Newform orbit 11.17.d.a

• Label: 11.17.d.a
• Level: $11$
• Weight: $17$
• Character orbit: 11.d
• Analytic conductor: $17.856$
• Analytic rank: $0$
• Dimension: $60$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 11 \)
Weight:	\( k \)	\(=\)	\( 17 \)
Character orbit:	\([\chi]\)	\(=\)	11.d (of order \(10\), degree \(4\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(17.8556998242\)
Analytic rank:	\(0\)
Dimension:	\(60\)
Relative dimension:	\(15\) over \(\Q(\zeta_{10})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 60 q - 5 q^{2} - 150 q^{3} + 542263 q^{4} - 7938 q^{5} - 2437125 q^{6} + 2885320 q^{7} + 30474235 q^{8} - 295234379 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
2.1	−416.677	−	135.386i	−4354.61	+	3163.81i	102270.	+	74303.7i	161336.	+	496541.i	2.24280e6	−	728730.i	1.02203e6	−	1.40670e6i	−1.56771e7	−	2.15776e7i	−4.34923e6	+	1.33856e7i		−	2.28740e8i
2.2	−414.369	−	134.637i	−1454.53	+	1056.78i	100555.	+	73057.2i	−204212.	−	628501.i	744994.	−	242063.i	−2.19314e6	+	3.01860e6i	−1.50472e7	−	2.07106e7i	−1.23033e7	+	3.78656e7i			2.87925e8i
2.3	−372.043	−	120.884i	8674.18	−	6302.16i	70783.1	+	51426.9i	30786.3	+	94750.4i	−3.98900e6	+	1.29610e6i	−2.24714e6	+	3.09293e6i	−5.04862e6	−	6.94883e6i	2.22220e7	−	6.83923e7i		−	3.89728e7i
2.4	−264.283	−	85.8708i	3023.54	−	2196.73i	9452.05	+	6867.32i	8272.56	+	25460.3i	−987707.	+	320926.i	4.84071e6	−	6.66267e6i	8.79607e6	+	1.21068e7i	−8.98598e6	+	2.76560e7i		−	7.43910e6i
2.5	−198.796	−	64.5929i	−8687.56	+	6311.88i	−17672.0	−	12839.4i	−96796.0	−	297907.i	2.13476e6	−	693625.i	4.08512e6	−	5.62269e6i	1.07357e7	+	1.47765e7i	2.23316e7	−	6.87297e7i			6.54753e7i
2.6	−163.957	−	53.2730i	−5585.28	+	4057.94i	−28975.8	−	21052.1i	80728.1	+	248456.i	1.13193e6	−	367785.i	−5.85897e6	+	8.06418e6i	1.02701e7	+	1.41356e7i	1.42627e6	−	4.38960e6i		−	4.50367e7i
2.7	−83.1115	−	27.0046i	4562.36	−	3314.75i	−46841.5	−	34032.3i	74193.1	+	228343.i	−468697.	+	152289.i	−1.88513e6	+	2.59466e6i	6.34034e6	+	8.72673e6i	−3.47462e6	+	1.06938e7i		−	2.09815e7i
2.8	−23.6019	−	7.66872i	2551.27	−	1853.60i	−52521.5	−	38159.1i	−201392.	−	619822.i	−74429.5	+	24183.6i	−468461.	+	644782.i	1.90294e6	+	2.61917e6i	−1.02291e7	+	3.14818e7i			1.61734e7i
2.9	124.121	+	40.3292i	−708.727	+	514.920i	−39240.3	−	28509.7i	205335.	+	631958.i	−108734.	+	35329.8i	4.31668e6	−	5.94140e6i	−8.74806e6	−	1.20407e7i	−1.30650e7	+	4.02100e7i			8.67199e7i
2.10	170.180	+	55.2949i	−6373.56	+	4630.66i	−27115.9	−	19700.9i	−25526.2	−	78561.7i	−1.34071e6	+	435622.i	578887.	−	796769.i	−1.04181e7	−	1.43393e7i	5.87704e6	−	1.80877e7i		−	1.47811e7i
2.11	180.242	+	58.5642i	9593.26	−	6969.91i	−23962.3	−	17409.6i	−34987.5	−	107681.i	2.13730e6	−	694450.i	902823.	−	1.24263e6i	−1.05999e7	−	1.45895e7i	3.01488e7	−	9.27884e7i		−	2.14576e7i
2.12	320.322	+	104.079i	−1491.53	+	1083.66i	38753.8	+	28156.3i	−114094.	−	351146.i	−590556.	+	191883.i	−3.13803e6	+	4.31913e6i	−3.49092e6	−	4.80484e6i	−1.22518e7	+	3.77072e7i		−	1.24355e8i
2.13	362.431	+	117.761i	4601.75	−	3343.37i	64469.0	+	46839.4i	167642.	+	515950.i	2.06154e6	−	669834.i	−5.21599e6	+	7.17920e6i	3.16998e6	+	4.36310e6i	−3.30415e6	+	1.01691e7i			2.06738e8i
2.14	425.330	+	138.198i	3272.46	−	2377.58i	108787.	+	79038.3i	−77718.2	−	239192.i	1.72045e6	−	559008.i	5.83265e6	−	8.02795e6i	1.81200e7	+	2.49401e7i	−8.24608e6	+	2.53788e7i		−	1.12476e8i
2.15	456.381	+	148.287i	−9871.99	+	7172.42i	133275.	+	96829.8i	119033.	+	366346.i	−5.56897e6	+	1.80947e6i	255853.	−	352152.i	2.79804e7	+	3.85118e7i	3.27104e7	−	1.00672e8i			1.84844e8i
6.1	−416.677	+	135.386i	−4354.61	−	3163.81i	102270.	−	74303.7i	161336.	−	496541.i	2.24280e6	+	728730.i	1.02203e6	+	1.40670e6i	−1.56771e7	+	2.15776e7i	−4.34923e6	−	1.33856e7i			2.28740e8i
6.2	−414.369	+	134.637i	−1454.53	−	1056.78i	100555.	−	73057.2i	−204212.	+	628501.i	744994.	+	242063.i	−2.19314e6	−	3.01860e6i	−1.50472e7	+	2.07106e7i	−1.23033e7	−	3.78656e7i		−	2.87925e8i
6.3	−372.043	+	120.884i	8674.18	+	6302.16i	70783.1	−	51426.9i	30786.3	−	94750.4i	−3.98900e6	−	1.29610e6i	−2.24714e6	−	3.09293e6i	−5.04862e6	+	6.94883e6i	2.22220e7	+	6.83923e7i			3.89728e7i
6.4	−264.283	+	85.8708i	3023.54	+	2196.73i	9452.05	−	6867.32i	8272.56	−	25460.3i	−987707.	−	320926.i	4.84071e6	+	6.66267e6i	8.79607e6	−	1.21068e7i	−8.98598e6	−	2.76560e7i			7.43910e6i
6.5	−198.796	+	64.5929i	−8687.56	−	6311.88i	−17672.0	+	12839.4i	−96796.0	+	297907.i	2.13476e6	+	693625.i	4.08512e6	+	5.62269e6i	1.07357e7	−	1.47765e7i	2.23316e7	+	6.87297e7i		−	6.54753e7i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
11.d	odd	10	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	11.17.d.a	✓	60
11.d	odd	10	1	inner	11.17.d.a	✓	60

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
11.17.d.a	✓	60	1.a	even	1	1	trivial
11.17.d.a	✓	60	11.d	odd	10	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{17}^{\mathrm{new}}(11, [\chi])\).