Properties

Label 108.5.j.a
Level 108
Weight 5
Character orbit 108.j
Analytic conductor 11.164
Analytic rank 0
Dimension 420
CM no
Inner twists 4

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 108 = 2^{2} \cdot 3^{3} \)
Weight: \( k \) = \( 5 \)
Character orbit: \([\chi]\) = 108.j (of order \(18\), degree \(6\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(11.1639560131\)
Analytic rank: \(0\)
Dimension: \(420\)
Relative dimension: \(70\) over \(\Q(\zeta_{18})\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 420q - 6q^{2} - 6q^{4} - 12q^{5} - 6q^{6} - 3q^{8} - 12q^{9} + O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \( 420q - 6q^{2} - 6q^{4} - 12q^{5} - 6q^{6} - 3q^{8} - 12q^{9} - 3q^{10} + 39q^{12} - 12q^{13} - 861q^{14} - 6q^{16} - 6q^{17} + 729q^{18} + 1947q^{20} - 12q^{21} - 6q^{22} - 354q^{24} - 12q^{25} - 4710q^{26} - 12q^{28} - 1596q^{29} + 3951q^{30} + 4944q^{32} - 3732q^{33} + 42q^{34} - 2136q^{36} - 6q^{37} - 6084q^{38} + 1869q^{40} + 8268q^{41} - 19566q^{42} + 1509q^{44} - 1212q^{45} - 3q^{46} + 31965q^{48} - 12q^{49} + 23163q^{50} - 2787q^{52} - 24q^{53} - 8994q^{54} - 33165q^{56} - 7386q^{57} + 12279q^{58} - 39102q^{60} - 12q^{61} - 12774q^{62} - 3q^{64} + 13524q^{65} + 47157q^{66} + 55671q^{68} + 6420q^{69} - 7257q^{70} + 6276q^{72} - 6q^{73} + 6783q^{74} - 774q^{76} - 17004q^{77} - 43746q^{78} - 64002q^{80} - 14892q^{81} - 12q^{82} - 39846q^{84} + 3738q^{85} - 2562q^{86} - 12294q^{88} - 15774q^{89} + 107706q^{90} + 66819q^{92} - 10092q^{93} + 6663q^{94} - 6870q^{96} - 16932q^{97} - 58998q^{98} + O(q^{100}) \)

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 \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
7.1 −3.99762 0.137857i 5.81196 6.87176i 15.9620 + 1.10220i −8.59701 48.7561i −24.1814 + 26.6695i 32.6195 38.8744i −63.6581 6.60665i −13.4422 79.8768i 27.6463 + 196.094i
7.2 −3.98892 0.297585i −6.50989 + 6.21461i 15.8229 + 2.37409i −0.917019 5.20068i 27.8168 22.8523i −5.99386 + 7.14320i −62.4097 14.1787i 3.75733 80.9128i 2.11027 + 21.0179i
7.3 −3.96940 0.493852i 8.74142 + 2.14186i 15.5122 + 3.92059i 3.38596 + 19.2027i −33.6404 12.8189i 59.9969 71.5016i −59.6380 23.2231i 71.8248 + 37.4459i −3.95691 77.8955i
7.4 −3.96518 0.526660i 6.87028 5.81371i 15.4453 + 4.17660i 4.27785 + 24.2609i −30.3037 + 19.4341i −42.2969 + 50.4075i −59.0435 24.6954i 13.4016 79.8836i −4.18518 98.4516i
7.5 −3.93992 + 0.690649i −2.62931 8.60736i 15.0460 5.44221i −0.426714 2.42002i 16.3040 + 32.0964i −27.6515 + 32.9538i −55.5215 + 31.8334i −67.1734 + 45.2629i 3.35260 + 9.23997i
7.6 −3.93576 + 0.713980i 0.964020 + 8.94822i 14.9805 5.62011i 7.19320 + 40.7946i −10.1830 34.5298i −36.3946 + 43.3734i −54.9469 + 32.8152i −79.1413 + 17.2525i −57.4373 155.422i
7.7 −3.88326 + 0.959324i −8.67232 2.40643i 14.1594 7.45061i −2.07418 11.7633i 35.9854 + 1.02521i 23.6467 28.1810i −47.8370 + 42.5161i 69.4182 + 41.7386i 19.3394 + 43.6900i
7.8 −3.76323 1.35575i 4.63322 + 7.71578i 12.3239 + 10.2040i −5.82341 33.0262i −6.97519 35.3178i −25.3950 + 30.2645i −32.5435 55.1083i −38.0666 + 71.4978i −22.8605 + 132.180i
7.9 −3.62636 1.68805i −8.87066 1.52033i 10.3010 + 12.2430i 7.76842 + 44.0569i 29.6018 + 20.4874i 7.01781 8.36350i −16.6883 61.7859i 76.3772 + 26.9726i 46.1991 172.880i
7.10 −3.59139 + 1.76123i 8.67232 + 2.40643i 9.79617 12.6505i −2.07418 11.7633i −35.3839 + 6.63149i −23.6467 + 28.1810i −12.9015 + 62.6861i 69.4182 + 41.7386i 28.1670 + 38.5934i
7.11 −3.47391 + 1.98292i −0.964020 8.94822i 8.13606 13.7770i 7.19320 + 40.7946i 21.0925 + 29.1737i 36.3946 43.3734i −0.945324 + 63.9930i −79.1413 + 17.2525i −105.881 127.453i
7.12 −3.46210 + 2.00347i 2.62931 + 8.60736i 7.97224 13.8724i −0.426714 2.42002i −26.3475 24.5318i 27.6515 32.9538i 0.192185 + 63.9997i −67.1734 + 45.2629i 6.32575 + 7.52343i
7.13 −3.43437 2.05063i 0.424142 8.99000i 7.58985 + 14.0852i 2.37776 + 13.4850i −19.8918 + 30.0053i 18.1869 21.6743i 2.81722 63.9380i −80.6402 7.62607i 19.4865 51.1883i
7.14 −3.38252 2.13508i −5.83883 6.84895i 6.88287 + 14.4439i −4.58821 26.0210i 5.12690 + 35.6331i −28.7538 + 34.2674i 7.55742 63.5522i −12.8162 + 79.9797i −40.0372 + 97.8128i
7.15 −3.23826 2.34812i −1.93752 + 8.78897i 4.97268 + 15.2076i 0.0896331 + 0.508335i 26.9118 23.9115i 39.0942 46.5907i 19.6065 60.9228i −73.4920 34.0577i 0.903374 1.85659i
7.16 −2.97374 + 2.67523i −5.81196 + 6.87176i 1.68632 15.9109i −8.59701 48.7561i −1.10023 35.9832i −32.6195 + 38.8744i 37.5506 + 51.8262i −13.4422 79.8768i 155.999 + 121.989i
7.17 −2.89182 2.76358i 8.96055 0.841750i 0.725269 + 15.9836i −0.256732 1.45600i −28.2386 22.3290i −22.3218 + 26.6021i 42.0745 48.2259i 79.5829 15.0851i −3.28135 + 4.91999i
7.18 −2.86440 + 2.79199i 6.50989 6.21461i 0.409598 15.9948i −0.917019 5.20068i −1.29583 + 35.9767i 5.99386 7.14320i 43.4839 + 46.9590i 3.75733 80.9128i 17.1469 + 12.3365i
7.19 −2.72329 + 2.92979i −8.74142 2.14186i −1.16736 15.9574i 3.38596 + 19.2027i 30.0807 19.7776i −59.9969 + 71.5016i 49.9308 + 40.0364i 71.8248 + 37.4459i −65.4810 42.3745i
7.20 −2.69897 + 2.95221i −6.87028 + 5.81371i −1.43111 15.9359i 4.27785 + 24.2609i 1.37940 35.9736i 42.2969 50.4075i 50.9086 + 38.7855i 13.4016 79.8836i −83.1690 52.8503i
See next 80 embeddings (of 420 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 103.70
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
4.b odd 2 1 inner
27.e even 9 1 inner
108.j odd 18 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 108.5.j.a 420
4.b odd 2 1 inner 108.5.j.a 420
27.e even 9 1 inner 108.5.j.a 420
108.j odd 18 1 inner 108.5.j.a 420
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
108.5.j.a 420 1.a even 1 1 trivial
108.5.j.a 420 4.b odd 2 1 inner
108.5.j.a 420 27.e even 9 1 inner
108.5.j.a 420 108.j odd 18 1 inner

Hecke kernels

This newform subspace is the entire newspace \(S_{5}^{\mathrm{new}}(108, [\chi])\).

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database