.8	−0.503119	+	0.503119i	−1.98889	+	1.98889i			1.49374i	−1.36457	+	1.77143i		−	2.00130i	2.43291	−	2.43291i	−1.75777	−	1.75777i		−	4.91135i	−0.204700	−	1.57778i
362.9	−0.436764	+	0.436764i	1.06258	−	1.06258i			1.61847i	−1.07825	+	1.95892i			0.928194i	−1.08812	+	1.08812i	−1.58042	−	1.58042i			0.741845i	−0.384643	−	1.32653i
362.10	−0.187165	+	0.187165i	−0.0374447	+	0.0374447i			1.92994i	1.76123	−	1.37770i		−	0.0140167i	−2.30359	+	2.30359i	−0.735548	−	0.735548i			2.99720i	−0.0717827	+	0.587500i
362.11	0.187165	−	0.187165i	−0.0374447	+	0.0374447i			1.92994i	1.76123	−	1.37770i			0.0140167i	2.30359	−	2.30359i	0.735548	+	0.735548i			2.99720i	0.0717827	−	0.587500i
362.12	0.436764	−	0.436764i	1.06258	−	1.06258i			1.61847i	−1.07825	+	1.95892i		−	0.928194i	1.08812	−	1.08812i	1.58042	+	1.58042i			0.741845i	0.384643	+	1.32653i
362.13	0.503119	−	0.503119i	−1.98889	+	1.98889i			1.49374i	−1.36457	+	1.77143i			2.00130i	−2.43291	+	2.43291i	1.75777	+	1.75777i		−	4.91135i	0.204700	+	1.57778i
362.14	0.848475	−	0.848475i	−0.258670	+	0.258670i			0.560180i	−0.152228	−	2.23088i			0.438950i	−1.06376	+	1.06376i	2.17225	+	2.17225i			2.86618i	−2.02201	−	1.76368i
362.15	1.05784	−	1.05784i	1.53861	−	1.53861i		−	0.238041i	−1.92587	−	1.13622i		−	3.25521i	1.66576	−	1.66576i	1.86387	+	1.86387i		−	1.73467i	−3.23920	+	0.835322i
362.16	1.29704	−	1.29704i	2.21032	−	2.21032i		−	1.36464i	0.668547	+	2.13379i		−	5.73375i	−0.351575	+	0.351575i	0.824089	+	0.824089i		−	6.77099i	3.63475	+	1.90048i
362.17	1.38689	−	1.38689i	−2.07537	+	2.07537i		−	1.84694i	−2.03181	−	0.933683i			5.75663i	1.48652	−	1.48652i	0.212274	+	0.212274i		−	5.61432i	−4.11281	+	1.52298i
362.18	1.63660	−	1.63660i	−0.722598	+	0.722598i		−	3.35690i	0.360665	+	2.20679i			2.36520i	−2.14665	+	2.14665i	−2.22069	−	2.22069i			1.95570i	4.20189	+	3.02136i
362.19	1.64949	−	1.64949i	1.43990	−	1.43990i		−	3.44167i	1.13534	−	1.92640i		−	4.75021i	−3.25511	+	3.25511i	−2.37802	−	2.37802i		−	1.14662i	−1.30484	−	5.05032i
362.20	1.91757	−	1.91757i	0.831561	−	0.831561i		−	5.35415i	1.62695	+	1.53396i		−	3.18915i	0.383282	−	0.383282i	−6.43181	−	6.43181i			1.61701i	6.06127	−	0.178306i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
5.c	odd	4	1	inner
11.b	odd	2	1	inner
55.e	even	4	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	605.2.e.c	✓	40
5.c	odd	4	1	inner	605.2.e.c	✓	40
11.b	odd	2	1	inner	605.2.e.c	✓	40
11.c	even	5	4		605.2.m.g		160
11.d	odd	10	4		605.2.m.g		160
55.e	even	4	1	inner	605.2.e.c	✓	40
55.k	odd	20	4		605.2.m.g		160
55.l	even	20	4		605.2.m.g		160

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
605.2.e.c	✓	40	1.a	even	1	1	trivial
605.2.e.c	✓	40	5.c	odd	4	1	inner
605.2.e.c	✓	40	11.b	odd	2	1	inner
605.2.e.c	✓	40	55.e	even	4	1	inner
605.2.m.g		160	11.c	even	5	4
605.2.m.g		160	11.d	odd	10	4
605.2.m.g		160	55.k	odd	20	4
605.2.m.g		160	55.l	even	20	4

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T2^40 + 146*T2^36 + 8157*T2^32 + 224416*T2^28 + 3234466*T2^24 + 23996516*T2^20 + 83316898*T2^16 + 110925168*T2^12 + 35430093*T2^8 + 3153946*T2^4 + 14641