Properties

Label 6011.2.a.f
Level 6011
Weight 2
Character orbit 6011.a
Self dual Yes
Analytic conductor 47.998
Analytic rank 0
Dimension 275
CM No

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Newspace parameters

Level: \( N \) = \( 6011 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6011.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(47.998076655\)
Analytic rank: \(0\)
Dimension: \(275\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \(275q \) \(\mathstrut +\mathstrut 16q^{2} \) \(\mathstrut +\mathstrut 9q^{3} \) \(\mathstrut +\mathstrut 316q^{4} \) \(\mathstrut +\mathstrut 36q^{5} \) \(\mathstrut +\mathstrut 30q^{6} \) \(\mathstrut +\mathstrut 41q^{7} \) \(\mathstrut +\mathstrut 36q^{8} \) \(\mathstrut +\mathstrut 322q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \(275q \) \(\mathstrut +\mathstrut 16q^{2} \) \(\mathstrut +\mathstrut 9q^{3} \) \(\mathstrut +\mathstrut 316q^{4} \) \(\mathstrut +\mathstrut 36q^{5} \) \(\mathstrut +\mathstrut 30q^{6} \) \(\mathstrut +\mathstrut 41q^{7} \) \(\mathstrut +\mathstrut 36q^{8} \) \(\mathstrut +\mathstrut 322q^{9} \) \(\mathstrut +\mathstrut 44q^{10} \) \(\mathstrut +\mathstrut 42q^{11} \) \(\mathstrut +\mathstrut 26q^{12} \) \(\mathstrut +\mathstrut 97q^{13} \) \(\mathstrut +\mathstrut 24q^{14} \) \(\mathstrut +\mathstrut 46q^{15} \) \(\mathstrut +\mathstrut 386q^{16} \) \(\mathstrut +\mathstrut 35q^{17} \) \(\mathstrut +\mathstrut 47q^{18} \) \(\mathstrut +\mathstrut 101q^{19} \) \(\mathstrut +\mathstrut 60q^{20} \) \(\mathstrut +\mathstrut 187q^{21} \) \(\mathstrut +\mathstrut 72q^{22} \) \(\mathstrut +\mathstrut 35q^{23} \) \(\mathstrut +\mathstrut 73q^{24} \) \(\mathstrut +\mathstrut 373q^{25} \) \(\mathstrut +\mathstrut 21q^{26} \) \(\mathstrut +\mathstrut 27q^{27} \) \(\mathstrut +\mathstrut 97q^{28} \) \(\mathstrut +\mathstrut 162q^{29} \) \(\mathstrut +\mathstrut 13q^{30} \) \(\mathstrut +\mathstrut 113q^{31} \) \(\mathstrut +\mathstrut 58q^{32} \) \(\mathstrut +\mathstrut 16q^{33} \) \(\mathstrut +\mathstrut 52q^{34} \) \(\mathstrut +\mathstrut 23q^{35} \) \(\mathstrut +\mathstrut 426q^{36} \) \(\mathstrut +\mathstrut 257q^{37} \) \(\mathstrut +\mathstrut 8q^{38} \) \(\mathstrut +\mathstrut 87q^{39} \) \(\mathstrut +\mathstrut 126q^{40} \) \(\mathstrut +\mathstrut 77q^{41} \) \(\mathstrut -\mathstrut 7q^{42} \) \(\mathstrut +\mathstrut 107q^{43} \) \(\mathstrut +\mathstrut 133q^{44} \) \(\mathstrut +\mathstrut 140q^{45} \) \(\mathstrut +\mathstrut 207q^{46} \) \(\mathstrut +\mathstrut 24q^{47} \) \(\mathstrut +\mathstrut 4q^{48} \) \(\mathstrut +\mathstrut 418q^{49} \) \(\mathstrut +\mathstrut 65q^{50} \) \(\mathstrut +\mathstrut 94q^{51} \) \(\mathstrut +\mathstrut 142q^{52} \) \(\mathstrut +\mathstrut 81q^{53} \) \(\mathstrut +\mathstrut 79q^{54} \) \(\mathstrut +\mathstrut 26q^{55} \) \(\mathstrut +\mathstrut 62q^{56} \) \(\mathstrut +\mathstrut 112q^{57} \) \(\mathstrut +\mathstrut 44q^{58} \) \(\mathstrut +\mathstrut 30q^{59} \) \(\mathstrut +\mathstrut 83q^{60} \) \(\mathstrut +\mathstrut 347q^{61} \) \(\mathstrut +\mathstrut 5q^{62} \) \(\mathstrut +\mathstrut 97q^{63} \) \(\mathstrut +\mathstrut 508q^{64} \) \(\mathstrut +\mathstrut 94q^{65} \) \(\mathstrut +\mathstrut 4q^{66} \) \(\mathstrut +\mathstrut 98q^{67} \) \(\mathstrut +\mathstrut 28q^{68} \) \(\mathstrut +\mathstrut 91q^{69} \) \(\mathstrut +\mathstrut 17q^{70} \) \(\mathstrut +\mathstrut 58q^{71} \) \(\mathstrut +\mathstrut 99q^{72} \) \(\mathstrut +\mathstrut 157q^{73} \) \(\mathstrut +\mathstrut 80q^{74} \) \(\mathstrut +\mathstrut 83q^{75} \) \(\mathstrut +\mathstrut 264q^{76} \) \(\mathstrut +\mathstrut 61q^{77} \) \(\mathstrut +\mathstrut 5q^{78} \) \(\mathstrut +\mathstrut 282q^{79} \) \(\mathstrut +\mathstrut 49q^{80} \) \(\mathstrut +\mathstrut 403q^{81} \) \(\mathstrut +\mathstrut 46q^{82} \) \(\mathstrut +\mathstrut 43q^{83} \) \(\mathstrut +\mathstrut 318q^{84} \) \(\mathstrut +\mathstrut 396q^{85} \) \(\mathstrut +\mathstrut 57q^{86} \) \(\mathstrut +\mathstrut 31q^{87} \) \(\mathstrut +\mathstrut 180q^{88} \) \(\mathstrut +\mathstrut 98q^{89} \) \(\mathstrut +\mathstrut 67q^{90} \) \(\mathstrut +\mathstrut 195q^{91} \) \(\mathstrut +\mathstrut 97q^{92} \) \(\mathstrut +\mathstrut 83q^{93} \) \(\mathstrut +\mathstrut 96q^{94} \) \(\mathstrut +\mathstrut 28q^{95} \) \(\mathstrut +\mathstrut 127q^{96} \) \(\mathstrut +\mathstrut 167q^{97} \) \(\mathstrut +\mathstrut 24q^{98} \) \(\mathstrut +\mathstrut 133q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1.1 −2.81994 −1.65347 5.95204 −2.82087 4.66269 −3.44538 −11.1445 −0.266030 7.95467
1.2 −2.79179 0.836540 5.79408 −1.93912 −2.33544 −2.85701 −10.5923 −2.30020 5.41362
1.3 −2.79091 −0.525145 5.78920 2.75280 1.46563 0.824362 −10.5753 −2.72422 −7.68283
1.4 −2.76662 0.922557 5.65417 0.0715024 −2.55236 5.08559 −10.1097 −2.14889 −0.197820
1.5 −2.75181 −3.27979 5.57245 0.268703 9.02535 −2.53711 −9.83069 7.75702 −0.739418
1.6 −2.71378 −2.39167 5.36460 −2.12248 6.49047 2.98262 −9.13079 2.72010 5.75996
1.7 −2.70543 2.79292 5.31937 2.92654 −7.55605 −0.481988 −8.98033 4.80038 −7.91756
1.8 −2.69174 1.47984 5.24548 −2.06553 −3.98336 0.925808 −8.73601 −0.810060 5.55987
1.9 −2.68457 2.63672 5.20694 0.421516 −7.07847 −3.33953 −8.60926 3.95229 −1.13159
1.10 −2.68065 −2.13914 5.18588 0.0996967 5.73429 3.53853 −8.54022 1.57593 −0.267252
1.11 −2.63588 1.89916 4.94785 −3.80955 −5.00596 −0.400599 −7.77017 0.606822 10.0415
1.12 −2.63570 3.36960 4.94691 2.50931 −8.88125 4.49964 −7.76717 8.35420 −6.61379
1.13 −2.61945 −2.32553 4.86151 4.35353 6.09159 −2.02403 −7.49557 2.40807 −11.4039
1.14 −2.61605 −0.908380 4.84374 −1.38921 2.37637 2.01973 −7.43937 −2.17484 3.63425
1.15 −2.61438 −2.85061 4.83497 −3.39585 7.45256 2.58882 −7.41168 5.12595 8.87805
1.16 −2.60468 −1.25355 4.78433 −3.42467 3.26509 −1.07098 −7.25228 −1.42861 8.92017
1.17 −2.59860 2.92349 4.75274 −3.28865 −7.59699 2.97734 −7.15327 5.54680 8.54591
1.18 −2.58380 −1.84401 4.67602 2.13817 4.76456 −0.0377922 −6.91430 0.400387 −5.52460
1.19 −2.53734 2.44850 4.43808 2.44812 −6.21267 1.86592 −6.18624 2.99515 −6.21172
1.20 −2.52281 0.402729 4.36459 0.845770 −1.01601 −3.10596 −5.96541 −2.83781 −2.13372
See next 80 embeddings (of 275 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.275
Significant digits:
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Inner twists

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

Atkin-Lehner signs

\( p \) Sign
\(6011\) \(-1\)

Hecke kernels

This newform can be constructed as the kernel of the linear operator \(T_{2}^{275} - \cdots\) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(6011))\).