Newform orbit 816.2.cj.b

• Label: 816.2.cj.b
• Level: $816$
• Weight: $2$
• Character orbit: 816.cj
• Analytic conductor: $6.516$
• Analytic rank: $0$
• Dimension: $24$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 816 = 2^{4} \cdot 3 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	816.cj (of order \(16\), degree \(8\), not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(6.51579280494\)
Analytic rank:	\(0\)
Dimension:	\(24\)
Relative dimension:	\(3\) over \(\Q(\zeta_{16})\)
Twist minimal:	no (minimal twist has level 102)
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.

\(\operatorname{Tr}(f)(q) = \) \( 24 q+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
65.1		0		−1.73044	+	0.0747517i		0		0.630232	+	0.943208i		0		4.16378	+	2.78215i		0		2.98882	−	0.258706i		0
65.2		0		−0.464518	−	1.66860i		0		−0.995238	−	1.48948i		0		−2.77729	−	1.85573i		0		−2.56845	+	1.55019i		0
65.3		0		1.48785	+	0.886741i		0		2.21277	+	3.31164i		0		−1.38649	−	0.926424i		0		1.42738	+	2.63867i		0
113.1		0		−1.73044	−	0.0747517i		0		0.630232	−	0.943208i		0		4.16378	−	2.78215i		0		2.98882	+	0.258706i		0
113.2		0		−0.464518	+	1.66860i		0		−0.995238	+	1.48948i		0		−2.77729	+	1.85573i		0		−2.56845	−	1.55019i		0
113.3		0		1.48785	−	0.886741i		0		2.21277	−	3.31164i		0		−1.38649	+	0.926424i		0		1.42738	−	2.63867i		0
209.1		0		−1.33894	−	1.09874i		0		0.715543	+	0.142330i		0		0.110207	+	0.554049i		0		0.585545	+	2.94230i		0
209.2		0		0.317070	+	1.70278i		0		−2.04899	−	0.407570i		0		0.635770	+	3.19623i		0		−2.79893	+	1.07980i		0
209.3		0		1.72898	+	0.103064i		0		2.09882	+	0.417480i		0		−0.745978	−	3.75028i		0		2.97876	+	0.356391i		0
401.1		0		−1.36418	−	1.06725i		0		−0.593905	−	2.98576i		0		3.74730	+	0.745385i		0		0.721973	+	2.91183i		0
401.2		0		0.799829	+	1.53632i		0		−0.456232	−	2.29363i		0		−3.60046	−	0.716176i		0		−1.72055	+	2.45758i		0
401.3		0		1.27146	−	1.17618i		0		0.284770	+	1.43164i		0		−0.146842	−	0.0292088i		0		0.233206	−	2.99092i		0
449.1		0		−1.33894	+	1.09874i		0		0.715543	−	0.142330i		0		0.110207	−	0.554049i		0		0.585545	−	2.94230i		0
449.2		0		0.317070	−	1.70278i		0		−2.04899	+	0.407570i		0		0.635770	−	3.19623i		0		−2.79893	−	1.07980i		0
449.3		0		1.72898	−	0.103064i		0		2.09882	−	0.417480i		0		−0.745978	+	3.75028i		0		2.97876	−	0.356391i		0
641.1		0		−1.36418	+	1.06725i		0		−0.593905	+	2.98576i		0		3.74730	−	0.745385i		0		0.721973	−	2.91183i		0
641.2		0		0.799829	−	1.53632i		0		−0.456232	+	2.29363i		0		−3.60046	+	0.716176i		0		−1.72055	−	2.45758i		0
641.3		0		1.27146	+	1.17618i		0		0.284770	−	1.43164i		0		−0.146842	+	0.0292088i		0		0.233206	+	2.99092i		0
737.1		0		−1.33960	+	1.09794i		0		0.904790	+	0.604561i		0		−0.0740832	−	0.110873i		0		0.589049	−	2.94160i		0
737.2		0		−0.573016	−	1.63452i		0		0.540978	+	0.361470i		0		−0.676748	−	1.01283i		0		−2.34331	+	1.87321i		0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
51.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.cj.b		24
3.b	odd	2	1		816.2.cj.a		24
4.b	odd	2	1		102.2.i.a	✓	24
12.b	even	2	1		102.2.i.b	yes	24
17.e	odd	16	1		816.2.cj.a		24
51.i	even	16	1	inner	816.2.cj.b		24
68.i	even	16	1		102.2.i.b	yes	24
204.t	odd	16	1		102.2.i.a	✓	24

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
102.2.i.a	✓	24	4.b	odd	2	1
102.2.i.a	✓	24	204.t	odd	16	1
102.2.i.b	yes	24	12.b	even	2	1
102.2.i.b	yes	24	68.i	even	16	1
816.2.cj.a		24	3.b	odd	2	1
816.2.cj.a		24	17.e	odd	16	1
816.2.cj.b		24	1.a	even	1	1	trivial
816.2.cj.b		24	51.i	even	16	1	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T5^24 + 8*T5^22 + 16*T5^21 + 156*T5^20 - 224*T5^19 + 1256*T5^18 - 7296*T5^17 + 7624*T5^16 - 10432*T5^15 + 10144*T5^14 + 103776*T5^13 - 246824*T5^12 + 363456*T5^11 - 252624*T5^10 - 264640*T5^9 + 1867652*T5^8 - 6000640*T5^7 + 14155328*T5^6 - 24078592*T5^5 + 28982656*T5^4 - 23968768*T5^3 + 12921856*T5^2 - 4108288*T5 + 591872