Newform orbit 17.17.e.a

• Label: 17.17.e.a
• Level: $17$
• Weight: $17$
• Character orbit: 17.e
• Analytic conductor: $27.595$
• Analytic rank: $0$
• Dimension: $184$
• CM: no
• Inner twists: $2$

Newspace parameters

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

Newform invariants

Self dual:	no
Analytic conductor:	\(27.5951724556\)
Analytic rank:	\(0\)
Dimension:	\(184\)
Relative dimension:	\(23\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 184 q - 8 q^{2} - 8 q^{3} - 8 q^{4} - 8 q^{5} - 8 q^{6} - 8 q^{7} - 8 q^{8} - 8 q^{9}+O(q^{10}) \)

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	−443.952	+	183.891i	859.944	+	171.053i	116937.	−	116937.i	−112015.	−	167642.i	−413229.	+	82196.4i	−2.65123e6	+	3.96785e6i	−1.83592e7	+	4.43230e7i	−3.90597e7	−	1.61791e7i	8.05570e7	+	5.38264e7i
3.2	−418.351	+	173.287i	−11532.1	−	2293.88i	98648.2	−	98648.2i	404359.	+	605167.i	5.22198e6	−	1.03872e6i	939047.	−	1.40538e6i	−1.28186e7	+	3.09469e7i	8.79582e7	+	3.64335e7i	−2.74031e8	−	1.83102e8i
3.3	−365.158	+	151.253i	4260.08	+	847.383i	64121.7	−	64121.7i	67877.5	+	101586.i	−1.68377e6	+	334923.i	6.14618e6	−	9.19841e6i	−3.80339e6	+	9.18220e6i	−2.23398e7	−	9.25343e6i	−4.01512e7	−	2.68282e7i
3.4	−330.665	+	136.966i	11976.8	+	2382.34i	44238.5	−	44238.5i	−168651.	−	252404.i	−4.28661e6	+	852661.i	−360277.	+	539193.i	407249.	−	983186.i	9.79991e7	+	4.05926e7i	9.03375e7	+	6.03616e7i
3.5	−324.713	+	134.500i	5311.23	+	1056.47i	41007.0	−	41007.0i	372010.	+	556752.i	−1.86672e6	+	371314.i	−3.21608e6	+	4.81320e6i	1.01458e6	−	2.44942e6i	−1.26769e7	−	5.25096e6i	−1.95680e8	−	1.30749e8i
3.6	−319.538	+	132.357i	−7220.97	−	1436.34i	38245.0	−	38245.0i	−213767.	−	319924.i	2.49748e6	−	496780.i	389865.	−	583474.i	1.51541e6	−	3.65852e6i	1.03093e7	+	4.27027e6i	1.10651e8	+	7.39344e7i
3.7	−196.493	+	81.3901i	−5629.38	−	1119.75i	−14355.7	+	14355.7i	39139.7	+	58576.7i	1.19727e6	−	238152.i	−2.51874e6	+	3.76955e6i	6.98637e6	−	1.68666e7i	−9.33386e6	−	3.86621e6i	−1.24583e7	−	8.32434e6i
3.8	−142.219	+	58.9091i	−1556.36	−	309.579i	−29584.9	+	29584.9i	260708.	+	390178.i	239581.	−	47655.6i	3.92566e6	−	5.87516e6i	6.32539e6	−	1.52708e7i	−3.74436e7	−	1.55096e7i	−6.00628e7	−	4.01327e7i
3.9	−136.273	+	56.4462i	6162.63	+	1225.82i	−30956.7	+	30956.7i	−9976.99	−	14931.6i	−908994.	+	180810.i	−3.70753e6	+	5.54871e6i	6.17044e6	−	1.48968e7i	−3.29467e6	−	1.36470e6i	2.20243e6	+	1.47162e6i
3.10	−119.132	+	49.3460i	3858.98	+	767.599i	−34583.6	+	34583.6i	−405316.	−	606599.i	−497605.	+	98979.8i	2.09338e6	−	3.13297e6i	5.64738e6	−	1.36340e7i	−2.54675e7	−	1.05490e7i	7.82192e7	+	5.22644e7i
3.11	7.52053	−	3.11510i	−12024.4	−	2391.79i	−46294.1	+	46294.1i	−103887.	−	155478.i	−97880.2	+	19469.6i	5.78145e6	−	8.65255e6i	−408097.	+	985232.i	9.90945e7	+	4.10463e7i	−1.26562e6	−	845660.i
3.12	16.6017	−	6.87665i	−8722.32	−	1734.98i	−46112.6	+	46112.6i	197877.	+	296143.i	−156736.	+	31176.8i	−3.64850e6	+	5.46037e6i	−899116.	+	2.17066e6i	3.32988e7	+	1.37928e7i	5.32157e6	+	3.55576e6i
3.13	22.9044	−	9.48730i	12113.5	+	2409.53i	−45906.3	+	45906.3i	303093.	+	453611.i	300313.	−	59735.9i	3.59130e6	−	5.37476e6i	−1.23769e6	+	2.98805e6i	1.01162e8	+	4.19025e7i	1.12457e7	+	7.51413e6i
3.14	75.0514	−	31.0873i	6386.08	+	1270.27i	−41674.7	+	41674.7i	−31852.5	−	47670.6i	518773.	−	103190.i	−170603.	+	255326.i	−3.86953e6	+	9.34186e6i	−601570.	−	249178.i	−3.87252e6	−	2.58754e6i
3.15	132.007	−	54.6792i	−1128.77	−	224.527i	−31904.8	+	31904.8i	−17061.2	−	25533.9i	−161283.	+	32081.2i	2.04706e6	−	3.06365e6i	−6.05060e6	+	1.46074e7i	−3.85463e7	−	1.59664e7i	−3.64838e6	−	2.43777e6i
3.16	140.600	−	58.2385i	−6905.20	−	1373.53i	−29964.3	+	29964.3i	−417571.	−	624939.i	−1.05087e6	+	209030.i	−5.26871e6	+	7.88518e6i	−6.28463e6	+	1.51724e7i	6.02525e6	+	2.49574e6i	−9.51060e7	−	6.35478e7i
3.17	228.888	−	94.8085i	−1921.32	−	382.173i	−2939.93	+	2939.93i	423244.	+	633429.i	−475999.	+	94682.1i	−1.32259e6	+	1.97939e6i	−6.60755e6	+	1.59520e7i	−3.62246e7	−	1.50047e7i	1.56930e8	+	1.04857e8i
3.18	281.590	−	116.639i	7425.48	+	1477.02i	19347.6	−	19347.6i	11331.0	+	16958.0i	2.26322e6	−	450183.i	−5.28715e6	+	7.91277e6i	−4.45260e6	+	1.07495e7i	1.31862e7	+	5.46190e6i	5.16866e6	+	3.45359e6i
3.19	315.627	−	130.737i	10262.4	+	2041.32i	36187.4	−	36187.4i	−330291.	−	494315.i	3.50597e6	−	697381.i	3.29701e6	−	4.93433e6i	−1.87730e6	+	4.53220e6i	6.13801e7	+	2.54245e7i	−1.68874e8	−	1.12838e8i
3.20	333.463	−	138.125i	−3669.48	−	729.904i	45778.1	−	45778.1i	−144636.	−	216463.i	−1.32445e6	+	263450.i	2.86237e6	−	4.28384e6i	−109946.	+	265434.i	−2.68377e7	−	1.11165e7i	−7.81295e7	−	5.22045e7i

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	17.17.e.a	✓	184
17.e	odd	16	1	inner	17.17.e.a	✓	184

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
17.17.e.a	✓	184	1.a	even	1	1	trivial
17.17.e.a	✓	184	17.e	odd	16	1	inner

Hecke kernels

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