Newform orbit 17.12.c.a

• Label: 17.12.c.a
• Level: $17$
• Weight: $12$
• Character orbit: 17.c
• Analytic conductor: $13.062$
• Analytic rank: $0$
• Dimension: $32$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 17 \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	17.c (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(13.0618340695\)
Analytic rank:	\(0\)
Dimension:	\(32\)
Relative dimension:	\(16\) over \(\Q(i)\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 32 q - 528 q^{3} - 32772 q^{4} - 15496 q^{5} + 39058 q^{6} - 38368 q^{7}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
4.1		−	85.4879i	62.9008	−	62.9008i	−5260.19			−835.746	+	835.746i	−5377.26	−	5377.26i	−4912.00	−	4912.00i			274603.i			169234.i	71446.2	+	71446.2i
4.2		−	66.0051i	−572.909	+	572.909i	−2308.67			−7460.40	+	7460.40i	37814.9	+	37814.9i	−24652.1	−	24652.1i			17205.8i		−	479304.i	492425.	+	492425.i
4.3		−	58.9332i	500.660	−	500.660i	−1425.12			2487.06	−	2487.06i	−29505.5	−	29505.5i	−731.266	−	731.266i		−	36708.3i		−	324174.i	−146570.	−	146570.i
4.4		−	58.2592i	−297.283	+	297.283i	−1346.14			8591.36	−	8591.36i	17319.5	+	17319.5i	−6474.40	−	6474.40i		−	40889.9i			393.067i	−500526.	−	500526.i
4.5		−	48.9428i	−20.4617	+	20.4617i	−347.397			−2628.43	+	2628.43i	1001.45	+	1001.45i	46739.6	+	46739.6i		−	83232.3i			176310.i	128643.	+	128643.i
4.6		−	32.2416i	149.760	−	149.760i	1008.48			−6170.50	+	6170.50i	−4828.50	−	4828.50i	−42929.1	−	42929.1i		−	98545.8i			132291.i	198947.	+	198947.i
4.7		−	5.06273i	−258.651	+	258.651i	2022.37			2155.39	−	2155.39i	1309.48	+	1309.48i	−31309.1	−	31309.1i		−	20607.2i			43346.3i	−10912.2	−	10912.2i
4.8			3.27628i	288.856	−	288.856i	2037.27			5645.17	−	5645.17i	946.373	+	946.373i	−182.666	−	182.666i			13384.5i			10271.8i	18495.2	+	18495.2i
4.9			4.94429i	−400.826	+	400.826i	2023.55			−1207.06	+	1207.06i	−1981.80	−	1981.80i	50168.6	+	50168.6i			20130.9i		−	144177.i	−5968.07	−	5968.07i
4.10			21.1462i	485.546	−	485.546i	1600.84			−8779.09	+	8779.09i	10267.5	+	10267.5i	43052.7	+	43052.7i			77159.1i		−	294363.i	−185644.	−	185644.i
4.11			44.2190i	−276.864	+	276.864i	92.6798			−5753.13	+	5753.13i	−12242.6	−	12242.6i	−23295.1	−	23295.1i			94658.7i			23839.8i	−254398.	−	254398.i
4.12			49.5175i	136.167	−	136.167i	−403.984			−1140.26	+	1140.26i	6742.65	+	6742.65i	−14036.7	−	14036.7i			81407.6i			140064.i	−56462.7	−	56462.7i
4.13			63.2626i	72.6870	−	72.6870i	−1954.16			5432.90	−	5432.90i	4598.37	+	4598.37i	37054.9	+	37054.9i			5936.57i			166580.i	343700.	+	343700.i
4.14			66.7457i	−522.898	+	522.898i	−2406.98			7524.98	−	7524.98i	−34901.2	−	34901.2i	−23035.1	−	23035.1i		−	23960.6i		−	369698.i	502260.	+	502260.i
4.15			77.1558i	534.614	−	534.614i	−3905.01			775.823	−	775.823i	41248.6	+	41248.6i	−52299.8	−	52299.8i		−	143279.i		−	394478.i	59859.2	+	59859.2i
4.16			88.6653i	−145.298	+	145.298i	−5813.53			−6386.08	+	6386.08i	−12882.9	−	12882.9i	27657.5	+	27657.5i		−	333872.i			134924.i	−566224.	−	566224.i
13.1		−	88.6653i	−145.298	−	145.298i	−5813.53			−6386.08	−	6386.08i	−12882.9	+	12882.9i	27657.5	−	27657.5i			333872.i		−	134924.i	−566224.	+	566224.i
13.2		−	77.1558i	534.614	+	534.614i	−3905.01			775.823	+	775.823i	41248.6	−	41248.6i	−52299.8	+	52299.8i			143279.i			394478.i	59859.2	−	59859.2i
13.3		−	66.7457i	−522.898	−	522.898i	−2406.98			7524.98	+	7524.98i	−34901.2	+	34901.2i	−23035.1	+	23035.1i			23960.6i			369698.i	502260.	−	502260.i
13.4		−	63.2626i	72.6870	+	72.6870i	−1954.16			5432.90	+	5432.90i	4598.37	−	4598.37i	37054.9	−	37054.9i		−	5936.57i		−	166580.i	343700.	−	343700.i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
17.c	even	4	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	17.12.c.a	✓	32
17.c	even	4	1	inner	17.12.c.a	✓	32

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
17.12.c.a	✓	32	1.a	even	1	1	trivial
17.12.c.a	✓	32	17.c	even	4	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{12}^{\mathrm{new}}(17, [\chi])\).