Properties

Label 11.6.a.a
Level 11
Weight 6
Character orbit 11.a
Self dual Yes
Analytic conductor 1.764
Analytic rank 1
Dimension 1
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 11 \)
Weight: \( k \) = \( 6 \)
Character orbit: \([\chi]\) = 11.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(1.76422201794\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \(q \) \(\mathstrut -\mathstrut 4q^{2} \) \(\mathstrut -\mathstrut 15q^{3} \) \(\mathstrut -\mathstrut 16q^{4} \) \(\mathstrut -\mathstrut 19q^{5} \) \(\mathstrut +\mathstrut 60q^{6} \) \(\mathstrut +\mathstrut 10q^{7} \) \(\mathstrut +\mathstrut 192q^{8} \) \(\mathstrut -\mathstrut 18q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(q \) \(\mathstrut -\mathstrut 4q^{2} \) \(\mathstrut -\mathstrut 15q^{3} \) \(\mathstrut -\mathstrut 16q^{4} \) \(\mathstrut -\mathstrut 19q^{5} \) \(\mathstrut +\mathstrut 60q^{6} \) \(\mathstrut +\mathstrut 10q^{7} \) \(\mathstrut +\mathstrut 192q^{8} \) \(\mathstrut -\mathstrut 18q^{9} \) \(\mathstrut +\mathstrut 76q^{10} \) \(\mathstrut -\mathstrut 121q^{11} \) \(\mathstrut +\mathstrut 240q^{12} \) \(\mathstrut -\mathstrut 1148q^{13} \) \(\mathstrut -\mathstrut 40q^{14} \) \(\mathstrut +\mathstrut 285q^{15} \) \(\mathstrut -\mathstrut 256q^{16} \) \(\mathstrut +\mathstrut 686q^{17} \) \(\mathstrut +\mathstrut 72q^{18} \) \(\mathstrut -\mathstrut 384q^{19} \) \(\mathstrut +\mathstrut 304q^{20} \) \(\mathstrut -\mathstrut 150q^{21} \) \(\mathstrut +\mathstrut 484q^{22} \) \(\mathstrut +\mathstrut 3709q^{23} \) \(\mathstrut -\mathstrut 2880q^{24} \) \(\mathstrut -\mathstrut 2764q^{25} \) \(\mathstrut +\mathstrut 4592q^{26} \) \(\mathstrut +\mathstrut 3915q^{27} \) \(\mathstrut -\mathstrut 160q^{28} \) \(\mathstrut -\mathstrut 5424q^{29} \) \(\mathstrut -\mathstrut 1140q^{30} \) \(\mathstrut -\mathstrut 6443q^{31} \) \(\mathstrut -\mathstrut 5120q^{32} \) \(\mathstrut +\mathstrut 1815q^{33} \) \(\mathstrut -\mathstrut 2744q^{34} \) \(\mathstrut -\mathstrut 190q^{35} \) \(\mathstrut +\mathstrut 288q^{36} \) \(\mathstrut +\mathstrut 12063q^{37} \) \(\mathstrut +\mathstrut 1536q^{38} \) \(\mathstrut +\mathstrut 17220q^{39} \) \(\mathstrut -\mathstrut 3648q^{40} \) \(\mathstrut -\mathstrut 1528q^{41} \) \(\mathstrut +\mathstrut 600q^{42} \) \(\mathstrut -\mathstrut 4026q^{43} \) \(\mathstrut +\mathstrut 1936q^{44} \) \(\mathstrut +\mathstrut 342q^{45} \) \(\mathstrut -\mathstrut 14836q^{46} \) \(\mathstrut +\mathstrut 7168q^{47} \) \(\mathstrut +\mathstrut 3840q^{48} \) \(\mathstrut -\mathstrut 16707q^{49} \) \(\mathstrut +\mathstrut 11056q^{50} \) \(\mathstrut -\mathstrut 10290q^{51} \) \(\mathstrut +\mathstrut 18368q^{52} \) \(\mathstrut -\mathstrut 29862q^{53} \) \(\mathstrut -\mathstrut 15660q^{54} \) \(\mathstrut +\mathstrut 2299q^{55} \) \(\mathstrut +\mathstrut 1920q^{56} \) \(\mathstrut +\mathstrut 5760q^{57} \) \(\mathstrut +\mathstrut 21696q^{58} \) \(\mathstrut -\mathstrut 6461q^{59} \) \(\mathstrut -\mathstrut 4560q^{60} \) \(\mathstrut -\mathstrut 16980q^{61} \) \(\mathstrut +\mathstrut 25772q^{62} \) \(\mathstrut -\mathstrut 180q^{63} \) \(\mathstrut +\mathstrut 28672q^{64} \) \(\mathstrut +\mathstrut 21812q^{65} \) \(\mathstrut -\mathstrut 7260q^{66} \) \(\mathstrut +\mathstrut 29999q^{67} \) \(\mathstrut -\mathstrut 10976q^{68} \) \(\mathstrut -\mathstrut 55635q^{69} \) \(\mathstrut +\mathstrut 760q^{70} \) \(\mathstrut +\mathstrut 31023q^{71} \) \(\mathstrut -\mathstrut 3456q^{72} \) \(\mathstrut +\mathstrut 1924q^{73} \) \(\mathstrut -\mathstrut 48252q^{74} \) \(\mathstrut +\mathstrut 41460q^{75} \) \(\mathstrut +\mathstrut 6144q^{76} \) \(\mathstrut -\mathstrut 1210q^{77} \) \(\mathstrut -\mathstrut 68880q^{78} \) \(\mathstrut +\mathstrut 65138q^{79} \) \(\mathstrut +\mathstrut 4864q^{80} \) \(\mathstrut -\mathstrut 54351q^{81} \) \(\mathstrut +\mathstrut 6112q^{82} \) \(\mathstrut -\mathstrut 102714q^{83} \) \(\mathstrut +\mathstrut 2400q^{84} \) \(\mathstrut -\mathstrut 13034q^{85} \) \(\mathstrut +\mathstrut 16104q^{86} \) \(\mathstrut +\mathstrut 81360q^{87} \) \(\mathstrut -\mathstrut 23232q^{88} \) \(\mathstrut +\mathstrut 17415q^{89} \) \(\mathstrut -\mathstrut 1368q^{90} \) \(\mathstrut -\mathstrut 11480q^{91} \) \(\mathstrut -\mathstrut 59344q^{92} \) \(\mathstrut +\mathstrut 96645q^{93} \) \(\mathstrut -\mathstrut 28672q^{94} \) \(\mathstrut +\mathstrut 7296q^{95} \) \(\mathstrut +\mathstrut 76800q^{96} \) \(\mathstrut +\mathstrut 66905q^{97} \) \(\mathstrut +\mathstrut 66828q^{98} \) \(\mathstrut +\mathstrut 2178q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 \(\iota_m(\nu)\) \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1.1
0
−4.00000 −15.0000 −16.0000 −19.0000 60.0000 10.0000 192.000 −18.0000 76.0000
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Inner twists

This newform does not admit any (nontrivial) inner twists.

Atkin-Lehner signs

\( p \) Sign
\(11\) \(1\)

Hecke kernels

This newform can be constructed as the kernel of the linear operator \(T_{2} \) \(\mathstrut +\mathstrut 4 \) acting on \(S_{6}^{\mathrm{new}}(\Gamma_0(11))\).