Newform orbit 468.2.cb.i

• Label: 468.2.cb.i
• Level: $468$
• Weight: $2$
• Character orbit: 468.cb
• Analytic conductor: $3.737$
• Analytic rank: $0$
• Dimension: $48$
• CM: no
• Inner twists: $8$

Newspace parameters

Level:	\( N \)	\(=\)	\( 468 = 2^{2} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	468.cb (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(3.73699881460\)
Analytic rank:	\(0\)
Dimension:	\(48\)
Relative dimension:	\(12\) over \(\Q(\zeta_{12})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

$q$-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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
19.1	−1.40355	+	0.173344i		0		1.93990	−	0.486594i	−1.97251	+	1.97251i		0		−3.25845	−	0.873098i	−2.63840	+	1.01923i		0		2.42659	−	3.11044i
19.2	−1.31308	−	0.525194i		0		1.44834	+	1.37924i	−0.540061	+	0.540061i		0		3.48216	+	0.933043i	−1.17741	−	2.57171i		0		0.992778	−	0.425504i
19.3	−1.30218	+	0.551655i		0		1.39135	−	1.43671i	1.97251	−	1.97251i		0		3.25845	+	0.873098i	−1.01923	+	2.63840i		0		−1.48042	+	3.65671i
19.4	−0.874561	+	1.11137i		0		−0.470287	−	1.94392i	0.540061	−	0.540061i		0		−3.48216	−	0.933043i	2.57171	+	1.17741i		0		0.127891	+	1.07252i
19.5	−0.830529	−	1.14465i		0		−0.620442	+	1.90133i	−1.16337	+	1.16337i		0		−0.631949	−	0.169330i	2.69165	−	0.868921i		0		2.29787	+	0.365439i
19.6	−0.146935	+	1.40656i		0		−1.95682	−	0.413346i	1.16337	−	1.16337i		0		0.631949	+	0.169330i	0.868921	−	2.69165i		0		1.46541	+	1.80730i
19.7	0.146935	−	1.40656i		0		−1.95682	−	0.413346i	−1.16337	+	1.16337i		0		0.631949	+	0.169330i	−0.868921	+	2.69165i		0		1.46541	+	1.80730i
19.8	0.830529	+	1.14465i		0		−0.620442	+	1.90133i	1.16337	−	1.16337i		0		−0.631949	−	0.169330i	−2.69165	+	0.868921i		0		2.29787	+	0.365439i
19.9	0.874561	−	1.11137i		0		−0.470287	−	1.94392i	−0.540061	+	0.540061i		0		−3.48216	−	0.933043i	−2.57171	−	1.17741i		0		0.127891	+	1.07252i
19.10	1.30218	−	0.551655i		0		1.39135	−	1.43671i	−1.97251	+	1.97251i		0		3.25845	+	0.873098i	1.01923	−	2.63840i		0		−1.48042	+	3.65671i
19.11	1.31308	+	0.525194i		0		1.44834	+	1.37924i	0.540061	−	0.540061i		0		3.48216	+	0.933043i	1.17741	+	2.57171i		0		0.992778	−	0.425504i
19.12	1.40355	−	0.173344i		0		1.93990	−	0.486594i	1.97251	−	1.97251i		0		−3.25845	−	0.873098i	2.63840	−	1.01923i		0		2.42659	−	3.11044i
163.1	−1.29394	−	0.570726i		0		1.34854	+	1.47697i	−0.478949	−	0.478949i		0		−0.796754	+	2.97353i	−0.901985	−	2.68075i		0		0.346381	+	0.893079i
163.2	−1.25356	−	0.654668i		0		1.14282	+	1.64133i	2.61559	+	2.61559i		0		1.22555	−	4.57382i	−0.358067	−	2.80567i		0		−1.56645	−	4.99113i
163.3	−0.835219	+	1.14123i		0		−0.604819	−	1.90636i	−0.478949	−	0.478949i		0		0.796754	−	2.97353i	2.68075	+	0.901985i		0		0.946619	−	0.146565i
163.4	−0.779986	−	1.17967i		0		−0.783245	+	1.84025i	−2.32237	−	2.32237i		0		0.470000	−	1.75406i	2.78181	−	0.511399i		0		−0.928217	+	4.55105i
163.5	−0.758280	+	1.19374i		0		−0.850023	−	1.81038i	2.61559	+	2.61559i		0		−1.22555	+	4.57382i	2.80567	+	0.358067i		0		−5.10567	+	1.13898i
163.6	−0.0856522	+	1.41162i		0		−1.98533	−	0.241816i	−2.32237	−	2.32237i		0		−0.470000	+	1.75406i	0.511399	−	2.78181i		0		3.47722	−	3.07938i
163.7	0.0856522	−	1.41162i		0		−1.98533	−	0.241816i	2.32237	+	2.32237i		0		−0.470000	+	1.75406i	−0.511399	+	2.78181i		0		3.47722	−	3.07938i
163.8	0.758280	−	1.19374i		0		−0.850023	−	1.81038i	−2.61559	−	2.61559i		0		−1.22555	+	4.57382i	−2.80567	−	0.358067i		0		−5.10567	+	1.13898i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	inner
4.b	odd	2	1	inner
12.b	even	2	1	inner
13.f	odd	12	1	inner
39.k	even	12	1	inner
52.l	even	12	1	inner
156.v	odd	12	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	468.2.cb.i	✓	48
3.b	odd	2	1	inner	468.2.cb.i	✓	48
4.b	odd	2	1	inner	468.2.cb.i	✓	48
12.b	even	2	1	inner	468.2.cb.i	✓	48
13.f	odd	12	1	inner	468.2.cb.i	✓	48
39.k	even	12	1	inner	468.2.cb.i	✓	48
52.l	even	12	1	inner	468.2.cb.i	✓	48
156.v	odd	12	1	inner	468.2.cb.i	✓	48

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
468.2.cb.i	✓	48	1.a	even	1	1	trivial
468.2.cb.i	✓	48	3.b	odd	2	1	inner
468.2.cb.i	✓	48	4.b	odd	2	1	inner
468.2.cb.i	✓	48	12.b	even	2	1	inner
468.2.cb.i	✓	48	13.f	odd	12	1	inner
468.2.cb.i	✓	48	39.k	even	12	1	inner
468.2.cb.i	✓	48	52.l	even	12	1	inner
468.2.cb.i	✓	48	156.v	odd	12	1	inner

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(468, [\chi])\):

\( T_{5}^{24} + 372T_{5}^{20} + 43038T_{5}^{16} + 1636964T_{5}^{12} + 10556553T_{5}^{8} + 5438592T_{5}^{4} + 692224 \)

T7^24 + 18*T7^22 - 289*T7^20 - 7146*T7^18 + 109569*T7^16 + 990804*T7^14 - 10250456*T7^12 - 87951288*T7^10 + 772487532*T7^8 + 4827836160*T7^6 + 6888663872*T7^4 - 6978085920*T7^2 + 1967454736

T17^24 - 144*T17^22 + 12786*T17^20 - 713152*T17^18 + 29105343*T17^16 - 866874528*T17^14 + 19749859386*T17^12 - 334620929232*T17^10 + 4291389771417*T17^8 - 38957884998880*T17^6 + 258021997055424*T17^4 - 1069409045133312*T17^2 + 2747524276916224