Properties

Label 124.5.l.a
Level $124$
Weight $5$
Character orbit 124.l
Analytic conductor $12.818$
Analytic rank $0$
Dimension $248$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 124 = 2^{2} \cdot 31 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 124.l (of order \(10\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(12.8178754224\)
Analytic rank: \(0\)
Dimension: \(248\)
Relative dimension: \(62\) over \(\Q(\zeta_{10})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 248 q - 3 q^{2} - 31 q^{4} - 16 q^{5} - 10 q^{6} - 237 q^{8} + 1560 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 248 q - 3 q^{2} - 31 q^{4} - 16 q^{5} - 10 q^{6} - 237 q^{8} + 1560 q^{9} - 250 q^{10} - 210 q^{12} + 346 q^{13} + 226 q^{14} + 73 q^{16} - 6 q^{17} + 818 q^{18} - 975 q^{20} + 102 q^{21} + 1540 q^{22} + 1023 q^{24} + 26248 q^{25} - 360 q^{26} + 160 q^{28} - 6 q^{29} - 4022 q^{30} + 6862 q^{32} + 1110 q^{33} + 3067 q^{34} - 4568 q^{36} - 2096 q^{37} + 5050 q^{38} - 3206 q^{40} - 6 q^{41} - 3884 q^{42} - 5660 q^{44} - 10272 q^{45} + 3185 q^{46} - 16516 q^{48} + 12392 q^{49} - 7878 q^{50} - 5935 q^{52} - 8454 q^{53} + 1362 q^{54} + 39536 q^{56} + 10892 q^{57} - 1105 q^{58} - 1267 q^{60} + 11696 q^{61} - 21020 q^{62} - 24493 q^{64} - 3756 q^{65} - 33182 q^{66} - 31014 q^{68} + 31734 q^{69} + 4205 q^{70} - 59598 q^{72} - 16646 q^{73} - 7683 q^{74} - 16019 q^{76} - 16618 q^{77} - 11625 q^{78} + 63150 q^{80} - 33864 q^{81} - 25974 q^{82} - 43055 q^{84} + 23956 q^{85} - 26357 q^{86} - 34700 q^{88} + 4170 q^{89} + 20102 q^{90} - 22738 q^{92} + 35990 q^{93} - 25646 q^{94} + 50490 q^{96} - 6614 q^{97} - 49748 q^{98}+O(q^{100}) \) Copy content Toggle raw display

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 \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
35.1 −3.99936 + 0.0713539i −12.2995 3.99635i 15.9898 0.570740i −9.81905 49.4753 + 15.1052i −39.5116 54.3830i −63.9084 + 3.42353i 69.7765 + 50.6956i 39.2699 0.700627i
35.2 −3.99862 0.105051i 7.35414 + 2.38950i 15.9779 + 0.840119i −14.1850 −29.1554 10.3273i 12.6030 + 17.3466i −63.8014 5.03782i −17.1567 12.4651i 56.7206 + 1.49015i
35.3 −3.93789 0.702183i −10.2382 3.32660i 15.0139 + 5.53023i 46.1374 37.9811 + 20.2889i 4.75019 + 6.53807i −55.2397 32.3199i 28.2248 + 20.5065i −181.684 32.3969i
35.4 −3.91239 0.832603i 1.75381 + 0.569849i 14.6135 + 6.51493i 6.69903 −6.38714 3.68970i −11.9816 16.4913i −51.7495 37.6562i −62.7792 45.6118i −26.2092 5.57763i
35.5 −3.87510 + 0.991761i −1.78210 0.579038i 14.0328 7.68635i 5.30562 7.48007 + 0.476417i 40.2102 + 55.3445i −46.7556 + 43.7026i −62.6898 45.5468i −20.5598 + 5.26191i
35.6 −3.85822 1.05551i −12.5298 4.07117i 13.7718 + 8.14480i −42.3430 44.0455 + 28.9328i 48.2598 + 66.4239i −44.5377 45.9608i 74.8906 + 54.4112i 163.369 + 44.6935i
35.7 −3.83059 1.15178i 14.8017 + 4.80936i 13.3468 + 8.82396i −27.7531 −51.1599 35.4709i −6.94187 9.55467i −40.9630 49.1735i 130.430 + 94.7627i 106.311 + 31.9653i
35.8 −3.74593 + 1.40285i 14.0191 + 4.55508i 12.0640 10.5100i 29.1074 −58.9047 + 2.60365i 16.1694 + 22.2552i −30.4472 + 56.2936i 110.256 + 80.1058i −109.034 + 40.8333i
35.9 −3.68342 + 1.55963i −0.0674233 0.0219071i 11.1351 11.4895i −46.6687 0.282515 0.0244621i −17.3603 23.8944i −23.0959 + 59.6874i −65.5263 47.6077i 171.900 72.7859i
35.10 −3.63647 + 1.66615i 2.24232 + 0.728573i 10.4479 12.1179i 22.7008 −9.36804 + 1.08661i −53.6590 73.8553i −17.8031 + 61.4740i −61.0332 44.3432i −82.5508 + 37.8230i
35.11 −3.39722 2.11161i 11.5855 + 3.76434i 7.08217 + 14.3472i 37.5609 −31.4095 37.2523i −50.0886 68.9410i 6.23614 63.6955i 54.5221 + 39.6126i −127.603 79.3142i
35.12 −3.34806 + 2.18871i −13.0122 4.22791i 6.41907 14.6559i 2.44474 52.8193 14.3246i 8.79561 + 12.1061i 10.5861 + 63.1184i 85.9112 + 62.4182i −8.18516 + 5.35084i
35.13 −3.12327 2.49904i 9.51100 + 3.09031i 3.50959 + 15.6103i 25.8175 −21.9826 33.4202i 52.0808 + 71.6831i 28.0495 57.5259i 15.3787 + 11.1732i −80.6349 64.5190i
35.14 −3.11474 2.50965i −5.26084 1.70935i 3.40327 + 15.6339i 8.56811 12.0963 + 18.5271i 14.7234 + 20.2651i 28.6353 57.2365i −40.7758 29.6254i −26.6875 21.5030i
35.15 −3.10903 2.51673i −3.93487 1.27852i 3.33209 + 15.6492i −23.8871 9.01594 + 13.8780i −31.1843 42.9214i 29.0253 57.0397i −51.6817 37.5490i 74.2656 + 60.1175i
35.16 −3.10796 + 2.51805i 12.5846 + 4.08897i 3.31889 15.6520i −25.4386 −49.4086 + 18.9801i −16.7342 23.0326i 29.0974 + 57.0030i 76.1209 + 55.3051i 79.0623 64.0556i
35.17 −2.55746 + 3.07561i −1.74347 0.566487i −2.91878 15.7315i 42.7016 6.20114 3.91346i 8.91114 + 12.2651i 55.8487 + 31.2557i −62.8116 45.6353i −109.208 + 131.334i
35.18 −2.39076 3.20691i −16.8121 5.46259i −4.56851 + 15.3339i 9.80967 22.6758 + 66.9747i −16.8606 23.2066i 60.0966 22.0089i 187.278 + 136.065i −23.4526 31.4587i
35.19 −2.29841 3.27373i 7.29605 + 2.37063i −5.43464 + 15.0487i −40.8790 −9.00849 29.3340i 39.2063 + 53.9628i 61.7566 16.7966i −17.9179 13.0181i 93.9566 + 133.827i
35.20 −2.22430 + 3.32453i 3.03403 + 0.985817i −6.10499 14.7895i −15.2943 −10.0260 + 7.89398i 44.5004 + 61.2496i 62.7474 + 12.6000i −57.2969 41.6286i 34.0190 50.8462i
See next 80 embeddings (of 248 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 95.62
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
4.b odd 2 1 inner
31.d even 5 1 inner
124.l odd 10 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 124.5.l.a 248
4.b odd 2 1 inner 124.5.l.a 248
31.d even 5 1 inner 124.5.l.a 248
124.l odd 10 1 inner 124.5.l.a 248
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
124.5.l.a 248 1.a even 1 1 trivial
124.5.l.a 248 4.b odd 2 1 inner
124.5.l.a 248 31.d even 5 1 inner
124.5.l.a 248 124.l odd 10 1 inner

Hecke kernels

This newform subspace is the entire newspace \(S_{5}^{\mathrm{new}}(124, [\chi])\).