Newform orbit 124.2.g.a

• Label: 124.2.g.a
• Level: $124$
• Weight: $2$
• Character orbit: 124.g
• Analytic conductor: $0.990$
• Analytic rank: $0$
• Dimension: $28$
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 124 = 2^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	124.g (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(0.990144985064\)
Analytic rank:	\(0\)
Dimension:	\(28\)
Relative dimension:	\(14\) 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.

\(\operatorname{Tr}(f)(q) = \) 28 * q - 4 * q^2 - 2 * q^5 + 18 * q^6 - 16 * q^8 - 12 * q^9 - 4 * q^10 + 6 * q^12 - 18 * q^13 + 6 * q^14 + 8 * q^16 - 6 * q^17 + 6 * q^18 + 6 * q^20 - 6 * q^21 - 12 * q^22 + 6 * q^24 - 16 * q^25 - 24 * q^26 + 6 * q^28 - 44 * q^32 + 12 * q^33 - 18 * q^37 - 4 * q^38 - 10 * q^40 - 2 * q^41 - 72 * q^42 + 6 * q^44 + 24 * q^45 + 48 * q^48 + 28 * q^49 + 28 * q^50 + 18 * q^53 + 54 * q^56 + 30 * q^57 - 4 * q^62 - 6 * q^65 + 96 * q^66 - 84 * q^68 - 60 * q^69 + 96 * q^70 + 54 * q^72 + 30 * q^73 + 30 * q^74 - 16 * q^76 - 36 * q^78 - 34 * q^80 - 6 * q^81 + 2 * q^82 - 12 * q^84 - 30 * q^86 + 72 * q^88 - 6 * q^90 + 42 * q^93 + 28 * q^94 - 30 * q^96 - 80 * q^97 - 10 * q^98

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
99.1	−1.40363	−	0.172732i	−1.45188	−	2.51473i	1.94033	+	0.484902i	1.26737	−	2.19514i	1.60352	+	3.78053i	−2.57513	+	1.48675i	−2.63973	−	1.01578i	−2.71592	+	4.70411i	−2.15808	+	2.86225i
99.2	−1.40363	+	0.172732i	1.45188	+	2.51473i	1.94033	−	0.484902i	1.26737	−	2.19514i	−2.47227	−	3.27895i	2.57513	−	1.48675i	−2.63973	+	1.01578i	−2.71592	+	4.70411i	−1.39974	+	3.30008i
99.3	−1.32920	−	0.482923i	0.532147	+	0.921706i	1.53357	+	1.28381i	−1.27521	+	2.20873i	−0.262219	−	1.48212i	−3.66546	+	2.11625i	−1.41845	−	2.44704i	0.933638	−	1.61711i	2.76166	−	2.32003i
99.4	−1.32920	+	0.482923i	−0.532147	−	0.921706i	1.53357	−	1.28381i	−1.27521	+	2.20873i	1.15245	+	0.968150i	3.66546	−	2.11625i	−1.41845	+	2.44704i	0.933638	−	1.61711i	0.628370	−	3.55169i
99.5	−0.724491	−	1.21454i	0.333793	+	0.578147i	−0.950226	+	1.75985i	1.39289	−	2.41255i	0.460354	−	0.824268i	−0.0661639	+	0.0381998i	2.82584	−	0.120905i	1.27716	−	2.21211i	−3.93928	+	0.0561512i
99.6	−0.724491	+	1.21454i	−0.333793	−	0.578147i	−0.950226	−	1.75985i	1.39289	−	2.41255i	0.944014	+	0.0134561i	0.0661639	−	0.0381998i	2.82584	+	0.120905i	1.27716	−	2.21211i	1.92101	+	3.43960i
99.7	−0.184509	−	1.40213i	1.25766	+	2.17833i	−1.93191	+	0.517409i	−1.98995	+	3.44669i	2.82224	−	2.16532i	2.69419	−	1.55549i	1.08193	+	2.61332i	−1.66341	+	2.88111i	5.19986	+	2.15421i
99.8	−0.184509	+	1.40213i	−1.25766	−	2.17833i	−1.93191	−	0.517409i	−1.98995	+	3.44669i	3.28634	−	1.36148i	−2.69419	+	1.55549i	1.08193	−	2.61332i	−1.66341	+	2.88111i	−4.46553	−	3.42610i
99.9	0.409944	−	1.35349i	−0.815109	−	1.41181i	−1.66389	−	1.10971i	0.174129	−	0.301600i	−2.24503	+	0.524482i	−0.151691	+	0.0875788i	−2.18409	+	1.79715i	0.171194	−	0.296516i	−0.336830	−	0.359321i
99.10	0.409944	+	1.35349i	0.815109	+	1.41181i	−1.66389	+	1.10971i	0.174129	−	0.301600i	−1.57673	+	1.68201i	0.151691	−	0.0875788i	−2.18409	−	1.79715i	0.171194	−	0.296516i	0.479596	+	0.112043i
99.11	0.965261	−	1.03357i	1.41049	+	2.44304i	−0.136541	−	1.99533i	0.855573	−	1.48190i	3.88655	+	0.900330i	−4.34999	+	2.51147i	−2.19412	−	1.78489i	−2.47896	+	4.29369i	−0.705794	−	2.31471i
99.12	0.965261	+	1.03357i	−1.41049	−	2.44304i	−0.136541	+	1.99533i	0.855573	−	1.48190i	1.16357	−	3.81601i	4.34999	−	2.51147i	−2.19412	+	1.78489i	−2.47896	+	4.29369i	2.35750	−	0.546121i
99.13	1.26662	−	0.629017i	0.108864	+	0.188557i	1.20867	−	1.59346i	−0.924797	+	1.60180i	0.256495	+	0.170354i	0.987210	−	0.569966i	0.528624	−	2.77859i	1.47630	−	2.55702i	−0.163813	+	2.61059i
99.14	1.26662	+	0.629017i	−0.108864	−	0.188557i	1.20867	+	1.59346i	−0.924797	+	1.60180i	−0.0192835	−	0.307308i	−0.987210	+	0.569966i	0.528624	+	2.77859i	1.47630	−	2.55702i	−2.17893	+	1.44716i
119.1	−1.40363	−	0.172732i	1.45188	−	2.51473i	1.94033	+	0.484902i	1.26737	+	2.19514i	−2.47227	+	3.27895i	2.57513	+	1.48675i	−2.63973	−	1.01578i	−2.71592	−	4.70411i	−1.39974	−	3.30008i
119.2	−1.40363	+	0.172732i	−1.45188	+	2.51473i	1.94033	−	0.484902i	1.26737	+	2.19514i	1.60352	−	3.78053i	−2.57513	−	1.48675i	−2.63973	+	1.01578i	−2.71592	−	4.70411i	−2.15808	−	2.86225i
119.3	−1.32920	−	0.482923i	−0.532147	+	0.921706i	1.53357	+	1.28381i	−1.27521	−	2.20873i	1.15245	−	0.968150i	3.66546	+	2.11625i	−1.41845	−	2.44704i	0.933638	+	1.61711i	0.628370	+	3.55169i
119.4	−1.32920	+	0.482923i	0.532147	−	0.921706i	1.53357	−	1.28381i	−1.27521	−	2.20873i	−0.262219	+	1.48212i	−3.66546	−	2.11625i	−1.41845	+	2.44704i	0.933638	+	1.61711i	2.76166	+	2.32003i
119.5	−0.724491	−	1.21454i	−0.333793	+	0.578147i	−0.950226	+	1.75985i	1.39289	+	2.41255i	0.944014	−	0.0134561i	0.0661639	+	0.0381998i	2.82584	−	0.120905i	1.27716	+	2.21211i	1.92101	−	3.43960i
119.6	−0.724491	+	1.21454i	0.333793	−	0.578147i	−0.950226	−	1.75985i	1.39289	+	2.41255i	0.460354	+	0.824268i	−0.0661639	−	0.0381998i	2.82584	+	0.120905i	1.27716	+	2.21211i	−3.93928	−	0.0561512i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
4.b	odd	2	1	inner
31.e	odd	6	1	inner
124.g	even	6	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	124.2.g.a	✓	28
4.b	odd	2	1	inner	124.2.g.a	✓	28
31.e	odd	6	1	inner	124.2.g.a	✓	28
124.g	even	6	1	inner	124.2.g.a	✓	28

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
124.2.g.a	✓	28	1.a	even	1	1	trivial
124.2.g.a	✓	28	4.b	odd	2	1	inner
124.2.g.a	✓	28	31.e	odd	6	1	inner
124.2.g.a	✓	28	124.g	even	6	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(124, [\chi])\).