Newform orbit 627.2.be.a

• Label: 627.2.be.a
• Level: $627$
• Weight: $2$
• Character orbit: 627.be
• Analytic conductor: $5.007$
• Analytic rank: $0$
• Dimension: $240$
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 627 = 3 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	627.be (of order \(18\), degree \(6\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(5.00662020673\)
Analytic rank:	\(0\)
Dimension:	\(240\)
Relative dimension:	\(40\) over \(\Q(\zeta_{18})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) 240 * q + 6 * q^11 - 48 * q^14 + 24 * q^15 - 216 * q^20 + 24 * q^26 - 36 * q^31 - 6 * q^33 - 132 * q^34 + 180 * q^38 + 12 * q^42 - 24 * q^44 - 12 * q^45 + 72 * q^47 + 48 * q^48 + 132 * q^49 + 108 * q^53 - 30 * q^55 - 24 * q^58 + 48 * q^60 - 120 * q^64 - 48 * q^66 + 48 * q^67 - 228 * q^70 - 84 * q^71 - 72 * q^77 + 84 * q^78 - 24 * q^80 - 156 * q^82 + 48 * q^86 + 108 * q^88 + 144 * q^89 - 24 * q^91 - 60 * q^92 - 24 * q^93 - 12 * q^99

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
10.1	−0.485290	−	2.75222i	0.642788	+	0.766044i	−5.45980	+	1.98721i	2.33741	+	0.850748i	1.79638	−	2.14084i	−2.71663	−	1.56845i	5.32413	+	9.22167i	−0.173648	+	0.984808i	1.20712	−	6.84592i
10.2	−0.452416	−	2.56578i	−0.642788	−	0.766044i	−4.49915	+	1.63756i	0.645086	+	0.234792i	−1.67469	+	1.99582i	1.91835	+	1.10756i	3.63174	+	6.29036i	−0.173648	+	0.984808i	0.310577	−	1.76137i
10.3	−0.450301	−	2.55378i	0.642788	+	0.766044i	−4.43965	+	1.61590i	−2.55901	−	0.931403i	1.66686	−	1.98649i	1.18777	+	0.685761i	3.53266	+	6.11874i	−0.173648	+	0.984808i	−1.22628	+	6.95456i
10.4	−0.434923	−	2.46657i	−0.642788	−	0.766044i	−4.01544	+	1.46150i	3.32981	+	1.21195i	−1.60994	+	1.91865i	−1.37672	−	0.794852i	2.84668	+	4.93059i	−0.173648	+	0.984808i	1.54116	−	8.74033i
10.5	−0.409779	−	2.32397i	−0.642788	−	0.766044i	−3.35354	+	1.22059i	−1.28121	−	0.466321i	−1.51686	+	1.80773i	−3.53290	−	2.03972i	1.85100	+	3.20602i	−0.173648	+	0.984808i	−0.558705	+	3.16858i
10.6	−0.359441	−	2.03849i	0.642788	+	0.766044i	−2.14686	+	0.781393i	0.143283	+	0.0521508i	1.33053	−	1.58566i	−2.77971	−	1.60487i	0.294595	+	0.510253i	−0.173648	+	0.984808i	0.0548071	−	0.310827i
10.7	−0.341690	−	1.93782i	0.642788	+	0.766044i	−1.75901	+	0.640227i	2.83928	+	1.03341i	1.26482	−	1.50736i	1.12046	+	0.646899i	−0.126035	−	0.218298i	−0.173648	+	0.984808i	1.03242	−	5.85512i
10.8	−0.308703	−	1.75074i	−0.642788	−	0.766044i	−1.09041	+	0.396879i	−0.129752	−	0.0472258i	−1.14272	+	1.36184i	2.51719	+	1.45330i	−0.746304	−	1.29264i	−0.173648	+	0.984808i	−0.0426254	+	0.241741i
10.9	−0.298396	−	1.69229i	−0.642788	−	0.766044i	−0.895420	+	0.325906i	−2.11525	−	0.769887i	−1.10456	+	1.31637i	1.79166	+	1.03441i	−0.899679	−	1.55829i	−0.173648	+	0.984808i	−0.671690	+	3.80934i
10.10	−0.296656	−	1.68242i	0.642788	+	0.766044i	−0.863144	+	0.314159i	−2.17291	−	0.790873i	1.09812	−	1.30869i	3.30762	+	1.90965i	−0.923770	−	1.60002i	−0.173648	+	0.984808i	−0.685974	+	3.89035i
10.11	−0.263484	−	1.49429i	0.642788	+	0.766044i	−0.284097	+	0.103403i	3.13219	+	1.14002i	0.975329	−	1.16235i	1.86040	+	1.07410i	−1.28797	−	2.23084i	−0.173648	+	0.984808i	0.878246	−	4.98078i
10.12	−0.251762	−	1.42781i	−0.642788	−	0.766044i	−0.0958771	+	0.0348964i	−3.52251	−	1.28209i	−0.931938	+	1.11064i	−1.53275	−	0.884935i	−1.37587	−	2.38308i	−0.173648	+	0.984808i	−0.943748	+	5.35226i
10.13	−0.249862	−	1.41704i	−0.642788	−	0.766044i	−0.0661850	+	0.0240894i	2.05628	+	0.748426i	−0.924907	+	1.10226i	−2.92865	−	1.69086i	−1.38823	−	2.40448i	−0.173648	+	0.984808i	0.546761	−	3.10084i
10.14	−0.173752	−	0.985397i	−0.642788	−	0.766044i	0.938568	−	0.341611i	3.11785	+	1.13481i	−0.643172	+	0.766503i	0.730564	+	0.421791i	−1.50030	−	2.59859i	−0.173648	+	0.984808i	0.576501	−	3.26950i
10.15	−0.166979	−	0.946983i	0.642788	+	0.766044i	1.01049	−	0.367789i	−3.69883	−	1.34626i	0.618099	−	0.736622i	0.270897	+	0.156403i	−1.47861	−	2.56103i	−0.173648	+	0.984808i	−0.657262	+	3.72752i
10.16	−0.166220	−	0.942679i	0.642788	+	0.766044i	1.01837	−	0.370657i	−0.837352	−	0.304771i	0.615290	−	0.733274i	−3.86246	−	2.22999i	−1.47590	−	2.55634i	−0.173648	+	0.984808i	−0.148117	+	0.840013i
10.17	−0.0860339	−	0.487922i	0.642788	+	0.766044i	1.64872	−	0.600085i	−0.122114	−	0.0444457i	0.318469	−	0.379536i	−1.58750	−	0.916543i	−0.930090	−	1.61096i	−0.173648	+	0.984808i	−0.0111802	+	0.0634058i
10.18	−0.0377067	−	0.213846i	−0.642788	−	0.766044i	1.83508	−	0.667913i	−2.08488	−	0.758835i	−0.139578	+	0.166342i	3.25299	+	1.87811i	−0.429169	−	0.743343i	−0.173648	+	0.984808i	−0.0836593	+	0.474456i
10.19	−0.0329979	−	0.187140i	−0.642788	−	0.766044i	1.84545	−	0.671690i	0.281468	+	0.102446i	−0.122147	+	0.145569i	−1.33226	−	0.769180i	−0.376624	−	0.652332i	−0.173648	+	0.984808i	0.00988394	−	0.0560546i
10.20	−0.00653270	−	0.0370488i	0.642788	+	0.766044i	1.87806	−	0.683556i	2.52052	+	0.917394i	0.0241819	−	0.0288188i	−1.94562	−	1.12331i	−0.0752140	−	0.130274i	−0.173648	+	0.984808i	0.0175225	−	0.0993752i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
11.b	odd	2	1	inner
19.f	odd	18	1	inner
209.p	even	18	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	627.2.be.a	✓	240
11.b	odd	2	1	inner	627.2.be.a	✓	240
19.f	odd	18	1	inner	627.2.be.a	✓	240
209.p	even	18	1	inner	627.2.be.a	✓	240

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
627.2.be.a	✓	240	1.a	even	1	1	trivial
627.2.be.a	✓	240	11.b	odd	2	1	inner
627.2.be.a	✓	240	19.f	odd	18	1	inner
627.2.be.a	✓	240	209.p	even	18	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(627, [\chi])\).