Properties

Label 6023.2.a.c
Level 6023
Weight 2
Character orbit 6023.a
Self dual Yes
Analytic conductor 48.094
Analytic rank 0
Dimension 138
CM No

Related objects

Downloads

Learn more about

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: \(0\)
Dimension: \(138\)
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.

\(\operatorname{Tr}(f)(q) = \) \(138q \) \(\mathstrut +\mathstrut 11q^{2} \) \(\mathstrut +\mathstrut 29q^{3} \) \(\mathstrut +\mathstrut 157q^{4} \) \(\mathstrut +\mathstrut 12q^{5} \) \(\mathstrut +\mathstrut 8q^{6} \) \(\mathstrut +\mathstrut 18q^{7} \) \(\mathstrut +\mathstrut 33q^{8} \) \(\mathstrut +\mathstrut 171q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \(138q \) \(\mathstrut +\mathstrut 11q^{2} \) \(\mathstrut +\mathstrut 29q^{3} \) \(\mathstrut +\mathstrut 157q^{4} \) \(\mathstrut +\mathstrut 12q^{5} \) \(\mathstrut +\mathstrut 8q^{6} \) \(\mathstrut +\mathstrut 18q^{7} \) \(\mathstrut +\mathstrut 33q^{8} \) \(\mathstrut +\mathstrut 171q^{9} \) \(\mathstrut +\mathstrut 40q^{10} \) \(\mathstrut +\mathstrut 4q^{11} \) \(\mathstrut +\mathstrut 69q^{12} \) \(\mathstrut +\mathstrut 72q^{13} \) \(\mathstrut +\mathstrut 3q^{14} \) \(\mathstrut +\mathstrut 30q^{15} \) \(\mathstrut +\mathstrut 191q^{16} \) \(\mathstrut +\mathstrut 31q^{17} \) \(\mathstrut +\mathstrut 31q^{18} \) \(\mathstrut +\mathstrut 138q^{19} \) \(\mathstrut +\mathstrut 16q^{20} \) \(\mathstrut +\mathstrut 16q^{21} \) \(\mathstrut +\mathstrut 95q^{22} \) \(\mathstrut +\mathstrut 34q^{23} \) \(\mathstrut +\mathstrut 3q^{24} \) \(\mathstrut +\mathstrut 244q^{25} \) \(\mathstrut -\mathstrut 13q^{26} \) \(\mathstrut +\mathstrut 107q^{27} \) \(\mathstrut +\mathstrut 43q^{28} \) \(\mathstrut +\mathstrut 30q^{29} \) \(\mathstrut -\mathstrut 14q^{30} \) \(\mathstrut +\mathstrut 60q^{31} \) \(\mathstrut +\mathstrut 62q^{32} \) \(\mathstrut +\mathstrut 77q^{33} \) \(\mathstrut +\mathstrut 36q^{34} \) \(\mathstrut +\mathstrut 2q^{35} \) \(\mathstrut +\mathstrut 205q^{36} \) \(\mathstrut +\mathstrut 142q^{37} \) \(\mathstrut +\mathstrut 11q^{38} \) \(\mathstrut +\mathstrut 20q^{39} \) \(\mathstrut +\mathstrut 76q^{40} \) \(\mathstrut +\mathstrut 46q^{41} \) \(\mathstrut -\mathstrut 21q^{42} \) \(\mathstrut +\mathstrut 69q^{43} \) \(\mathstrut -\mathstrut 7q^{44} \) \(\mathstrut +\mathstrut 30q^{45} \) \(\mathstrut +\mathstrut 39q^{46} \) \(\mathstrut +\mathstrut 8q^{47} \) \(\mathstrut +\mathstrut 116q^{48} \) \(\mathstrut +\mathstrut 236q^{49} \) \(\mathstrut +\mathstrut 34q^{51} \) \(\mathstrut +\mathstrut 165q^{52} \) \(\mathstrut +\mathstrut 49q^{53} \) \(\mathstrut +\mathstrut 6q^{55} \) \(\mathstrut -\mathstrut 33q^{56} \) \(\mathstrut +\mathstrut 29q^{57} \) \(\mathstrut +\mathstrut 75q^{58} \) \(\mathstrut +\mathstrut 8q^{59} \) \(\mathstrut -\mathstrut 24q^{60} \) \(\mathstrut +\mathstrut 38q^{61} \) \(\mathstrut -\mathstrut 10q^{62} \) \(\mathstrut +\mathstrut 2q^{63} \) \(\mathstrut +\mathstrut 251q^{64} \) \(\mathstrut +\mathstrut 72q^{65} \) \(\mathstrut -\mathstrut 15q^{66} \) \(\mathstrut +\mathstrut 158q^{67} \) \(\mathstrut -\mathstrut 19q^{68} \) \(\mathstrut +\mathstrut 33q^{69} \) \(\mathstrut +\mathstrut 48q^{70} \) \(\mathstrut +\mathstrut 23q^{71} \) \(\mathstrut +\mathstrut 88q^{72} \) \(\mathstrut +\mathstrut 134q^{73} \) \(\mathstrut +\mathstrut 4q^{74} \) \(\mathstrut +\mathstrut 118q^{75} \) \(\mathstrut +\mathstrut 157q^{76} \) \(\mathstrut +\mathstrut 13q^{77} \) \(\mathstrut +\mathstrut 12q^{78} \) \(\mathstrut +\mathstrut 78q^{79} \) \(\mathstrut -\mathstrut 48q^{80} \) \(\mathstrut +\mathstrut 254q^{81} \) \(\mathstrut +\mathstrut 89q^{82} \) \(\mathstrut -\mathstrut 27q^{83} \) \(\mathstrut -\mathstrut 15q^{84} \) \(\mathstrut +\mathstrut 37q^{85} \) \(\mathstrut +\mathstrut 66q^{86} \) \(\mathstrut +\mathstrut 43q^{87} \) \(\mathstrut +\mathstrut 224q^{88} \) \(\mathstrut +\mathstrut 26q^{89} \) \(\mathstrut +\mathstrut 38q^{90} \) \(\mathstrut +\mathstrut 108q^{91} \) \(\mathstrut +\mathstrut 113q^{92} \) \(\mathstrut +\mathstrut 83q^{93} \) \(\mathstrut +\mathstrut 48q^{94} \) \(\mathstrut +\mathstrut 12q^{95} \) \(\mathstrut +\mathstrut 40q^{96} \) \(\mathstrut +\mathstrut 254q^{97} \) \(\mathstrut +\mathstrut 47q^{98} \) \(\mathstrut +\mathstrut 11q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 −2.80790 2.44752 5.88430 0.306657 −6.87238 −4.87771 −10.9067 2.99034 −0.861061
1.2 −2.76304 −0.570737 5.63440 2.36853 1.57697 1.21818 −10.0420 −2.67426 −6.54436
1.3 −2.74148 −0.0386597 5.51569 −1.76662 0.105985 3.31998 −9.63818 −2.99851 4.84315
1.4 −2.68395 2.15160 5.20359 1.49960 −5.77479 0.747166 −8.59827 1.62938 −4.02486
1.5 −2.67199 3.08563 5.13955 −4.31422 −8.24478 2.33147 −8.38886 6.52111 11.5276
1.6 −2.67164 −1.61720 5.13764 −4.16220 4.32056 −1.04033 −8.38264 −0.384677 11.1199
1.7 −2.58182 −0.634269 4.66582 2.08330 1.63757 3.68872 −6.88267 −2.59770 −5.37871
1.8 −2.57032 −2.26358 4.60652 −0.389233 5.81812 0.261062 −6.69959 2.12381 1.00045
1.9 −2.56824 −3.23259 4.59584 −2.23172 8.30205 3.00174 −6.66674 7.44963 5.73158
1.10 −2.53137 2.03677 4.40782 3.56698 −5.15582 −0.371412 −6.09508 1.14845 −9.02935
1.11 −2.51157 0.714819 4.30797 −1.12509 −1.79532 −0.994631 −5.79662 −2.48903 2.82573
1.12 −2.40954 1.37728 3.80590 −2.93809 −3.31862 −1.98041 −4.35139 −1.10309 7.07945
1.13 −2.39602 −1.69365 3.74091 −0.534671 4.05801 −0.0216661 −4.17126 −0.131565 1.28108
1.14 −2.39507 3.00458 3.73634 −1.01813 −7.19617 −4.72960 −4.15865 6.02752 2.43848
1.15 −2.33668 3.18243 3.46006 4.06905 −7.43630 5.05493 −3.41169 7.12783 −9.50807
1.16 −2.26801 0.709403 3.14388 −4.17389 −1.60894 3.35218 −2.59433 −2.49675 9.46643
1.17 −2.24651 −2.33680 3.04682 3.03120 5.24966 −0.990135 −2.35169 2.46065 −6.80962
1.18 −2.22566 −1.96365 2.95355 3.43373 4.37041 −3.81546 −2.12228 0.855918 −7.64232
1.19 −2.22132 1.60897 2.93428 0.172135 −3.57405 −2.94325 −2.07533 −0.411206 −0.382368
1.20 −2.14132 0.0864735 2.58523 2.84531 −0.185167 1.71112 −1.25317 −2.99252 −6.09271
See next 80 embeddings (of 138 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.138
Significant digits:
Format:

Inner twists

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

Atkin-Lehner signs

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