Newform orbit 440.2.l.c

• Label: 440.2.l.c
• Level: $440$
• Weight: $2$
• Character orbit: 440.l
• Analytic conductor: $3.513$
• Analytic rank: $0$
• Dimension: $56$
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 440 = 2^{3} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	440.l (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(3.51341768894\)
Analytic rank:	\(0\)
Dimension:	\(56\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) 56 * q + 4 * q^4 - 12 * q^6 + 56 * q^9 - 10 * q^10 - 32 * q^14 - 8 * q^15 + 16 * q^16 + 8 * q^20 - 16 * q^24 + 16 * q^25 - 12 * q^26 + 38 * q^30 + 72 * q^34 - 24 * q^36 - 16 * q^39 + 12 * q^40 - 32 * q^41 - 12 * q^44 + 20 * q^46 - 24 * q^49 - 54 * q^50 - 52 * q^54 - 8 * q^55 + 4 * q^64 - 32 * q^65 - 8 * q^66 + 48 * q^71 + 12 * q^74 - 32 * q^76 - 32 * q^79 + 24 * q^80 + 88 * q^81 + 16 * q^84 - 68 * q^86 - 16 * q^89 - 8 * q^90 - 24 * q^94 + 24 * q^95 - 16 * q^96

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
309.1	−1.39945	−	0.203802i	2.02800			1.91693	+	0.570422i	1.17627	+	1.90168i	−2.83809	−	0.413310i		−	1.20527i	−2.56640	−	1.18895i	1.11278			−1.25857	−	2.90103i
309.2	−1.39945	+	0.203802i	2.02800			1.91693	−	0.570422i	1.17627	−	1.90168i	−2.83809	+	0.413310i			1.20527i	−2.56640	+	1.18895i	1.11278			−1.25857	+	2.90103i
309.3	−1.39753	−	0.216578i	−0.580260			1.90619	+	0.605348i	0.0314342	−	2.23585i	0.810932	+	0.125671i			2.52547i	−2.53285	−	1.25883i	−2.66330			−0.528165	+	3.11786i
309.4	−1.39753	+	0.216578i	−0.580260			1.90619	−	0.605348i	0.0314342	+	2.23585i	0.810932	−	0.125671i		−	2.52547i	−2.53285	+	1.25883i	−2.66330			−0.528165	−	3.11786i
309.5	−1.38159	−	0.302030i	2.45029			1.81756	+	0.834560i	−1.88833	+	1.19759i	−3.38529	−	0.740061i			4.10058i	−2.25905	−	1.70197i	3.00393			2.97059	−	1.08424i
309.6	−1.38159	+	0.302030i	2.45029			1.81756	−	0.834560i	−1.88833	−	1.19759i	−3.38529	+	0.740061i		−	4.10058i	−2.25905	+	1.70197i	3.00393			2.97059	+	1.08424i
309.7	−1.32543	−	0.493200i	−2.29285			1.51351	+	1.30740i	2.06667	+	0.853738i	3.03901	+	1.13084i		−	0.918608i	−1.36123	−	2.47933i	2.25717			−2.31816	−	2.15085i
309.8	−1.32543	+	0.493200i	−2.29285			1.51351	−	1.30740i	2.06667	−	0.853738i	3.03901	−	1.13084i			0.918608i	−1.36123	+	2.47933i	2.25717			−2.31816	+	2.15085i
309.9	−1.32219	−	0.501822i	−0.955334			1.49635	+	1.32700i	−2.20319	−	0.382012i	1.26313	+	0.479408i		−	0.432693i	−1.31253	−	2.50545i	−2.08734			2.72133	+	1.61070i
309.10	−1.32219	+	0.501822i	−0.955334			1.49635	−	1.32700i	−2.20319	+	0.382012i	1.26313	−	0.479408i			0.432693i	−1.31253	+	2.50545i	−2.08734			2.72133	−	1.61070i
309.11	−1.20436	−	0.741302i	0.702572			0.900943	+	1.78558i	1.35163	−	1.78132i	−0.846147	−	0.520818i		−	4.75522i	0.238599	−	2.81835i	−2.50639			−2.94834	+	1.14337i
309.12	−1.20436	+	0.741302i	0.702572			0.900943	−	1.78558i	1.35163	+	1.78132i	−0.846147	+	0.520818i			4.75522i	0.238599	+	2.81835i	−2.50639			−2.94834	−	1.14337i
309.13	−1.04726	−	0.950394i	2.84044			0.193504	+	1.99062i	2.20930	−	0.344972i	−2.97468	−	2.69954i			1.82515i	1.68922	−	2.26860i	5.06811			−2.64157	−	1.73843i
309.14	−1.04726	+	0.950394i	2.84044			0.193504	−	1.99062i	2.20930	+	0.344972i	−2.97468	+	2.69954i		−	1.82515i	1.68922	+	2.26860i	5.06811			−2.64157	+	1.73843i
309.15	−0.959354	−	1.03906i	−3.02021			−0.159281	+	1.99365i	0.177003	−	2.22905i	2.89745	+	3.13817i			1.23027i	2.22432	−	1.74711i	6.12165			−2.48592	+	1.95453i
309.16	−0.959354	+	1.03906i	−3.02021			−0.159281	−	1.99365i	0.177003	+	2.22905i	2.89745	−	3.13817i		−	1.23027i	2.22432	+	1.74711i	6.12165			−2.48592	−	1.95453i
309.17	−0.878518	−	1.10824i	0.467880			−0.456413	+	1.94723i	0.955644	+	2.02157i	−0.411040	−	0.518525i			0.427420i	2.55897	−	1.20485i	−2.78109			1.40084	−	2.83507i
309.18	−0.878518	+	1.10824i	0.467880			−0.456413	−	1.94723i	0.955644	−	2.02157i	−0.411040	+	0.518525i		−	0.427420i	2.55897	+	1.20485i	−2.78109			1.40084	+	2.83507i
309.19	−0.634602	−	1.26384i	3.29264			−1.19456	+	1.60407i	−1.69658	+	1.45657i	−2.08951	−	4.16135i		−	3.97318i	2.78535	+	0.491786i	7.84147			2.91752	+	1.21986i
309.20	−0.634602	+	1.26384i	3.29264			−1.19456	−	1.60407i	−1.69658	−	1.45657i	−2.08951	+	4.16135i			3.97318i	2.78535	−	0.491786i	7.84147			2.91752	−	1.21986i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
5.b	even	2	1	inner
8.b	even	2	1	inner
40.f	even	2	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	440.2.l.c	✓	56
4.b	odd	2	1		1760.2.l.c		56
5.b	even	2	1	inner	440.2.l.c	✓	56
8.b	even	2	1	inner	440.2.l.c	✓	56
8.d	odd	2	1		1760.2.l.c		56
20.d	odd	2	1		1760.2.l.c		56
40.e	odd	2	1		1760.2.l.c		56
40.f	even	2	1	inner	440.2.l.c	✓	56

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
440.2.l.c	✓	56	1.a	even	1	1	trivial
440.2.l.c	✓	56	5.b	even	2	1	inner
440.2.l.c	✓	56	8.b	even	2	1	inner
440.2.l.c	✓	56	40.f	even	2	1	inner
1760.2.l.c		56	4.b	odd	2	1
1760.2.l.c		56	8.d	odd	2	1
1760.2.l.c		56	20.d	odd	2	1
1760.2.l.c		56	40.e	odd	2	1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T3^28 - 56*T3^26 + 1368*T3^24 - 19172*T3^22 + 170574*T3^20 - 1007388*T3^18 + 4016420*T3^16 - 10808556*T3^14 + 19407353*T3^12 - 22827564*T3^10 + 17203884*T3^8 - 8067760*T3^6 + 2245520*T3^4 - 336384*T3^2 + 20736