Newform orbit 603.2.y.a

• Label: 603.2.y.a
• Level: $603$
• Weight: $2$
• Character orbit: 603.y
• Analytic conductor: $4.815$
• Analytic rank: $0$
• Dimension: $1320$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 603 = 3^{2} \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	603.y (of order \(33\), degree \(20\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(4.81497924188\)
Analytic rank:	\(0\)
Dimension:	\(1320\)
Relative dimension:	\(66\) over \(\Q(\zeta_{33})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{33}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 1320 q - 5 q^{2} - 19 q^{3} - 137 q^{4} - 14 q^{5} - 16 q^{6} - 11 q^{7} - 20 q^{8} - 15 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
4.1	−1.15955	−	2.53905i	0.402100	−	1.68473i	−3.79251	+	4.37679i	−1.51665	−	0.607175i	−4.74387	+	0.932570i	−4.49247	−	0.428979i	10.1540	+	2.98149i	−2.67663	−	1.35486i	0.216977	+	4.55490i
4.2	−1.11403	−	2.43939i	1.69572	+	0.352879i	−3.39982	+	3.92361i	−0.837696	−	0.335363i	−1.02828	−	4.52964i	0.151277	+	0.0144452i	8.21250	+	2.41141i	2.75095	+	1.19677i	0.115139	+	2.41707i
4.3	−1.11294	−	2.43701i	0.428896	+	1.67811i	−3.39064	+	3.91301i	1.72089	+	0.688942i	3.61223	−	2.91286i	3.66627	+	0.350087i	8.16844	+	2.39847i	−2.63210	+	1.43947i	−0.236302	−	4.96058i
4.4	−1.08589	−	2.37776i	−1.44842	−	0.949777i	−3.16487	+	3.65246i	−3.44500	−	1.37917i	−0.685521	+	4.47535i	4.95017	+	0.472684i	7.10516	+	2.08626i	1.19585	+	2.75135i	0.461545	+	9.68902i
4.5	−1.08130	−	2.36771i	−1.72152	+	0.190672i	−3.12714	+	3.60892i	2.07131	+	0.829229i	2.31294	+	3.86990i	−0.856451	−	0.0817811i	6.93126	+	2.03520i	2.92729	−	0.656494i	−0.276332	−	5.80093i
4.6	−1.02077	−	2.23518i	−1.11462	+	1.32575i	−2.64432	+	3.05170i	−3.66875	−	1.46875i	4.10106	+	1.13808i	−2.93749	−	0.280497i	4.80494	+	1.41086i	−0.515249	−	2.95542i	0.462047	+	9.69957i
4.7	−0.967082	−	2.11762i	0.711584	−	1.57913i	−2.23932	+	2.58432i	−0.394326	−	0.157864i	−4.03215	+	0.0202857i	3.44566	+	0.329021i	3.17082	+	0.931037i	−1.98730	−	2.24737i	0.0470498	+	0.987698i
4.8	−0.959052	−	2.10003i	1.65818	+	0.500426i	−2.18063	+	2.51658i	3.55599	+	1.42361i	−0.539374	−	3.96217i	−2.65444	−	0.253468i	2.94595	+	0.865009i	2.49915	+	1.65960i	−0.420768	−	8.83301i
4.9	−0.940367	−	2.05912i	0.192657	+	1.72130i	−2.04595	+	2.36115i	−0.480385	−	0.192317i	3.36319	−	2.01536i	−0.548041	−	0.0523316i	2.44186	+	0.716994i	−2.92577	+	0.663243i	0.0557348	+	1.17002i
4.10	−0.929661	−	2.03567i	−0.481843	−	1.66368i	−1.96997	+	2.27347i	2.90470	+	1.16287i	−2.93875	+	2.52753i	2.26585	+	0.216363i	2.16493	+	0.635681i	−2.53565	+	1.60327i	−0.333169	−	6.99409i
4.11	−0.918977	−	2.01228i	−0.842148	−	1.51353i	−1.89503	+	2.18698i	1.15998	+	0.464386i	−2.27174	+	3.08554i	−2.47192	−	0.236040i	1.89714	+	0.557052i	−1.58157	+	2.54924i	−0.131521	−	2.76096i
4.12	−0.855928	−	1.87422i	1.13566	+	1.30777i	−1.47037	+	1.69690i	−1.76428	−	0.706311i	1.47901	−	3.24784i	−2.16210	−	0.206456i	0.484980	+	0.142403i	−0.420544	+	2.97038i	0.186313	+	3.91120i
4.13	−0.848158	−	1.85721i	−1.73202	+	0.00952723i	−1.42012	+	1.63891i	−0.374098	−	0.149766i	1.48672	+	3.20865i	−0.762785	−	0.0728371i	0.330270	+	0.0969759i	2.99982	−	0.0330028i	0.0391473	+	0.821802i
4.14	−0.780310	−	1.70864i	1.39056	−	1.03264i	−1.00085	+	1.15504i	1.45707	+	0.583323i	−2.84947	−	1.57019i	−4.03153	−	0.384965i	−0.850084	−	0.249607i	0.867322	−	2.87189i	−0.140277	−	2.94478i
4.15	−0.761040	−	1.66645i	−1.03789	+	1.38665i	−0.888137	+	1.02496i	3.74579	+	1.49959i	3.10064	+	0.674293i	2.09908	+	0.200438i	−1.13163	−	0.332275i	−0.845572	−	2.87837i	−0.351715	−	7.38341i
4.16	−0.735540	−	1.61061i	−0.836456	+	1.51669i	−0.743320	+	0.857837i	−1.49471	−	0.598391i	3.05804	+	0.231619i	2.83507	+	0.270716i	−1.46941	−	0.431456i	−1.60068	−	2.53729i	0.135645	+	2.84753i
4.17	−0.634208	−	1.38872i	0.629270	−	1.61370i	−0.216609	+	0.249980i	−3.53304	−	1.41442i	−2.64007	+	0.149539i	−0.628274	−	0.0599929i	−2.44516	−	0.717964i	−2.20804	−	2.03090i	0.276453	+	5.80345i
4.18	−0.608303	−	1.33200i	1.29661	+	1.14839i	−0.0944641	+	0.109017i	−2.16014	−	0.864788i	0.740915	−	2.42565i	5.10130	+	0.487115i	−2.60735	−	0.765586i	0.362415	+	2.97803i	0.162121	+	3.40335i
4.19	−0.607142	−	1.32945i	1.69190	+	0.370779i	−0.0891071	+	0.102835i	2.40251	+	0.961822i	−0.534289	−	2.47442i	3.57597	+	0.341463i	−2.61384	−	0.767493i	2.72505	+	1.25464i	−0.179968	−	3.77800i
4.20	−0.558230	−	1.22235i	1.26728	−	1.18067i	0.127194	−	0.146789i	0.953627	+	0.381775i	−2.15064	−	0.889983i	0.642878	+	0.0613874i	−2.82914	−	0.830712i	0.212021	−	2.99250i	−0.0656798	−	1.37879i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
603.y	even	33	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	603.2.y.a	✓	1320
9.c	even	3	1		603.2.ba.a	yes	1320
67.g	even	33	1		603.2.ba.a	yes	1320
603.y	even	33	1	inner	603.2.y.a	✓	1320

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
603.2.y.a	✓	1320	1.a	even	1	1	trivial
603.2.y.a	✓	1320	603.y	even	33	1	inner
603.2.ba.a	yes	1320	9.c	even	3	1
603.2.ba.a	yes	1320	67.g	even	33	1

Hecke kernels

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