Newform orbit 936.2.q.g

• Label: 936.2.q.g
• Level: $936$
• Weight: $2$
• Character orbit: 936.q
• Analytic conductor: $7.474$
• Analytic rank: $0$
• Dimension: $22$
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 936 = 2^{3} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	936.q (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(7.47399762919\)
Analytic rank:	\(0\)
Dimension:	\(22\)
Relative dimension:	\(11\) over \(\Q(\zeta_{3})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

$q$-expansion

The algebraic \(q\)-expansion of this newform has not been computed, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) 22 * q - 3 * q^5 - 4 * q^7 - 4 * q^9 + 5 * q^11 - 11 * q^13 + 5 * q^15 + 8 * q^17 + 10 * q^19 + 4 * q^21 + 9 * q^23 - 24 * q^25 - 12 * q^27 - 16 * q^29 - q^31 + 9 * q^33 + 18 * q^37 + 3 * q^39 - 6 * q^41 - 7 * q^43 - 21 * q^45 + 21 * q^47 - 27 * q^49 - 11 * q^51 + 32 * q^53 + 34 * q^55 + 2 * q^57 + 11 * q^59 - 2 * q^61 - 27 * q^63 - 3 * q^65 - 18 * q^67 + 7 * q^69 - 30 * q^71 + 18 * q^73 + 62 * q^75 - 9 * q^77 - 30 * q^79 + 4 * q^81 - 16 * q^83 - 32 * q^85 + 33 * q^87 + 26 * q^89 + 8 * q^91 + 20 * q^95 - 10 * q^97 - 109 * q^99

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
313.1		0		−1.73199	−	0.0148978i		0		0.550001	+	0.952629i		0		−2.20940	+	3.82679i		0		2.99956	+	0.0516057i		0
313.2		0		−1.73144	+	0.0459606i		0		−1.66784	−	2.88878i		0		1.59859	−	2.76884i		0		2.99578	−	0.159156i		0
313.3		0		−1.06380	+	1.36687i		0		0.662426	+	1.14736i		0		0.798467	−	1.38299i		0		−0.736678	−	2.90814i		0
313.4		0		−0.722210	−	1.57430i		0		−1.89006	−	3.27368i		0		−0.659907	+	1.14299i		0		−1.95682	+	2.27395i		0
313.5		0		−0.377983	−	1.69030i		0		2.15452	+	3.73175i		0		−0.803576	+	1.39183i		0		−2.71426	+	1.27781i		0
313.6		0		−0.215114	+	1.71864i		0		−1.80041	−	3.11840i		0		−2.42567	+	4.20138i		0		−2.90745	−	0.739406i		0
313.7		0		0.400278	+	1.68516i		0		0.618351	+	1.07102i		0		2.31092	−	4.00263i		0		−2.67955	+	1.34907i		0
313.8		0		1.17494	−	1.27260i		0		0.279527	+	0.484154i		0		−0.154587	+	0.267752i		0		−0.239012	−	2.99046i		0
313.9		0		1.26749	+	1.18045i		0		1.53775	+	2.66347i		0		−0.728405	+	1.26163i		0		0.213067	+	2.99242i		0
313.10		0		1.41854	+	0.993855i		0		−0.804884	−	1.39410i		0		−1.44881	+	2.50941i		0		1.02450	+	2.81964i		0
313.11		0		1.58128	−	0.706796i		0		−1.13939	−	1.97349i		0		1.72237	−	2.98324i		0		2.00088	−	2.23528i		0
625.1		0		−1.73199	+	0.0148978i		0		0.550001	−	0.952629i		0		−2.20940	−	3.82679i		0		2.99956	−	0.0516057i		0
625.2		0		−1.73144	−	0.0459606i		0		−1.66784	+	2.88878i		0		1.59859	+	2.76884i		0		2.99578	+	0.159156i		0
625.3		0		−1.06380	−	1.36687i		0		0.662426	−	1.14736i		0		0.798467	+	1.38299i		0		−0.736678	+	2.90814i		0
625.4		0		−0.722210	+	1.57430i		0		−1.89006	+	3.27368i		0		−0.659907	−	1.14299i		0		−1.95682	−	2.27395i		0
625.5		0		−0.377983	+	1.69030i		0		2.15452	−	3.73175i		0		−0.803576	−	1.39183i		0		−2.71426	−	1.27781i		0
625.6		0		−0.215114	−	1.71864i		0		−1.80041	+	3.11840i		0		−2.42567	−	4.20138i		0		−2.90745	+	0.739406i		0
625.7		0		0.400278	−	1.68516i		0		0.618351	−	1.07102i		0		2.31092	+	4.00263i		0		−2.67955	−	1.34907i		0
625.8		0		1.17494	+	1.27260i		0		0.279527	−	0.484154i		0		−0.154587	−	0.267752i		0		−0.239012	+	2.99046i		0
625.9		0		1.26749	−	1.18045i		0		1.53775	−	2.66347i		0		−0.728405	−	1.26163i		0		0.213067	−	2.99242i		0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
9.c	even	3	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	936.2.q.g	✓	22
3.b	odd	2	1		2808.2.q.g		22
9.c	even	3	1	inner	936.2.q.g	✓	22
9.c	even	3	1		8424.2.a.bf		11
9.d	odd	6	1		2808.2.q.g		22
9.d	odd	6	1		8424.2.a.be		11

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
936.2.q.g	✓	22	1.a	even	1	1	trivial
936.2.q.g	✓	22	9.c	even	3	1	inner
2808.2.q.g		22	3.b	odd	2	1
2808.2.q.g		22	9.d	odd	6	1
8424.2.a.be		11	9.d	odd	6	1
8424.2.a.bf		11	9.c	even	3	1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(936, [\chi])\):

T5^22 + 3*T5^21 + 44*T5^20 + 97*T5^19 + 1126*T5^18 + 2123*T5^17 + 17163*T5^16 + 19990*T5^15 + 165501*T5^14 + 112841*T5^13 + 1095150*T5^12 - 71273*T5^11 + 4412688*T5^10 - 2976478*T5^9 + 14794194*T5^8 - 13796366*T5^7 + 32270781*T5^6 - 32126176*T5^5 + 50860582*T5^4 - 41966672*T5^3 + 36428132*T5^2 - 14424864*T5 + 4946176

T7^22 + 4*T7^21 + 60*T7^20 + 180*T7^19 + 2056*T7^18 + 5711*T7^17 + 43148*T7^16 + 101916*T7^15 + 615233*T7^14 + 1386728*T7^13 + 5943773*T7^12 + 11956452*T7^11 + 39789928*T7^10 + 73850010*T7^9 + 171060160*T7^8 + 245376872*T7^7 + 422902265*T7^6 + 501273570*T7^5 + 663104392*T7^4 + 535106184*T7^3 + 397810720*T7^2 + 107806752*T7 + 23270976