Newform orbit 17.14.c.a

• Label: 17.14.c.a
• Level: $17$
• Weight: $14$
• Character orbit: 17.c
• Analytic conductor: $18.229$
• Analytic rank: $0$
• Dimension: $36$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 17 \)
Weight:	\( k \)	\(=\)	\( 14 \)
Character orbit:	\([\chi]\)	\(=\)	17.c (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(18.2292579218\)
Analytic rank:	\(0\)
Dimension:	\(36\)
Relative dimension:	\(18\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 36 q - 264 q^{3} - 131076 q^{4} + 73220 q^{5} + 330802 q^{6} + 5040 q^{7}+O(q^{10}) \)

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		−	168.321i	−1344.08	+	1344.08i	−20140.1			21623.8	−	21623.8i	226238.	+	226238.i	226230.	+	226230.i			2.01113e6i		−	2.01880e6i	−3.63975e6	−	3.63975e6i
4.2		−	151.391i	−84.0710	+	84.0710i	−14727.1			−15077.8	+	15077.8i	12727.6	+	12727.6i	−419260.	−	419260.i			989353.i			1.58019e6i	2.28263e6	+	2.28263e6i
4.3		−	145.499i	942.870	−	942.870i	−12977.9			−36674.2	+	36674.2i	−137186.	−	137186.i	346991.	+	346991.i			696342.i		−	183683.i	5.33606e6	+	5.33606e6i
4.4		−	145.462i	978.878	−	978.878i	−12967.1			33465.2	−	33465.2i	−142389.	−	142389.i	10706.6	+	10706.6i			694599.i		−	322083.i	−4.86791e6	−	4.86791e6i
4.5		−	103.597i	−912.538	+	912.538i	−2540.27			−25852.7	+	25852.7i	94535.9	+	94535.9i	180354.	+	180354.i		−	585501.i		−	71127.3i	2.67826e6	+	2.67826e6i
4.6		−	86.1209i	−739.906	+	739.906i	775.189			5992.96	−	5992.96i	63721.4	+	63721.4i	−127456.	−	127456.i		−	772262.i			499401.i	−516119.	−	516119.i
4.7		−	56.9880i	1368.01	−	1368.01i	4944.37			−11471.9	+	11471.9i	−77960.1	−	77960.1i	−184718.	−	184718.i		−	748615.i		−	2.14857e6i	653763.	+	653763.i
4.8		−	55.6078i	213.027	−	213.027i	5099.78			34071.1	−	34071.1i	−11845.9	−	11845.9i	168398.	+	168398.i		−	739126.i			1.50356e6i	−1.89462e6	−	1.89462e6i
4.9		−	6.32594i	−1753.22	+	1753.22i	8151.98			18771.6	−	18771.6i	11090.7	+	11090.7i	−41446.6	−	41446.6i		−	103391.i		−	4.55322e6i	−118748.	−	118748.i
4.10			7.99084i	443.858	−	443.858i	8128.15			−15319.7	+	15319.7i	3546.80	+	3546.80i	175886.	+	175886.i			130412.i			1.20030e6i	−122417.	−	122417.i
4.11			21.2195i	−899.415	+	899.415i	7741.73			−49058.6	+	49058.6i	−19085.2	−	19085.2i	−123164.	−	123164.i			338106.i		−	23571.1i	−1.04100e6	−	1.04100e6i
4.12			51.7604i	−206.794	+	206.794i	5512.87			32627.4	−	32627.4i	−10703.7	−	10703.7i	−417738.	−	417738.i			709369.i			1.50880e6i	1.68881e6	+	1.68881e6i
4.13			74.5417i	1722.79	−	1722.79i	2635.53			35079.6	−	35079.6i	128420.	+	128420.i	205551.	+	205551.i			807103.i		−	4.34171e6i	2.61489e6	+	2.61489e6i
4.14			88.1622i	−743.250	+	743.250i	419.429			13478.5	−	13478.5i	−65526.5	−	65526.5i	301054.	+	301054.i			759202.i			489482.i	1.18830e6	+	1.18830e6i
4.15			89.7930i	833.087	−	833.087i	129.221			−10536.6	+	10536.6i	74805.4	+	74805.4i	−253522.	−	253522.i			747187.i			206255.i	−946117.	−	946117.i
4.16			143.905i	856.012	−	856.012i	−12516.7			−25460.6	+	25460.6i	123184.	+	123184.i	109059.	+	109059.i		−	622339.i			128811.i	−3.66391e6	−	3.66391e6i
4.17			144.477i	−1145.78	+	1145.78i	−12681.6			−11825.8	+	11825.8i	−165539.	−	165539.i	−101313.	−	101313.i		−	648643.i		−	1.03131e6i	−1.70856e6	−	1.70856e6i
4.18			169.462i	338.523	−	338.523i	−20525.5			42778.0	−	42778.0i	57367.0	+	57367.0i	−53092.6	−	53092.6i		−	2.09006e6i			1.36513e6i	7.24925e6	+	7.24925e6i
13.1		−	169.462i	338.523	+	338.523i	−20525.5			42778.0	+	42778.0i	57367.0	−	57367.0i	−53092.6	+	53092.6i			2.09006e6i		−	1.36513e6i	7.24925e6	−	7.24925e6i
13.2		−	144.477i	−1145.78	−	1145.78i	−12681.6			−11825.8	−	11825.8i	−165539.	+	165539.i	−101313.	+	101313.i			648643.i			1.03131e6i	−1.70856e6	+	1.70856e6i

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	17.14.c.a	✓	36
17.c	even	4	1	inner	17.14.c.a	✓	36

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
17.14.c.a	✓	36	1.a	even	1	1	trivial
17.14.c.a	✓	36	17.c	even	4	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{14}^{\mathrm{new}}(17, [\chi])\).