Newform orbit 29.15.c.a

• Label: 29.15.c.a
• Level: $29$
• Weight: $15$
• Character orbit: 29.c
• Analytic conductor: $36.055$
• Analytic rank: $0$
• Dimension: $68$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 29 \)
Weight:	\( k \)	\(=\)	\( 15 \)
Character orbit:	\([\chi]\)	\(=\)	29.c (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(36.0554007641\)
Analytic rank:	\(0\)
Dimension:	\(68\)
Relative dimension:	\(34\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 68 q - 312 q^{2} - 2 q^{3} - 4 q^{7} - 689310 q^{8}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
12.1	−168.771	−	168.771i	−2665.63	−	2665.63i			40583.2i		−	37437.0i			899760.i	644600.			4.08412e6	−	4.08412e6i			9.42815e6i	−6.31827e6	+	6.31827e6i
12.2	−168.212	−	168.212i	1372.65	+	1372.65i			40206.7i		−	110532.i		−	461791.i	806243.			4.00726e6	−	4.00726e6i		−	1.01466e6i	−1.85928e7	+	1.85928e7i
12.3	−165.801	−	165.801i	−544.841	−	544.841i			38595.9i			15745.6i			180670.i	−1.09500e6			3.68274e6	−	3.68274e6i		−	4.18927e6i	2.61063e6	−	2.61063e6i
12.4	−157.774	−	157.774i	3020.51	+	3020.51i			33401.0i			76455.0i		−	953113.i	−1.19070e6			2.68483e6	−	2.68483e6i			1.34640e7i	1.20626e7	−	1.20626e7i
12.5	−152.203	−	152.203i	−362.559	−	362.559i			29947.3i			149475.i			110365.i	876221.			2.06437e6	−	2.06437e6i		−	4.52007e6i	2.27505e7	−	2.27505e7i
12.6	−126.672	−	126.672i	1067.39	+	1067.39i			15707.8i		−	7103.16i		−	270419.i	−354580.			−85651.6	+	85651.6i		−	2.50431e6i	−899774.	+	899774.i
12.7	−120.665	−	120.665i	−1296.13	−	1296.13i			12736.1i		−	36154.9i			312796.i	−444023.			−440176.	+	440176.i		−	1.42305e6i	−4.36263e6	+	4.36263e6i
12.8	−118.027	−	118.027i	1825.31	+	1825.31i			11476.7i			35591.1i		−	430872.i	1.00122e6			−579197.	+	579197.i			1.88056e6i	4.20070e6	−	4.20070e6i
12.9	−99.0246	−	99.0246i	−2875.09	−	2875.09i			3227.73i			105139.i			569409.i	−619848.			−1.30279e6	+	1.30279e6i			1.17493e7i	1.04113e7	−	1.04113e7i
12.10	−94.2182	−	94.2182i	−1537.46	−	1537.46i			1370.15i		−	119266.i			289713.i	1.40104e6			−1.41458e6	+	1.41458e6i		−	55424.1i	−1.12371e7	+	1.12371e7i
12.11	−84.8508	−	84.8508i	1293.97	+	1293.97i		−	1984.68i		−	144289.i		−	219589.i	−1.06721e6			−1.55860e6	+	1.55860e6i		−	1.43426e6i	−1.22430e7	+	1.22430e7i
12.12	−59.1433	−	59.1433i	−1441.85	−	1441.85i		−	9388.15i			74847.5i			170552.i	888867.			−1.52425e6	+	1.52425e6i		−	625088.i	4.42672e6	−	4.42672e6i
12.13	−55.9098	−	55.9098i	1465.84	+	1465.84i		−	10132.2i			40470.7i		−	163909.i	363644.			−1.48251e6	+	1.48251e6i		−	485606.i	2.26271e6	−	2.26271e6i
12.14	−50.6787	−	50.6787i	910.227	+	910.227i		−	11247.3i			127648.i		−	92258.2i	−1.54934e6			−1.40032e6	+	1.40032e6i		−	3.12594e6i	6.46904e6	−	6.46904e6i
12.15	−48.4316	−	48.4316i	2910.35	+	2910.35i		−	11692.8i		−	56568.4i		−	281906.i	166969.			−1.35980e6	+	1.35980e6i			1.21573e7i	−2.73969e6	+	2.73969e6i
12.16	−34.5470	−	34.5470i	−634.913	−	634.913i		−	13997.0i			29356.7i			43868.6i	160670.			−1.04957e6	+	1.04957e6i		−	3.97674e6i	1.01419e6	−	1.01419e6i
12.17	−26.8284	−	26.8284i	−2568.33	−	2568.33i		−	14944.5i		−	116825.i			137808.i	−1.09289e6			−840493.	+	840493.i			8.40968e6i	−3.13424e6	+	3.13424e6i
12.18	12.2697	+	12.2697i	−17.2708	−	17.2708i		−	16082.9i		−	67606.8i		−	423.814i	−248594.			398359.	−	398359.i		−	4.78237e6i	829515.	−	829515.i
12.19	13.7439	+	13.7439i	888.946	+	888.946i		−	16006.2i		−	102078.i			24435.1i	1.24811e6			445167.	−	445167.i		−	3.20252e6i	1.40294e6	−	1.40294e6i
12.20	18.0493	+	18.0493i	−1757.84	−	1757.84i		−	15732.4i			22055.5i		−	63455.4i	−823925.			579679.	−	579679.i			1.39700e6i	−398086.	+	398086.i

Inner twists

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

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	29.15.c.a	✓	68
29.c	odd	4	1	inner	29.15.c.a	✓	68

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
29.15.c.a	✓	68	1.a	even	1	1	trivial
29.15.c.a	✓	68	29.c	odd	4	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{15}^{\mathrm{new}}(29, [\chi])\).