Newform orbit 3024.2.ca.e

• Label: 3024.2.ca.e
• Level: $3024$
• Weight: $2$
• Character orbit: 3024.ca
• Analytic conductor: $24.147$
• Analytic rank: $0$
• Dimension: $48$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3024.ca (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(24.1467615712\)
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.

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

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
2033.1		0			0			0		−2.05742	+	3.56356i		0		−1.89056	−	1.85089i		0			0			0
2033.2		0			0			0		−2.04942	+	3.54970i		0		2.21443	−	1.44785i		0			0			0
2033.3		0			0			0		−1.76701	+	3.06054i		0		−1.34480	+	2.27849i		0			0			0
2033.4		0			0			0		−1.38468	+	2.39834i		0		1.42373	−	2.23002i		0			0			0
2033.5		0			0			0		−1.29668	+	2.24592i		0		−1.66807	−	2.05367i		0			0			0
2033.6		0			0			0		−1.11415	+	1.92977i		0		0.553477	+	2.58721i		0			0			0
2033.7		0			0			0		−1.10442	+	1.91291i		0		−0.234181	+	2.63537i		0			0			0
2033.8		0			0			0		−1.02449	+	1.77447i		0		2.64365	+	0.105420i		0			0			0
2033.9		0			0			0		−0.684139	+	1.18496i		0		1.25206	+	2.33074i		0			0			0
2033.10		0			0			0		0.0262870	−	0.0455305i		0		2.10354	+	1.60471i		0			0			0
2033.11		0			0			0		0.101589	−	0.175958i		0		1.37377	−	2.26114i		0			0			0
2033.12		0			0			0		0.103514	−	0.179292i		0		−2.64517	−	0.0556151i		0			0			0
2033.13		0			0			0		0.271038	−	0.469451i		0		−1.60655	−	2.10214i		0			0			0
2033.14		0			0			0		0.311798	−	0.540051i		0		−2.62086	+	0.362103i		0			0			0
2033.15		0			0			0		0.527910	−	0.914367i		0		−0.781227	+	2.52778i		0			0			0
2033.16		0			0			0		0.537427	−	0.930850i		0		1.37797	−	2.25858i		0			0			0
2033.17		0			0			0		0.643917	−	1.11530i		0		2.63392	−	0.249885i		0			0			0
2033.18		0			0			0		0.793002	−	1.37352i		0		−2.62988	+	0.289398i		0			0			0
2033.19		0			0			0		0.905867	−	1.56901i		0		2.60735	+	0.449161i		0			0			0
2033.20		0			0			0		1.11047	−	1.92339i		0		−0.362456	−	2.62081i		0			0			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	3024.2.ca.e		48
3.b	odd	2	1		1008.2.ca.e		48
4.b	odd	2	1		1512.2.bs.a		48
7.d	odd	6	1		3024.2.df.e		48
9.c	even	3	1		1008.2.df.e		48
9.d	odd	6	1		3024.2.df.e		48
12.b	even	2	1		504.2.bs.a	✓	48
21.g	even	6	1		1008.2.df.e		48
28.f	even	6	1		1512.2.cx.a		48
36.f	odd	6	1		504.2.cx.a	yes	48
36.h	even	6	1		1512.2.cx.a		48
63.i	even	6	1	inner	3024.2.ca.e		48
63.t	odd	6	1		1008.2.ca.e		48
84.j	odd	6	1		504.2.cx.a	yes	48
252.r	odd	6	1		1512.2.bs.a		48
252.bj	even	6	1		504.2.bs.a	✓	48

    

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