Newform orbit 816.2.ck.b

• Label: 816.2.ck.b
• Level: $816$
• Weight: $2$
• Character orbit: 816.ck
• Analytic conductor: $6.516$
• Analytic rank: $0$
• Dimension: $96$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 816 = 2^{4} \cdot 3 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	816.ck (of order \(16\), degree \(8\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(6.51579280494\)
Analytic rank:	\(0\)
Dimension:	\(96\)
Relative dimension:	\(12\) over \(\Q(\zeta_{16})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 96 q+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
31.1		0		−0.980785	−	0.195090i		0		−2.81893	+	1.88355i		0		1.62928	−	2.43839i		0		0.923880	+	0.382683i		0
31.2		0		−0.980785	−	0.195090i		0		−1.61438	+	1.07869i		0		0.284723	−	0.426119i		0		0.923880	+	0.382683i		0
31.3		0		−0.980785	−	0.195090i		0		−0.502087	+	0.335484i		0		−0.665068	+	0.995344i		0		0.923880	+	0.382683i		0
31.4		0		−0.980785	−	0.195090i		0		2.02779	−	1.35493i		0		−2.31714	+	3.46785i		0		0.923880	+	0.382683i		0
31.5		0		−0.980785	−	0.195090i		0		2.27504	−	1.52013i		0		1.65696	−	2.47981i		0		0.923880	+	0.382683i		0
31.6		0		−0.980785	−	0.195090i		0		3.12917	−	2.09085i		0		−0.588751	+	0.881128i		0		0.923880	+	0.382683i		0
31.7		0		0.980785	+	0.195090i		0		−2.81893	+	1.88355i		0		−1.62928	+	2.43839i		0		0.923880	+	0.382683i		0
31.8		0		0.980785	+	0.195090i		0		−1.61438	+	1.07869i		0		−0.284723	+	0.426119i		0		0.923880	+	0.382683i		0
31.9		0		0.980785	+	0.195090i		0		−0.502087	+	0.335484i		0		0.665068	−	0.995344i		0		0.923880	+	0.382683i		0
31.10		0		0.980785	+	0.195090i		0		2.02779	−	1.35493i		0		2.31714	−	3.46785i		0		0.923880	+	0.382683i		0
31.11		0		0.980785	+	0.195090i		0		2.27504	−	1.52013i		0		−1.65696	+	2.47981i		0		0.923880	+	0.382683i		0
31.12		0		0.980785	+	0.195090i		0		3.12917	−	2.09085i		0		0.588751	−	0.881128i		0		0.923880	+	0.382683i		0
79.1		0		−0.980785	+	0.195090i		0		−2.81893	−	1.88355i		0		1.62928	+	2.43839i		0		0.923880	−	0.382683i		0
79.2		0		−0.980785	+	0.195090i		0		−1.61438	−	1.07869i		0		0.284723	+	0.426119i		0		0.923880	−	0.382683i		0
79.3		0		−0.980785	+	0.195090i		0		−0.502087	−	0.335484i		0		−0.665068	−	0.995344i		0		0.923880	−	0.382683i		0
79.4		0		−0.980785	+	0.195090i		0		2.02779	+	1.35493i		0		−2.31714	−	3.46785i		0		0.923880	−	0.382683i		0
79.5		0		−0.980785	+	0.195090i		0		2.27504	+	1.52013i		0		1.65696	+	2.47981i		0		0.923880	−	0.382683i		0
79.6		0		−0.980785	+	0.195090i		0		3.12917	+	2.09085i		0		−0.588751	−	0.881128i		0		0.923880	−	0.382683i		0
79.7		0		0.980785	−	0.195090i		0		−2.81893	−	1.88355i		0		−1.62928	−	2.43839i		0		0.923880	−	0.382683i		0
79.8		0		0.980785	−	0.195090i		0		−1.61438	−	1.07869i		0		−0.284723	−	0.426119i		0		0.923880	−	0.382683i		0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
4.b	odd	2	1	inner
17.e	odd	16	1	inner
68.i	even	16	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	816.2.ck.b	✓	96
4.b	odd	2	1	inner	816.2.ck.b	✓	96
17.e	odd	16	1	inner	816.2.ck.b	✓	96
68.i	even	16	1	inner	816.2.ck.b	✓	96

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
816.2.ck.b	✓	96	1.a	even	1	1	trivial
816.2.ck.b	✓	96	4.b	odd	2	1	inner
816.2.ck.b	✓	96	17.e	odd	16	1	inner
816.2.ck.b	✓	96	68.i	even	16	1	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T5^48 - 8*T5^46 + 112*T5^45 - 1136*T5^43 + 6328*T5^42 + 8432*T5^41 - 76480*T5^40 + 110608*T5^39 + 1078504*T5^38 - 2185232*T5^37 - 7098968*T5^36 + 21151520*T5^35 + 20562872*T5^34 - 319108960*T5^33 + 353789929*T5^32 + 4263704512*T5^31 - 5901916560*T5^30 - 32445036048*T5^29 + 41930131064*T5^28 + 174832816608*T5^27 - 39463898784*T5^26 - 435384668960*T5^25 - 96695400160*T5^24 + 1008713755200*T5^23 + 2400548489760*T5^22 + 1410122160096*T5^21 - 1060021951248*T5^20 + 6599085561536*T5^19 + 14773077815872*T5^18 - 17019271828224*T5^17 - 130461922225000*T5^16 - 300088251941120*T5^15 - 291501948241856*T5^14 + 364243650010816*T5^13 + 2259812471825760*T5^12 + 5435225843074688*T5^11 + 8943264670536192*T5^10 + 11213207795650688*T5^9 + 11151454970486912*T5^8 + 8948842303264768*T5^7 + 5815263490649600*T5^6 + 3041675094109312*T5^5 + 1259654112707136*T5^4 + 399412501092608*T5^3 + 91447874598272*T5^2 + 13652876769792*T5 + 1103953678864