Newform orbit 1008.2.ca.e

• Label: 1008.2.ca.e
• Level: $1008$
• Weight: $2$
• Character orbit: 1008.ca
• Analytic conductor: $8.049$
• Analytic rank: $0$
• Dimension: $48$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1008.ca (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(8.04892052375\)
Analytic rank:	\(0\)
Dimension:	\(48\)
Relative dimension:	\(24\) over \(\Q(\zeta_{6})\)
Twist minimal:	no (minimal twist has level 504)
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.

\(\operatorname{Tr}(f)(q) = \) \( 48 q - 4 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
257.1		0		−1.73040	+	0.0755121i		0		0.684139	+	1.18496i		0		1.25206	−	2.33074i		0		2.98860	−	0.261333i		0
257.2		0		−1.72860	+	0.109329i		0		2.05742	+	3.56356i		0		−1.89056	+	1.85089i		0		2.97609	−	0.377972i		0
257.3		0		−1.72539	+	0.151709i		0		−0.793002	−	1.37352i		0		−2.62988	−	0.289398i		0		2.95397	−	0.523514i		0
257.4		0		−1.38355	−	1.04201i		0		−0.537427	−	0.930850i		0		1.37797	+	2.25858i		0		0.828420	+	2.88335i		0
257.5		0		−1.29769	+	1.14717i		0		−0.643917	−	1.11530i		0		2.63392	+	0.249885i		0		0.368015	−	2.97734i		0
257.6		0		−1.10617	−	1.33281i		0		−0.103514	−	0.179292i		0		−2.64517	+	0.0556151i		0		−0.552770	+	2.94863i		0
257.7		0		−0.957290	+	1.44347i		0		−1.80389	−	3.12442i		0		−2.05506	−	1.66636i		0		−1.16719	−	2.76363i		0
257.8		0		−0.872943	−	1.49598i		0		−2.09905	−	3.63567i		0		2.61186	−	0.422135i		0		−1.47594	+	2.61182i		0
257.9		0		−0.859678	+	1.50365i		0		1.29668	+	2.24592i		0		−1.66807	+	2.05367i		0		−1.52191	−	2.58530i		0
257.10		0		−0.690387	−	1.58851i		0		1.10442	+	1.91291i		0		−0.234181	−	2.63537i		0		−2.04673	+	2.19337i		0
257.11		0		−0.589575	+	1.62862i		0		1.11415	+	1.92977i		0		0.553477	−	2.58721i		0		−2.30480	−	1.92039i		0
257.12		0		−0.0709339	−	1.73060i		0		2.04942	+	3.54970i		0		2.21443	+	1.44785i		0		−2.98994	+	0.245516i		0
257.13		0		−0.0250939	+	1.73187i		0		−1.42382	−	2.46612i		0		−1.38343	+	2.25524i		0		−2.99874	−	0.0869188i		0
257.14		0		0.419673	+	1.68044i		0		1.02449	+	1.77447i		0		2.64365	−	0.105420i		0		−2.64775	+	1.41047i		0
257.15		0		0.445548	−	1.67376i		0		−0.101589	−	0.175958i		0		1.37377	+	2.26114i		0		−2.60297	−	1.49148i		0
257.16		0		0.559017	−	1.63936i		0		−1.82284	−	3.15725i		0		−1.57353	−	2.12697i		0		−2.37500	−	1.83286i		0
257.17		0		1.09564	−	1.34148i		0		−0.271038	−	0.469451i		0		−1.60655	+	2.10214i		0		−0.599164	−	2.93956i		0
257.18		0		1.14780	+	1.29713i		0		−0.527910	−	0.914367i		0		−0.781227	−	2.52778i		0		−0.365108	+	2.97770i		0
257.19		0		1.32026	+	1.12112i		0		1.38468	+	2.39834i		0		1.42373	+	2.23002i		0		0.486198	+	2.96034i		0
257.20		0		1.41991	+	0.991901i		0		−1.11047	−	1.92339i		0		−0.362456	+	2.62081i		0		1.03226	+	2.81681i		0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
63.i	even	6	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	1008.2.ca.e		48
3.b	odd	2	1		3024.2.ca.e		48
4.b	odd	2	1		504.2.bs.a	✓	48
7.d	odd	6	1		1008.2.df.e		48
9.c	even	3	1		3024.2.df.e		48
9.d	odd	6	1		1008.2.df.e		48
12.b	even	2	1		1512.2.bs.a		48
21.g	even	6	1		3024.2.df.e		48
28.f	even	6	1		504.2.cx.a	yes	48
36.f	odd	6	1		1512.2.cx.a		48
36.h	even	6	1		504.2.cx.a	yes	48
63.i	even	6	1	inner	1008.2.ca.e		48
63.t	odd	6	1		3024.2.ca.e		48
84.j	odd	6	1		1512.2.cx.a		48
252.r	odd	6	1		504.2.bs.a	✓	48
252.bj	even	6	1		1512.2.bs.a		48

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
504.2.bs.a	✓	48	4.b	odd	2	1
504.2.bs.a	✓	48	252.r	odd	6	1
504.2.cx.a	yes	48	28.f	even	6	1
504.2.cx.a	yes	48	36.h	even	6	1
1008.2.ca.e		48	1.a	even	1	1	trivial
1008.2.ca.e		48	63.i	even	6	1	inner
1008.2.df.e		48	7.d	odd	6	1
1008.2.df.e		48	9.d	odd	6	1
1512.2.bs.a		48	12.b	even	2	1
1512.2.bs.a		48	252.bj	even	6	1
1512.2.cx.a		48	36.f	odd	6	1
1512.2.cx.a		48	84.j	odd	6	1
3024.2.ca.e		48	3.b	odd	2	1
3024.2.ca.e		48	63.t	odd	6	1
3024.2.df.e		48	9.c	even	3	1
3024.2.df.e		48	21.g	even	6	1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T5^48 + 72*T5^46 + 24*T5^45 + 3009*T5^44 + 1632*T5^43 + 84734*T5^42 + 64212*T5^41 + 1789725*T5^40 + 1690992*T5^39 + 29328876*T5^38 + 33168990*T5^37 + 385363151*T5^36 + 500652036*T5^35 + 4115069949*T5^34 + 5999164830*T5^33 + 36285631098*T5^32 + 57645264312*T5^31 + 266141164643*T5^30 + 449709485598*T5^29 + 1636898178273*T5^28 + 2853866039016*T5^27 + 8451598014642*T5^26 + 14798623920432*T5^25 + 36587740285111*T5^24 + 62467984667532*T5^23 + 131678185867350*T5^22 + 213875289949482*T5^21 + 389153062300836*T5^20 + 585747309545844*T5^19 + 924568000946827*T5^18 + 1261511813553930*T5^17 + 1719650092876149*T5^16 + 2066810301152478*T5^15 + 2395969544016237*T5^14 + 2468516823228132*T5^13 + 2377857622622489*T5^12 + 2000408534226306*T5^11 + 1495973367754740*T5^10 + 933493746045522*T5^9 + 488427545980857*T5^8 + 202067582942454*T5^7 + 66435826217155*T5^6 + 16164010690950*T5^5 + 2975048711901*T5^4 + 375739140924*T5^3 + 33076493100*T5^2 + 1426403760*T5 + 41938576