Newform orbit 17.15.e.a

• Label: 17.15.e.a
• Level: $17$
• Weight: $15$
• Character orbit: 17.e
• Analytic conductor: $21.136$
• Analytic rank: $0$
• Dimension: $160$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 17 \)
Weight:	\( k \)	\(=\)	\( 15 \)
Character orbit:	\([\chi]\)	\(=\)	17.e (of order \(16\), degree \(8\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(21.1359245858\)
Analytic rank:	\(0\)
Dimension:	\(160\)
Relative dimension:	\(20\) over \(\Q(\zeta_{16})\)
Twist minimal:	yes
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.

\(\operatorname{Tr}(f)(q) = \) \( 160 q - 8 q^{2} - 8 q^{3} - 8 q^{4} - 8 q^{5} - 8 q^{6} - 8 q^{7} - 8 q^{8} - 8 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
3.1	−234.526	+	97.1438i	3672.13	+	730.432i	33980.2	−	33980.2i	49782.8	+	74505.3i	−932167.	+	185420.i	38727.2	−	57959.4i	−3.07667e6	+	7.42774e6i	8.53213e6	+	3.53413e6i	−1.89131e7	−	1.26373e7i
3.2	−215.425	+	89.2321i	−2134.35	−	424.549i	26860.4	−	26860.4i	−35101.6	−	52533.2i	497676.	−	98994.0i	798960.	−	1.19573e6i	−1.92763e6	+	4.65370e6i	−43674.0	−	18090.3i	1.22494e7	+	8.18480e6i
3.3	−183.655	+	76.0723i	−1388.00	−	276.090i	16356.9	−	16356.9i	40104.6	+	60020.8i	275916.	−	54883.0i	−363051.	+	543345.i	−513346.	+	1.23933e6i	−2.56857e6	−	1.06394e6i	−1.19313e7	−	7.97225e6i
3.4	−175.609	+	72.7398i	1545.27	+	307.373i	13962.4	−	13962.4i	−79884.5	−	119556.i	−293722.	+	58424.9i	−573365.	+	858102.i	−244535.	+	590360.i	−2.12551e6	−	880416.i	2.27249e7	+	1.51843e7i
3.5	−147.321	+	61.0224i	1223.44	+	243.357i	6394.52	−	6394.52i	5039.58	+	7542.27i	−195088.	+	38805.5i	60978.9	−	91261.4i	447952.	−	1.08145e6i	−2.98131e6	−	1.23490e6i	−1.20268e6	−	803608.i
3.6	−120.742	+	50.0132i	−4265.73	−	848.507i	492.195	−	492.195i	−31338.6	−	46901.5i	557492.	−	110892.i	−490968.	+	734786.i	784603.	−	1.89420e6i	1.30576e7	+	5.40864e6i	6.12959e6	+	4.09566e6i
3.7	−97.5050	+	40.3879i	2936.62	+	584.130i	−3709.19	+	3709.19i	1188.06	+	1778.06i	−309927.	+	61648.3i	436771.	−	653675.i	873574.	−	2.10899e6i	3.86364e6	+	1.60037e6i	−187654.	−	125387.i
3.8	−79.2906	+	32.8432i	−2010.46	−	399.905i	−6376.91	+	6376.91i	59402.9	+	88902.8i	172545.	−	34321.2i	391709.	−	586234.i	834295.	−	2.01417e6i	−536874.	−	222380.i	−7.62995e6	−	5.09817e6i
3.9	−40.1001	+	16.6100i	−1447.47	−	287.919i	−10253.1	+	10253.1i	−55768.5	−	83463.4i	62826.0	−	12496.9i	590430.	−	883641.i	512985.	−	1.23846e6i	−2.40662e6	−	996855.i	3.62265e6	+	2.42058e6i
3.10	−15.3498	+	6.35810i	2281.31	+	453.781i	−11390.0	+	11390.0i	73557.2	+	110086.i	−37902.9	+	7539.35i	−615585.	+	921288.i	206587.	−	498745.i	579576.	+	240068.i	−1.82903e6	−	1.22212e6i
3.11	−9.78643	+	4.05367i	−785.891	−	156.324i	−11505.9	+	11505.9i	−23400.9	−	35022.0i	8324.75	−	1655.90i	−527915.	+	790081.i	132376.	−	319584.i	−3.82570e6	−	1.58466e6i	370979.	+	247880.i
3.12	39.1174	−	16.2030i	3936.76	+	783.071i	−10317.6	+	10317.6i	−56234.4	−	84160.8i	166684.	−	33155.5i	−326420.	+	488522.i	−501892.	+	1.21167e6i	1.04660e7	+	4.33517e6i	−3.56340e6	−	2.38099e6i
3.13	70.2620	−	29.1035i	−3056.55	−	607.985i	−7495.50	+	7495.50i	43355.2	+	64885.6i	−232454.	+	46237.9i	63481.6	−	95006.9i	−785335.	+	1.89597e6i	4.55395e6	+	1.88631e6i	4.93462e6	+	3.29721e6i
3.14	87.6082	−	36.2885i	1264.81	+	251.587i	−5226.90	+	5226.90i	−23900.3	−	35769.3i	119938.	−	23857.1i	186723.	−	279451.i	−862794.	+	2.08297e6i	−2.88243e6	−	1.19394e6i	−3.39187e6	−	2.26638e6i
3.15	103.719	−	42.9620i	1409.73	+	280.413i	−2673.26	+	2673.26i	49652.7	+	74310.5i	158263.	−	31480.6i	748728.	−	1.12055e6i	−866309.	+	2.09146e6i	−2.51018e6	−	1.03975e6i	8.34248e6	+	5.57426e6i
3.16	145.986	−	60.4692i	−3175.99	−	631.744i	6070.02	−	6070.02i	−51778.6	−	77492.1i	−501850.	+	99824.1i	44253.0	−	66229.3i	−471641.	+	1.13864e6i	5.26893e6	+	2.18246e6i	−1.22448e7	−	8.18172e6i
3.17	168.435	−	69.7680i	−516.074	−	102.654i	11917.5	−	11917.5i	22332.4	+	33422.7i	−94086.7	+	18715.0i	−716339.	+	1.07208e6i	32779.2	−	79135.9i	−4.16309e6	−	1.72441e6i	6.09338e6	+	4.07147e6i
3.18	191.681	−	79.3970i	3478.09	+	691.836i	18852.6	−	18852.6i	25743.6	+	38527.9i	721616.	−	143538.i	−138515.	+	207302.i	816015.	−	1.97003e6i	7.19962e6	+	2.98218e6i	7.99357e6	+	5.34113e6i
3.19	201.744	−	83.5651i	988.215	+	196.568i	22132.3	−	22132.3i	−73096.1	−	109396.i	215793.	−	42923.9i	206918.	−	309675.i	1.24644e6	−	3.00917e6i	−3.48096e6	−	1.44186e6i	−2.38884e7	−	1.59617e7i
3.20	225.431	−	93.3766i	−2134.35	−	424.549i	30514.8	−	30514.8i	44900.9	+	67199.0i	−520793.	+	103592.i	527765.	−	789856.i	2.49973e6	−	6.03487e6i	−43666.2	−	18087.1i	1.63969e7	+	1.09560e7i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
17.e	odd	16	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	17.15.e.a	✓	160
17.e	odd	16	1	inner	17.15.e.a	✓	160

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
17.15.e.a	✓	160	1.a	even	1	1	trivial
17.15.e.a	✓	160	17.e	odd	16	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{15}^{\mathrm{new}}(17, [\chi])\).