Newform orbit 228.2.c.a

• Label: 228.2.c.a
• Level: $228$
• Weight: $2$
• Character orbit: 228.c
• Analytic conductor: $1.821$
• Analytic rank: $0$
• Dimension: $36$
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 228 = 2^{2} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	228.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(1.82058916609\)
Analytic rank:	\(0\)
Dimension:	\(36\)
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.

\(\operatorname{Tr}(f)(q) = \) 36 * q - 6 * q^6 + 8 * q^10 + 4 * q^12 - 8 * q^16 + 16 * q^18 + 8 * q^21 - 12 * q^22 - 2 * q^24 - 28 * q^25 + 12 * q^28 - 12 * q^30 - 28 * q^34 - 22 * q^36 - 16 * q^37 - 12 * q^40 + 10 * q^42 + 16 * q^45 - 4 * q^46 + 32 * q^48 - 44 * q^49 - 36 * q^52 - 20 * q^54 - 4 * q^58 - 4 * q^60 + 16 * q^61 + 24 * q^64 + 24 * q^66 - 16 * q^69 + 36 * q^70 - 36 * q^72 - 8 * q^73 - 32 * q^78 - 40 * q^81 + 72 * q^82 - 20 * q^84 + 16 * q^85 - 16 * q^88 - 56 * q^90 + 8 * q^93 - 56 * q^94 + 2 * q^96 + 40 * q^97

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
191.1	−1.41330	−	0.0507215i	−0.756793	−	1.55797i	1.99485	+	0.143370i			0.762708i	0.990556	+	2.24027i			3.87706i	−2.81206	−	0.303807i	−1.85453	+	2.35812i	0.0386857	−	1.07794i
191.2	−1.41330	+	0.0507215i	−0.756793	+	1.55797i	1.99485	−	0.143370i		−	0.762708i	0.990556	−	2.24027i		−	3.87706i	−2.81206	+	0.303807i	−1.85453	−	2.35812i	0.0386857	+	1.07794i
191.3	−1.39068	−	0.256903i	1.58499	−	0.698441i	1.86800	+	0.714541i		−	3.19367i	−2.38365	+	0.564123i		−	0.170940i	−2.41423	−	1.47359i	2.02436	−	2.21404i	−0.820463	+	4.44139i
191.4	−1.39068	+	0.256903i	1.58499	+	0.698441i	1.86800	−	0.714541i			3.19367i	−2.38365	−	0.564123i			0.170940i	−2.41423	+	1.47359i	2.02436	+	2.21404i	−0.820463	−	4.44139i
191.5	−1.17379	−	0.788801i	0.726100	−	1.57251i	0.755587	+	1.85178i			2.76393i	−2.09269	+	1.27305i		−	4.18351i	0.573780	−	2.76962i	−1.94556	−	2.28359i	2.18019	−	3.24429i
191.6	−1.17379	+	0.788801i	0.726100	+	1.57251i	0.755587	−	1.85178i		−	2.76393i	−2.09269	−	1.27305i			4.18351i	0.573780	+	2.76962i	−1.94556	+	2.28359i	2.18019	+	3.24429i
191.7	−1.13655	−	0.841583i	0.0680243	+	1.73071i	0.583476	+	1.91300i			1.36832i	1.37923	−	2.02429i			1.12940i	0.946798	−	2.66525i	−2.99075	+	0.235461i	1.15156	−	1.55516i
191.8	−1.13655	+	0.841583i	0.0680243	−	1.73071i	0.583476	−	1.91300i		−	1.36832i	1.37923	+	2.02429i		−	1.12940i	0.946798	+	2.66525i	−2.99075	−	0.235461i	1.15156	+	1.55516i
191.9	−1.08992	−	0.901156i	−1.45940	−	0.932823i	0.375835	+	1.96437i		−	2.01739i	0.750003	+	2.33184i		−	2.54076i	1.36058	−	2.47968i	1.25968	+	2.72272i	−1.81798	+	2.19879i
191.10	−1.08992	+	0.901156i	−1.45940	+	0.932823i	0.375835	−	1.96437i			2.01739i	0.750003	−	2.33184i			2.54076i	1.36058	+	2.47968i	1.25968	−	2.72272i	−1.81798	−	2.19879i
191.11	−0.791500	−	1.17198i	1.69893	−	0.337110i	−0.747055	+	1.85524i			0.951020i	−1.73979	−	1.72428i			4.82396i	2.76559	−	0.592892i	2.77271	−	1.14545i	1.11457	−	0.752732i
191.12	−0.791500	+	1.17198i	1.69893	+	0.337110i	−0.747055	−	1.85524i		−	0.951020i	−1.73979	+	1.72428i		−	4.82396i	2.76559	+	0.592892i	2.77271	+	1.14545i	1.11457	+	0.752732i
191.13	−0.557018	−	1.29990i	1.17516	+	1.27240i	−1.37946	+	1.44813i		−	3.63294i	0.999396	−	2.23634i		−	2.62764i	2.65081	+	0.986525i	−0.237980	+	2.99055i	−4.72245	+	2.02361i
191.14	−0.557018	+	1.29990i	1.17516	−	1.27240i	−1.37946	−	1.44813i			3.63294i	0.999396	+	2.23634i			2.62764i	2.65081	−	0.986525i	−0.237980	−	2.99055i	−4.72245	−	2.02361i
191.15	−0.474569	−	1.33221i	−1.60213	+	0.658173i	−1.54957	+	1.26445i		−	0.191837i	1.63714	+	1.82202i			0.733628i	2.41989	+	1.46428i	2.13362	−	2.10895i	−0.255567	+	0.0910397i
191.16	−0.474569	+	1.33221i	−1.60213	−	0.658173i	−1.54957	−	1.26445i			0.191837i	1.63714	−	1.82202i		−	0.733628i	2.41989	−	1.46428i	2.13362	+	2.10895i	−0.255567	−	0.0910397i
191.17	−0.221733	−	1.39672i	−0.958759	−	1.44249i	−1.90167	+	0.619399i			3.67393i	−1.80217	+	1.65897i			1.73008i	1.28679	+	2.51876i	−1.16156	+	2.76600i	5.13146	−	0.814631i
191.18	−0.221733	+	1.39672i	−0.958759	+	1.44249i	−1.90167	−	0.619399i		−	3.67393i	−1.80217	−	1.65897i		−	1.73008i	1.28679	−	2.51876i	−1.16156	−	2.76600i	5.13146	+	0.814631i
191.19	0.221733	−	1.39672i	0.958759	+	1.44249i	−1.90167	−	0.619399i			3.67393i	2.22735	−	1.01927i		−	1.73008i	−1.28679	+	2.51876i	−1.16156	+	2.76600i	5.13146	+	0.814631i
191.20	0.221733	+	1.39672i	0.958759	−	1.44249i	−1.90167	+	0.619399i		−	3.67393i	2.22735	+	1.01927i			1.73008i	−1.28679	−	2.51876i	−1.16156	−	2.76600i	5.13146	−	0.814631i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	inner
4.b	odd	2	1	inner
12.b	even	2	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	228.2.c.a	✓	36
3.b	odd	2	1	inner	228.2.c.a	✓	36
4.b	odd	2	1	inner	228.2.c.a	✓	36
12.b	even	2	1	inner	228.2.c.a	✓	36

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
228.2.c.a	✓	36	1.a	even	1	1	trivial
228.2.c.a	✓	36	3.b	odd	2	1	inner
228.2.c.a	✓	36	4.b	odd	2	1	inner
228.2.c.a	✓	36	12.b	even	2	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(228, [\chi])\).