Properties

Label 6023.2.a.a
Level 6023
Weight 2
Character orbit 6023.a
Self dual Yes
Analytic conductor 48.094
Analytic rank 1
Dimension 98
CM No

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Newspace parameters

Level: \( N \) = \( 6023 = 19 \cdot 317 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6023.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.0938971374\)
Analytic rank: \(1\)
Dimension: \(98\)
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.

\(\operatorname{Tr}(f)(q) = \) \(98q \) \(\mathstrut -\mathstrut 8q^{2} \) \(\mathstrut -\mathstrut 25q^{3} \) \(\mathstrut +\mathstrut 82q^{4} \) \(\mathstrut -\mathstrut 10q^{5} \) \(\mathstrut -\mathstrut 4q^{6} \) \(\mathstrut -\mathstrut 18q^{7} \) \(\mathstrut -\mathstrut 18q^{8} \) \(\mathstrut +\mathstrut 61q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \(98q \) \(\mathstrut -\mathstrut 8q^{2} \) \(\mathstrut -\mathstrut 25q^{3} \) \(\mathstrut +\mathstrut 82q^{4} \) \(\mathstrut -\mathstrut 10q^{5} \) \(\mathstrut -\mathstrut 4q^{6} \) \(\mathstrut -\mathstrut 18q^{7} \) \(\mathstrut -\mathstrut 18q^{8} \) \(\mathstrut +\mathstrut 61q^{9} \) \(\mathstrut -\mathstrut 24q^{10} \) \(\mathstrut -\mathstrut 12q^{11} \) \(\mathstrut -\mathstrut 51q^{12} \) \(\mathstrut -\mathstrut 58q^{13} \) \(\mathstrut -\mathstrut 15q^{14} \) \(\mathstrut -\mathstrut 18q^{15} \) \(\mathstrut +\mathstrut 58q^{16} \) \(\mathstrut -\mathstrut 25q^{17} \) \(\mathstrut -\mathstrut 40q^{18} \) \(\mathstrut +\mathstrut 98q^{19} \) \(\mathstrut -\mathstrut 12q^{20} \) \(\mathstrut -\mathstrut 24q^{21} \) \(\mathstrut -\mathstrut 59q^{22} \) \(\mathstrut -\mathstrut 38q^{23} \) \(\mathstrut -\mathstrut 9q^{24} \) \(\mathstrut -\mathstrut 12q^{25} \) \(\mathstrut -\mathstrut 3q^{26} \) \(\mathstrut -\mathstrut 85q^{27} \) \(\mathstrut -\mathstrut 33q^{28} \) \(\mathstrut -\mathstrut 24q^{29} \) \(\mathstrut -\mathstrut 22q^{30} \) \(\mathstrut -\mathstrut 56q^{31} \) \(\mathstrut -\mathstrut 29q^{32} \) \(\mathstrut -\mathstrut 51q^{33} \) \(\mathstrut -\mathstrut 38q^{34} \) \(\mathstrut -\mathstrut 10q^{35} \) \(\mathstrut +\mathstrut 50q^{36} \) \(\mathstrut -\mathstrut 124q^{37} \) \(\mathstrut -\mathstrut 8q^{38} \) \(\mathstrut -\mathstrut 4q^{39} \) \(\mathstrut -\mathstrut 80q^{40} \) \(\mathstrut -\mathstrut 28q^{41} \) \(\mathstrut -\mathstrut 37q^{42} \) \(\mathstrut -\mathstrut 63q^{43} \) \(\mathstrut -\mathstrut 7q^{44} \) \(\mathstrut -\mathstrut 32q^{45} \) \(\mathstrut -\mathstrut 47q^{46} \) \(\mathstrut -\mathstrut 10q^{47} \) \(\mathstrut -\mathstrut 88q^{48} \) \(\mathstrut +\mathstrut 6q^{49} \) \(\mathstrut -\mathstrut 17q^{50} \) \(\mathstrut -\mathstrut 22q^{51} \) \(\mathstrut -\mathstrut 119q^{52} \) \(\mathstrut -\mathstrut 65q^{53} \) \(\mathstrut +\mathstrut 24q^{54} \) \(\mathstrut -\mathstrut 30q^{55} \) \(\mathstrut -\mathstrut 39q^{56} \) \(\mathstrut -\mathstrut 25q^{57} \) \(\mathstrut -\mathstrut 91q^{58} \) \(\mathstrut -\mathstrut 26q^{59} \) \(\mathstrut -\mathstrut 60q^{60} \) \(\mathstrut -\mathstrut 60q^{61} \) \(\mathstrut +\mathstrut 6q^{62} \) \(\mathstrut -\mathstrut 26q^{63} \) \(\mathstrut +\mathstrut 50q^{64} \) \(\mathstrut -\mathstrut 40q^{65} \) \(\mathstrut +\mathstrut 57q^{66} \) \(\mathstrut -\mathstrut 108q^{67} \) \(\mathstrut -\mathstrut 41q^{68} \) \(\mathstrut -\mathstrut 15q^{69} \) \(\mathstrut -\mathstrut 36q^{70} \) \(\mathstrut -\mathstrut 19q^{71} \) \(\mathstrut -\mathstrut 47q^{72} \) \(\mathstrut -\mathstrut 136q^{73} \) \(\mathstrut +\mathstrut 22q^{74} \) \(\mathstrut -\mathstrut 48q^{75} \) \(\mathstrut +\mathstrut 82q^{76} \) \(\mathstrut -\mathstrut 35q^{77} \) \(\mathstrut -\mathstrut 56q^{78} \) \(\mathstrut -\mathstrut 98q^{79} \) \(\mathstrut -\mathstrut 42q^{80} \) \(\mathstrut +\mathstrut 6q^{81} \) \(\mathstrut -\mathstrut 37q^{82} \) \(\mathstrut -\mathstrut 31q^{83} \) \(\mathstrut -\mathstrut 24q^{84} \) \(\mathstrut -\mathstrut 71q^{85} \) \(\mathstrut -\mathstrut 24q^{86} \) \(\mathstrut +\mathstrut 7q^{87} \) \(\mathstrut -\mathstrut 166q^{88} \) \(\mathstrut -\mathstrut 38q^{89} \) \(\mathstrut +\mathstrut 26q^{90} \) \(\mathstrut -\mathstrut 100q^{91} \) \(\mathstrut -\mathstrut 59q^{92} \) \(\mathstrut -\mathstrut 21q^{93} \) \(\mathstrut -\mathstrut 48q^{94} \) \(\mathstrut -\mathstrut 10q^{95} \) \(\mathstrut -\mathstrut 16q^{96} \) \(\mathstrut -\mathstrut 190q^{97} \) \(\mathstrut -\mathstrut 80q^{98} \) \(\mathstrut -\mathstrut 17q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 −2.78159 0.980083 5.73723 −2.26646 −2.72619 0.130985 −10.3954 −2.03944 6.30436
1.2 −2.72324 −3.03839 5.41603 −0.824121 8.27426 −3.50609 −9.30267 6.23182 2.24428
1.3 −2.72317 −0.516928 5.41568 3.12322 1.40769 −3.06631 −9.30149 −2.73279 −8.50508
1.4 −2.63244 −2.81028 4.92974 1.41252 7.39789 3.18061 −7.71236 4.89767 −3.71838
1.5 −2.52650 1.56416 4.38319 1.08994 −3.95184 4.94624 −6.02111 −0.553409 −2.75372
1.6 −2.52400 −0.270526 4.37060 −2.19505 0.682808 −4.06184 −5.98340 −2.92682 5.54031
1.7 −2.51733 −2.83375 4.33693 3.33686 7.13347 2.06105 −5.88281 5.03014 −8.39997
1.8 −2.51387 −0.144321 4.31953 2.01567 0.362803 1.13174 −5.83100 −2.97917 −5.06713
1.9 −2.51046 3.07291 4.30243 0.528149 −7.71443 −0.975247 −5.78017 6.44278 −1.32590
1.10 −2.36387 −1.85446 3.58790 −2.76467 4.38371 3.05083 −3.75360 0.439017 6.53534
1.11 −2.30301 −0.172789 3.30385 −0.809544 0.397934 0.778568 −3.00278 −2.97014 1.86439
1.12 −2.23585 2.07159 2.99900 2.91944 −4.63176 −1.89696 −2.23362 1.29150 −6.52741
1.13 −2.22980 2.83472 2.97200 −0.749386 −6.32084 0.730492 −2.16735 5.03561 1.67098
1.14 −2.16233 −1.79610 2.67567 −1.92302 3.88377 3.63289 −1.46101 0.225992 4.15820
1.15 −2.15437 −1.80294 2.64131 1.24504 3.88420 −4.16426 −1.38162 0.250590 −2.68227
1.16 −2.11992 0.896090 2.49404 2.73729 −1.89963 −3.12431 −1.04733 −2.19702 −5.80282
1.17 −2.03453 −2.81750 2.13929 −2.44691 5.73228 −2.76718 −0.283395 4.93833 4.97829
1.18 −2.01585 1.02156 2.06364 0.907276 −2.05931 1.44669 −0.128285 −1.95642 −1.82893
1.19 −1.95295 2.01904 1.81400 −3.44278 −3.94307 −1.14802 0.363246 1.07651 6.72357
1.20 −1.88657 −2.34604 1.55916 1.12157 4.42598 2.57604 0.831673 2.50392 −2.11593
See all 98 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.98
Significant digits:
Format:

Inner twists

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

Atkin-Lehner signs

\( p \) Sign
\(19\) \(-1\)
\(317\) \(-1\)