Properties

Label 23.4.c.a
Level 23
Weight 4
Character orbit 23.c
Analytic conductor 1.357
Analytic rank 0
Dimension 50
CM No

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Newspace parameters

Level: \( N \) = \( 23 \)
Weight: \( k \) = \( 4 \)
Character orbit: \([\chi]\) = 23.c (of order \(11\) and degree \(10\))

Newform invariants

Self dual: No
Analytic conductor: \(1.35704393013\)
Analytic rank: \(0\)
Dimension: \(50\)
Relative dimension: \(5\) over \(\Q(\zeta_{11})\)
Sato-Tate group: $\mathrm{SU}(2)[C_{11}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \(50q \) \(\mathstrut -\mathstrut 11q^{2} \) \(\mathstrut -\mathstrut 13q^{3} \) \(\mathstrut -\mathstrut 27q^{4} \) \(\mathstrut -\mathstrut 19q^{5} \) \(\mathstrut -\mathstrut 4q^{6} \) \(\mathstrut -\mathstrut 19q^{7} \) \(\mathstrut +\mathstrut 28q^{8} \) \(\mathstrut +\mathstrut 24q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \(50q \) \(\mathstrut -\mathstrut 11q^{2} \) \(\mathstrut -\mathstrut 13q^{3} \) \(\mathstrut -\mathstrut 27q^{4} \) \(\mathstrut -\mathstrut 19q^{5} \) \(\mathstrut -\mathstrut 4q^{6} \) \(\mathstrut -\mathstrut 19q^{7} \) \(\mathstrut +\mathstrut 28q^{8} \) \(\mathstrut +\mathstrut 24q^{9} \) \(\mathstrut +\mathstrut 47q^{10} \) \(\mathstrut -\mathstrut 53q^{11} \) \(\mathstrut +\mathstrut 36q^{12} \) \(\mathstrut -\mathstrut 65q^{13} \) \(\mathstrut +\mathstrut 117q^{14} \) \(\mathstrut -\mathstrut 425q^{15} \) \(\mathstrut -\mathstrut 499q^{16} \) \(\mathstrut -\mathstrut 117q^{17} \) \(\mathstrut +\mathstrut 24q^{18} \) \(\mathstrut +\mathstrut 73q^{19} \) \(\mathstrut +\mathstrut 529q^{20} \) \(\mathstrut +\mathstrut 429q^{21} \) \(\mathstrut +\mathstrut 310q^{22} \) \(\mathstrut +\mathstrut 542q^{23} \) \(\mathstrut +\mathstrut 1606q^{24} \) \(\mathstrut +\mathstrut 246q^{25} \) \(\mathstrut +\mathstrut 324q^{26} \) \(\mathstrut +\mathstrut 65q^{27} \) \(\mathstrut -\mathstrut 677q^{28} \) \(\mathstrut -\mathstrut 497q^{29} \) \(\mathstrut -\mathstrut 1041q^{30} \) \(\mathstrut -\mathstrut 471q^{31} \) \(\mathstrut -\mathstrut 915q^{32} \) \(\mathstrut -\mathstrut 391q^{33} \) \(\mathstrut -\mathstrut 2751q^{34} \) \(\mathstrut -\mathstrut 737q^{35} \) \(\mathstrut -\mathstrut 1865q^{36} \) \(\mathstrut -\mathstrut 1071q^{37} \) \(\mathstrut -\mathstrut 1504q^{38} \) \(\mathstrut +\mathstrut 127q^{39} \) \(\mathstrut +\mathstrut 1479q^{40} \) \(\mathstrut +\mathstrut 569q^{41} \) \(\mathstrut +\mathstrut 3059q^{42} \) \(\mathstrut +\mathstrut 1615q^{43} \) \(\mathstrut +\mathstrut 2518q^{44} \) \(\mathstrut +\mathstrut 2768q^{45} \) \(\mathstrut +\mathstrut 4041q^{46} \) \(\mathstrut +\mathstrut 2904q^{47} \) \(\mathstrut +\mathstrut 2702q^{48} \) \(\mathstrut +\mathstrut 1226q^{49} \) \(\mathstrut +\mathstrut 1322q^{50} \) \(\mathstrut +\mathstrut 589q^{51} \) \(\mathstrut -\mathstrut 2156q^{52} \) \(\mathstrut +\mathstrut 391q^{53} \) \(\mathstrut -\mathstrut 5862q^{54} \) \(\mathstrut -\mathstrut 3323q^{55} \) \(\mathstrut -\mathstrut 7028q^{56} \) \(\mathstrut -\mathstrut 7623q^{57} \) \(\mathstrut -\mathstrut 5639q^{58} \) \(\mathstrut -\mathstrut 2445q^{59} \) \(\mathstrut -\mathstrut 3157q^{60} \) \(\mathstrut -\mathstrut 1059q^{61} \) \(\mathstrut +\mathstrut 1468q^{62} \) \(\mathstrut +\mathstrut 3155q^{63} \) \(\mathstrut +\mathstrut 4570q^{64} \) \(\mathstrut +\mathstrut 2641q^{65} \) \(\mathstrut +\mathstrut 5206q^{66} \) \(\mathstrut +\mathstrut 27q^{67} \) \(\mathstrut +\mathstrut 8350q^{68} \) \(\mathstrut +\mathstrut 4005q^{69} \) \(\mathstrut +\mathstrut 9702q^{70} \) \(\mathstrut +\mathstrut 3465q^{71} \) \(\mathstrut +\mathstrut 5629q^{72} \) \(\mathstrut +\mathstrut 435q^{73} \) \(\mathstrut -\mathstrut 994q^{74} \) \(\mathstrut -\mathstrut 7819q^{75} \) \(\mathstrut -\mathstrut 3598q^{76} \) \(\mathstrut -\mathstrut 5931q^{77} \) \(\mathstrut -\mathstrut 8996q^{78} \) \(\mathstrut -\mathstrut 2559q^{79} \) \(\mathstrut -\mathstrut 14052q^{80} \) \(\mathstrut -\mathstrut 4788q^{81} \) \(\mathstrut -\mathstrut 3822q^{82} \) \(\mathstrut -\mathstrut 3967q^{83} \) \(\mathstrut -\mathstrut 8427q^{84} \) \(\mathstrut +\mathstrut 299q^{85} \) \(\mathstrut +\mathstrut 721q^{86} \) \(\mathstrut +\mathstrut 8363q^{87} \) \(\mathstrut +\mathstrut 5825q^{88} \) \(\mathstrut +\mathstrut 3717q^{89} \) \(\mathstrut +\mathstrut 16742q^{90} \) \(\mathstrut +\mathstrut 7238q^{91} \) \(\mathstrut +\mathstrut 9550q^{92} \) \(\mathstrut +\mathstrut 12750q^{93} \) \(\mathstrut +\mathstrut 6035q^{94} \) \(\mathstrut +\mathstrut 4551q^{95} \) \(\mathstrut +\mathstrut 2493q^{96} \) \(\mathstrut -\mathstrut 2419q^{97} \) \(\mathstrut -\mathstrut 5687q^{98} \) \(\mathstrut -\mathstrut 755q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
2.1 −3.24175 2.08335i 1.21610 + 8.45817i 2.84529 + 6.23031i 12.7969 + 3.75752i 13.6790 29.9528i −11.3462 + 13.0942i −0.631070 + 4.38919i −44.1554 + 12.9652i −33.6563 38.8414i
2.2 −2.68394 1.72487i −0.220662 1.53474i 0.905070 + 1.98183i −18.5174 5.43720i −2.05498 + 4.49977i 13.0047 15.0082i −2.64311 + 18.3833i 23.5996 6.92946i 40.3212 + 46.5331i
2.3 −0.442460 0.284352i −0.784628 5.45721i −3.20841 7.02543i 12.7367 + 3.73985i −1.20460 + 2.63770i −5.26652 + 6.07789i −1.17691 + 8.18558i −3.25915 + 0.956973i −4.57207 5.27645i
2.4 1.91736 + 1.23221i 0.776967 + 5.40392i −1.16540 2.55188i −0.907869 0.266574i −5.16905 + 11.3186i 8.82725 10.1872i 3.50483 24.3766i −2.69237 + 0.790552i −1.41223 1.62980i
2.5 3.73432 + 2.39990i −0.655499 4.55909i 4.86229 + 10.6469i −9.99480 2.93474i 8.49353 18.5982i −17.7583 + 20.4942i −2.34036 + 16.2775i 5.55065 1.62982i −30.2807 34.9458i
3.1 −0.589312 4.09876i 1.03962 2.27645i −8.77657 + 2.57703i −3.66646 + 4.23132i −9.94329 2.91961i 16.9812 10.9132i 1.97323 + 4.32077i 13.5798 + 15.6719i 19.5039 + 12.5344i
3.2 −0.132292 0.920110i 0.209861 0.459531i 6.84684 2.01041i 6.87249 7.93128i −0.450582 0.132303i −25.4560 + 16.3596i −5.84485 12.7984i 17.5141 + 20.2124i −8.20682 5.27420i
3.3 0.0282746 + 0.196654i −3.66027 + 8.01487i 7.63807 2.24274i −6.59261 + 7.60828i −1.67965 0.493191i 21.3237 13.7039i 1.31727 + 2.88443i −33.1594 38.2680i −1.68261 1.08135i
3.4 0.306014 + 2.12837i 3.96829 8.68933i 3.23961 0.951236i −11.4648 + 13.2311i 19.7085 + 5.78694i −2.65189 + 1.70427i 10.1620 + 22.2516i −42.0760 48.5583i −31.6691 20.3525i
3.5 0.619909 + 4.31156i −0.504759 + 1.10527i −10.5293 + 3.09169i 4.52322 5.22007i −5.07833 1.49113i 2.36872 1.52228i −5.38116 11.7831i 16.7144 + 19.2894i 25.3106 + 16.2662i
4.1 −2.10729 4.61431i 8.43369 2.47635i −11.6123 + 13.4013i −5.02341 3.22835i −29.1989 33.6973i 3.12135 + 21.7095i 47.3705 + 13.9092i 42.2809 27.1723i −4.31085 + 29.9826i
4.2 −1.58245 3.46509i −7.04544 + 2.06873i −4.26380 + 4.92069i −4.88780 3.14120i 18.3174 + 21.1394i −2.25200 15.6630i −5.44232 1.59801i 22.6448 14.5529i −3.14982 + 21.9075i
4.3 −0.308069 0.674576i 1.68484 0.494713i 4.87874 5.63037i 3.36936 + 2.16536i −0.852766 0.984145i 0.387311 + 2.69380i −10.9935 3.22799i −20.1199 + 12.9303i 0.422704 2.93997i
4.4 1.49850 + 3.28126i −7.64281 + 2.24413i −3.28227 + 3.78794i 15.0482 + 9.67090i −18.8163 21.7152i −2.56161 17.8164i 10.3412 + 3.03646i 30.6625 19.7056i −9.18297 + 63.8690i
4.5 1.61009 + 3.52560i 3.27467 0.961529i −4.59861 + 5.30707i −10.7624 6.91659i 8.66248 + 9.99703i −0.249078 1.73238i 3.63606 + 1.06764i −12.9149 + 8.29992i 7.05669 49.0804i
6.1 −2.10729 + 4.61431i 8.43369 + 2.47635i −11.6123 13.4013i −5.02341 + 3.22835i −29.1989 + 33.6973i 3.12135 21.7095i 47.3705 13.9092i 42.2809 + 27.1723i −4.31085 29.9826i
6.2 −1.58245 + 3.46509i −7.04544 2.06873i −4.26380 4.92069i −4.88780 + 3.14120i 18.3174 21.1394i −2.25200 + 15.6630i −5.44232 + 1.59801i 22.6448 + 14.5529i −3.14982 21.9075i
6.3 −0.308069 + 0.674576i 1.68484 + 0.494713i 4.87874 + 5.63037i 3.36936 2.16536i −0.852766 + 0.984145i 0.387311 2.69380i −10.9935 + 3.22799i −20.1199 12.9303i 0.422704 + 2.93997i
6.4 1.49850 3.28126i −7.64281 2.24413i −3.28227 3.78794i 15.0482 9.67090i −18.8163 + 21.7152i −2.56161 + 17.8164i 10.3412 3.03646i 30.6625 + 19.7056i −9.18297 63.8690i
6.5 1.61009 3.52560i 3.27467 + 0.961529i −4.59861 5.30707i −10.7624 + 6.91659i 8.66248 9.99703i −0.249078 + 1.73238i 3.63606 1.06764i −12.9149 8.29992i 7.05669 + 49.0804i
See all 50 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 18.5
Significant digits:
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Inner twists

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

Hecke kernels

There are no other newforms in \(S_{4}^{\mathrm{new}}(23, [\chi])\).