Properties

Label 6007.2.a.c
Level 6007
Weight 2
Character orbit 6007.a
Self dual Yes
Analytic conductor 47.966
Analytic rank 0
Dimension 261
CM No

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Newspace parameters

Level: \( N \) = \( 6007 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6007.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(47.9661364942\)
Analytic rank: \(0\)
Dimension: \(261\)
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.

\(\operatorname{Tr}(f)(q) = \) \(261q \) \(\mathstrut +\mathstrut 26q^{2} \) \(\mathstrut +\mathstrut 25q^{3} \) \(\mathstrut +\mathstrut 274q^{4} \) \(\mathstrut +\mathstrut 66q^{5} \) \(\mathstrut +\mathstrut 25q^{6} \) \(\mathstrut +\mathstrut 37q^{7} \) \(\mathstrut +\mathstrut 72q^{8} \) \(\mathstrut +\mathstrut 310q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \(261q \) \(\mathstrut +\mathstrut 26q^{2} \) \(\mathstrut +\mathstrut 25q^{3} \) \(\mathstrut +\mathstrut 274q^{4} \) \(\mathstrut +\mathstrut 66q^{5} \) \(\mathstrut +\mathstrut 25q^{6} \) \(\mathstrut +\mathstrut 37q^{7} \) \(\mathstrut +\mathstrut 72q^{8} \) \(\mathstrut +\mathstrut 310q^{9} \) \(\mathstrut +\mathstrut 35q^{10} \) \(\mathstrut +\mathstrut 32q^{11} \) \(\mathstrut +\mathstrut 51q^{12} \) \(\mathstrut +\mathstrut 60q^{13} \) \(\mathstrut +\mathstrut 55q^{14} \) \(\mathstrut +\mathstrut 16q^{15} \) \(\mathstrut +\mathstrut 288q^{16} \) \(\mathstrut +\mathstrut 270q^{17} \) \(\mathstrut +\mathstrut 45q^{18} \) \(\mathstrut +\mathstrut 34q^{19} \) \(\mathstrut +\mathstrut 157q^{20} \) \(\mathstrut +\mathstrut 27q^{21} \) \(\mathstrut +\mathstrut 38q^{22} \) \(\mathstrut +\mathstrut 116q^{23} \) \(\mathstrut +\mathstrut 48q^{24} \) \(\mathstrut +\mathstrut 335q^{25} \) \(\mathstrut +\mathstrut 46q^{26} \) \(\mathstrut +\mathstrut 73q^{27} \) \(\mathstrut +\mathstrut 70q^{28} \) \(\mathstrut +\mathstrut 99q^{29} \) \(\mathstrut +\mathstrut 33q^{30} \) \(\mathstrut +\mathstrut 33q^{31} \) \(\mathstrut +\mathstrut 150q^{32} \) \(\mathstrut +\mathstrut 172q^{33} \) \(\mathstrut +\mathstrut 24q^{34} \) \(\mathstrut +\mathstrut 114q^{35} \) \(\mathstrut +\mathstrut 339q^{36} \) \(\mathstrut +\mathstrut 36q^{37} \) \(\mathstrut +\mathstrut 112q^{38} \) \(\mathstrut +\mathstrut 30q^{39} \) \(\mathstrut +\mathstrut 106q^{40} \) \(\mathstrut +\mathstrut 209q^{41} \) \(\mathstrut +\mathstrut 64q^{42} \) \(\mathstrut +\mathstrut 64q^{43} \) \(\mathstrut +\mathstrut 65q^{44} \) \(\mathstrut +\mathstrut 153q^{45} \) \(\mathstrut +\mathstrut 135q^{47} \) \(\mathstrut +\mathstrut 87q^{48} \) \(\mathstrut +\mathstrut 332q^{49} \) \(\mathstrut +\mathstrut 82q^{50} \) \(\mathstrut +\mathstrut 52q^{51} \) \(\mathstrut +\mathstrut 102q^{52} \) \(\mathstrut +\mathstrut 163q^{53} \) \(\mathstrut +\mathstrut 52q^{54} \) \(\mathstrut +\mathstrut 56q^{55} \) \(\mathstrut +\mathstrut 134q^{56} \) \(\mathstrut +\mathstrut 181q^{57} \) \(\mathstrut +\mathstrut q^{58} \) \(\mathstrut +\mathstrut 89q^{59} \) \(\mathstrut -\mathstrut 43q^{60} \) \(\mathstrut +\mathstrut 112q^{61} \) \(\mathstrut +\mathstrut 228q^{62} \) \(\mathstrut +\mathstrut 130q^{63} \) \(\mathstrut +\mathstrut 268q^{64} \) \(\mathstrut +\mathstrut 248q^{65} \) \(\mathstrut +\mathstrut 5q^{66} \) \(\mathstrut +\mathstrut 42q^{67} \) \(\mathstrut +\mathstrut 453q^{68} \) \(\mathstrut +\mathstrut 51q^{69} \) \(\mathstrut -\mathstrut 22q^{70} \) \(\mathstrut +\mathstrut 98q^{71} \) \(\mathstrut +\mathstrut 113q^{72} \) \(\mathstrut +\mathstrut 206q^{73} \) \(\mathstrut +\mathstrut 81q^{74} \) \(\mathstrut +\mathstrut 29q^{75} \) \(\mathstrut +\mathstrut 62q^{76} \) \(\mathstrut +\mathstrut 185q^{77} \) \(\mathstrut -\mathstrut 25q^{78} \) \(\mathstrut +\mathstrut 29q^{79} \) \(\mathstrut +\mathstrut 258q^{80} \) \(\mathstrut +\mathstrut 393q^{81} \) \(\mathstrut +\mathstrut 79q^{82} \) \(\mathstrut +\mathstrut 265q^{83} \) \(\mathstrut -\mathstrut 25q^{84} \) \(\mathstrut +\mathstrut 84q^{85} \) \(\mathstrut +\mathstrut 36q^{86} \) \(\mathstrut +\mathstrut 131q^{87} \) \(\mathstrut +\mathstrut 24q^{88} \) \(\mathstrut +\mathstrut 195q^{89} \) \(\mathstrut +\mathstrut 89q^{90} \) \(\mathstrut -\mathstrut 18q^{91} \) \(\mathstrut +\mathstrut 261q^{92} \) \(\mathstrut +\mathstrut 52q^{93} \) \(\mathstrut +\mathstrut 3q^{94} \) \(\mathstrut +\mathstrut 104q^{95} \) \(\mathstrut +\mathstrut 92q^{96} \) \(\mathstrut +\mathstrut 213q^{97} \) \(\mathstrut +\mathstrut 156q^{98} \) \(\mathstrut +\mathstrut 47q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 −2.82040 1.97504 5.95465 −2.55663 −5.57039 −3.03915 −11.1537 0.900772 7.21072
1.2 −2.81023 −2.20286 5.89742 4.33627 6.19056 0.601928 −10.9527 1.85260 −12.1859
1.3 −2.72871 0.0576599 5.44587 −1.32868 −0.157337 0.160488 −9.40280 −2.99668 3.62560
1.4 −2.68856 2.47306 5.22837 0.0319975 −6.64899 3.92320 −8.67966 3.11605 −0.0860273
1.5 −2.66623 −2.56917 5.10878 0.348811 6.85001 3.60714 −8.28872 3.60066 −0.930012
1.6 −2.65529 2.71142 5.05057 3.32212 −7.19960 −2.23518 −8.10014 4.35179 −8.82118
1.7 −2.63601 0.145552 4.94856 0.530894 −0.383678 0.464377 −7.77243 −2.97881 −1.39944
1.8 −2.63092 0.625555 4.92176 3.53160 −1.64579 2.86224 −7.68693 −2.60868 −9.29136
1.9 −2.57859 −1.33205 4.64914 0.797435 3.43482 −0.447865 −6.83106 −1.22564 −2.05626
1.10 −2.56111 −3.17696 4.55927 0.542831 8.13653 −2.10285 −6.55456 7.09306 −1.39025
1.11 −2.55274 −1.51769 4.51649 −0.0618695 3.87427 −0.267248 −6.42394 −0.696618 0.157937
1.12 −2.53967 2.55882 4.44992 2.30710 −6.49855 −1.02038 −6.22199 3.54756 −5.85928
1.13 −2.53843 −2.17354 4.44361 −2.13295 5.51736 −4.01617 −6.20293 1.72426 5.41433
1.14 −2.52735 0.935367 4.38748 −0.964544 −2.36400 −4.26765 −6.03399 −2.12509 2.43774
1.15 −2.52396 2.90244 4.37039 −2.11388 −7.32566 −3.46277 −5.98279 5.42417 5.33537
1.16 −2.49977 0.0230289 4.24887 3.35515 −0.0575671 0.906816 −5.62166 −2.99947 −8.38713
1.17 −2.47861 −3.39135 4.14353 2.04119 8.40584 3.41777 −5.31299 8.50123 −5.05931
1.18 −2.47715 2.24713 4.13629 −0.500546 −5.56650 2.06873 −5.29193 2.04961 1.23993
1.19 −2.47082 3.41011 4.10496 1.44488 −8.42576 2.75509 −5.20098 8.62882 −3.57005
1.20 −2.46886 −1.31806 4.09526 2.84222 3.25411 −1.17521 −5.17289 −1.26271 −7.01703
See next 80 embeddings (of 261 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.261
Significant digits:
Format:

Inner twists

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

Atkin-Lehner signs

\( p \) Sign
\(6007\) \(-1\)

Hecke kernels

This newform can be constructed as the kernel of the linear operator \(T_{2}^{261} - \cdots\) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(6007))\).