Newform orbit 603.2.l.a

• Label: 603.2.l.a
• Level: $603$
• Weight: $2$
• Character orbit: 603.l
• Analytic conductor: $4.815$
• Analytic rank: $0$
• Dimension: $132$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 603 = 3^{2} \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	603.l (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(4.81497924188\)
Analytic rank:	\(0\)
Dimension:	\(132\)
Relative dimension:	\(66\) over \(\Q(\zeta_{6})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 132 q - 66 q^{4} + 10 q^{6} + 8 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
200.1	−1.39584	+	2.41767i	−1.57689	−	0.716525i	−2.89677	−	5.01735i	0.979162	+	1.69596i	3.93342	−	2.81226i	−0.484838	−	0.279921i	10.5904			1.97318	+	2.25977i	−5.46704
200.2	−1.34567	+	2.33076i	0.375699	−	1.69081i	−2.62164	−	4.54082i	−1.69632	−	2.93811i	3.43532	+	3.15094i	−2.38340	−	1.37606i	8.72877			−2.71770	−	1.27048i	9.13072
200.3	−1.33814	+	2.31773i	0.836295	+	1.51678i	−2.58126	−	4.47087i	−0.663575	−	1.14934i	−4.63456	−	0.0913554i	2.68931	+	1.55268i	8.46378			−1.60122	+	2.53695i	3.55183
200.4	−1.24929	+	2.16383i	1.72470	−	0.159387i	−2.12144	−	3.67444i	2.04806	+	3.54734i	−1.80976	+	3.93108i	1.26737	+	0.731715i	5.60401			2.94919	−	0.549790i	−10.2345
200.5	−1.23668	+	2.14199i	−1.34361	+	1.09302i	−2.05875	−	3.56586i	−1.63023	−	2.82365i	−0.679631	−	4.22973i	−2.34312	−	1.35280i	5.23732			0.610593	−	2.93721i	8.06430
200.6	−1.22339	+	2.11898i	−0.333349	+	1.69967i	−1.99338	−	3.45263i	0.149207	+	0.258435i	−3.19375	−	2.78572i	0.0311178	+	0.0179659i	4.86116			−2.77776	−	1.13317i	−0.730156
200.7	−1.18642	+	2.05493i	0.117735	−	1.72804i	−1.81517	−	3.14397i	0.408528	+	0.707591i	3.41134	+	2.29212i	4.18823	+	2.41807i	3.86854			−2.97228	−	0.406902i	−1.93874
200.8	−1.18232	+	2.04784i	0.779490	−	1.54674i	−1.79576	−	3.11035i	1.18737	+	2.05659i	2.24586	+	3.42501i	−3.42944	−	1.97999i	3.76339			−1.78479	−	2.41133i	−5.61541
200.9	−1.16336	+	2.01499i	−1.59193	+	0.682477i	−1.70679	−	2.95625i	0.719334	+	1.24592i	0.476791	−	4.00168i	1.79079	+	1.03391i	3.28900			2.06845	−	2.17290i	−3.34736
200.10	−1.13151	+	1.95983i	1.69797	−	0.341928i	−1.56063	−	2.70309i	−1.14681	−	1.98634i	−1.25114	+	3.71462i	0.398259	+	0.229935i	2.53742			2.76617	−	1.16116i	5.19052
200.11	−1.00472	+	1.74023i	−1.02992	−	1.39258i	−1.01894	−	1.76486i	−0.0100438	−	0.0173963i	3.45819	−	0.393147i	−1.41764	−	0.818474i	0.0761201			−0.878531	+	2.86848i	0.0403649
200.12	−1.00027	+	1.73252i	−1.71459	−	0.245331i	−1.00108	−	1.73392i	−1.52156	−	2.63541i	2.14009	−	2.72516i	3.85817	+	2.22752i	0.00431800			2.87962	+	0.841285i	6.08787
200.13	−0.948352	+	1.64259i	0.853494	+	1.50717i	−0.798743	−	1.38346i	1.60208	+	2.77488i	−3.28507	−	0.0273793i	0.395721	+	0.228469i	−0.763450			−1.54310	+	2.57271i	−6.07734
200.14	−0.930733	+	1.61208i	1.58684	+	0.694223i	−0.732528	−	1.26878i	−0.136455	−	0.236347i	−2.59606	+	1.91197i	−2.43107	−	1.40358i	−0.995781			2.03611	+	2.20324i	0.508012
200.15	−0.838601	+	1.45250i	1.47894	+	0.901512i	−0.406503	−	0.704084i	−1.89359	−	3.27979i	−2.54969	+	1.39216i	2.42055	+	1.39750i	−1.99083			1.37455	+	2.66657i	6.35186
200.16	−0.803054	+	1.39093i	−1.71183	+	0.263919i	−0.289792	−	0.501935i	1.80724	+	3.13023i	1.00760	−	2.59297i	−4.37008	−	2.52307i	−2.28134			2.86069	−	0.903565i	−5.80525
200.17	−0.797907	+	1.38202i	1.31849	−	1.12321i	−0.273312	−	0.473390i	0.456179	+	0.790125i	0.500259	+	2.71838i	−2.17126	−	1.25358i	−2.31932			0.476814	−	2.96187i	−1.45595
200.18	−0.762360	+	1.32045i	0.182202	+	1.72244i	−0.162384	−	0.281258i	−0.908294	−	1.57321i	−2.41329	−	1.07253i	−2.60798	−	1.50572i	−2.55426			−2.93360	+	0.627664i	2.76979
200.19	−0.746535	+	1.29304i	−0.997353	+	1.41608i	−0.114628	−	0.198542i	1.00458	+	1.73999i	−1.08649	−	2.34677i	1.99677	+	1.15284i	−2.64384			−1.01057	−	2.82467i	−2.99982
200.20	−0.716678	+	1.24132i	0.0154551	−	1.73198i	−0.0272550	−	0.0472070i	−2.10023	−	3.63771i	2.13887	+	1.26046i	0.623932	+	0.360227i	−2.78858			−2.99952	−	0.0535358i	6.02077

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
9.d	odd	6	1	inner
67.b	odd	2	1	inner
603.l	even	6	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	603.2.l.a	✓	132
9.d	odd	6	1	inner	603.2.l.a	✓	132
67.b	odd	2	1	inner	603.2.l.a	✓	132
603.l	even	6	1	inner	603.2.l.a	✓	132

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
603.2.l.a	✓	132	1.a	even	1	1	trivial
603.2.l.a	✓	132	9.d	odd	6	1	inner
603.2.l.a	✓	132	67.b	odd	2	1	inner
603.2.l.a	✓	132	603.l	even	6	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(603, [\chi])\).