Properties

Label 201.5.b.a
Level 201
Weight 5
Character orbit 201.b
Analytic conductor 20.777
Analytic rank 0
Dimension 46
CM No

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Newspace parameters

Level: \( N \) = \( 201 = 3 \cdot 67 \)
Weight: \( k \) = \( 5 \)
Character orbit: \([\chi]\) = 201.b (of order \(2\) and degree \(1\))

Newform invariants

Self dual: No
Analytic conductor: \(20.7773625799\)
Analytic rank: \(0\)
Dimension: \(46\)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 46q - 396q^{4} - 1242q^{9} + O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \( 46q - 396q^{4} - 1242q^{9} + 396q^{10} + 792q^{14} - 252q^{15} + 3396q^{16} + 462q^{17} - 590q^{19} - 936q^{21} + 3184q^{22} - 1446q^{23} - 1404q^{24} - 6278q^{25} + 2700q^{26} - 1014q^{29} + 540q^{33} + 9924q^{35} + 10692q^{36} - 386q^{37} + 4968q^{39} - 9988q^{40} - 2754q^{47} - 19062q^{49} - 2320q^{55} - 3396q^{56} - 7098q^{59} + 72q^{60} - 21180q^{62} - 75644q^{64} + 18396q^{65} + 8574q^{67} + 9084q^{68} - 23040q^{71} - 22338q^{73} + 28016q^{76} + 45084q^{77} + 33534q^{81} + 17564q^{82} + 35856q^{83} + 40176q^{84} + 31764q^{86} - 19448q^{88} - 14538q^{89} - 10692q^{90} + 13792q^{91} - 67692q^{92} + 22464q^{93} + 22464q^{96} + O(q^{100}) \)

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 \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
133.1 7.92273i 5.19615i −46.7696 21.6231i 41.1677 44.7619i 243.779i −27.0000 −171.314
133.2 7.58193i 5.19615i −41.4857 47.0403i 39.3969 16.7186i 193.231i −27.0000 356.657
133.3 7.56976i 5.19615i −41.3013 14.1982i −39.3336 91.6507i 191.525i −27.0000 107.477
133.4 7.50857i 5.19615i −40.3787 11.1565i −39.0157 57.6520i 183.049i −27.0000 83.7695
133.5 6.42716i 5.19615i −25.3083 17.3951i 33.3965 16.4564i 59.8260i −27.0000 −111.801
133.6 6.38763i 5.19615i −24.8019 26.0927i −33.1911 27.5510i 56.2231i −27.0000 −166.670
133.7 5.76041i 5.19615i −17.1823 16.3188i 29.9320 86.3035i 6.81074i −27.0000 −94.0028
133.8 5.58118i 5.19615i −15.1496 19.0393i 29.0007 39.7168i 4.74646i −27.0000 106.262
133.9 5.56808i 5.19615i −15.0035 37.5105i −28.9326 91.3831i 5.54876i −27.0000 −208.861
133.10 5.06350i 5.19615i −9.63908 45.6253i −26.3107 49.9699i 32.2086i −27.0000 231.024
133.11 5.02761i 5.19615i −9.27688 18.9854i 26.1242 67.2401i 33.8013i −27.0000 95.4513
133.12 4.92431i 5.19615i −8.24886 24.9820i −25.5875 17.9795i 38.1691i −27.0000 123.019
133.13 4.05388i 5.19615i −0.433982 2.19375i −21.0646 19.8533i 63.1028i −27.0000 8.89321
133.14 4.01365i 5.19615i −0.109374 45.0940i 20.8555 18.6226i 63.7794i −27.0000 −180.991
133.15 3.88997i 5.19615i 0.868144 32.6108i −20.2129 59.7846i 65.6166i −27.0000 −126.855
133.16 3.33762i 5.19615i 4.86032 44.8464i 17.3428 17.0019i 69.6237i −27.0000 149.680
133.17 2.53609i 5.19615i 9.56827 8.16007i 13.1779 69.7059i 64.8433i −27.0000 −20.6946
133.18 2.40473i 5.19615i 10.2173 10.5361i −12.4953 65.1996i 63.0455i −27.0000 25.3364
133.19 2.12514i 5.19615i 11.4838 15.4974i 11.0426 14.1489i 58.4069i −27.0000 32.9341
133.20 1.39569i 5.19615i 14.0521 17.8182i −7.25221 70.8079i 41.9433i −27.0000 −24.8687
See all 46 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 133.46
Significant digits:
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Inner twists

This newform does not have CM; other inner twists have not been computed.

Hecke kernels

There are no other newforms in \(S_{5}^{\mathrm{new}}(201, [\chi])\).