Properties

 Label 5.27.c.a Level $5$ Weight $27$ Character orbit 5.c Analytic conductor $21.415$ Analytic rank $0$ Dimension $24$ CM no Inner twists $2$

Related objects

Newspace parameters

 Level: $$N$$ $$=$$ $$5$$ Weight: $$k$$ $$=$$ $$27$$ Character orbit: $$[\chi]$$ $$=$$ 5.c (of order $$4$$, degree $$2$$, minimal)

Newform invariants

 Self dual: no Analytic conductor: $$21.4146460365$$ Analytic rank: $$0$$ Dimension: $$24$$ Relative dimension: $$12$$ over $$\Q(i)$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

$q$-expansion

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

 $$\operatorname{Tr}(f)(q) =$$ $$24 q + 8190 q^{2} + 1867680 q^{3} - 140947920 q^{5} - 3382472712 q^{6} - 99234643200 q^{7} - 2004366809340 q^{8}+O(q^{10})$$ 24 * q + 8190 * q^2 + 1867680 * q^3 - 140947920 * q^5 - 3382472712 * q^6 - 99234643200 * q^7 - 2004366809340 * q^8 $$\operatorname{Tr}(f)(q) =$$ $$24 q + 8190 q^{2} + 1867680 q^{3} - 140947920 q^{5} - 3382472712 q^{6} - 99234643200 q^{7} - 2004366809340 q^{8} - 1486502924970 q^{10} - 60046450487712 q^{11} + 474303804173880 q^{12} - 175933888149240 q^{13} + 81\!\cdots\!60 q^{15}+ \cdots + 37\!\cdots\!90 q^{98}+O(q^{100})$$ 24 * q + 8190 * q^2 + 1867680 * q^3 - 140947920 * q^5 - 3382472712 * q^6 - 99234643200 * q^7 - 2004366809340 * q^8 - 1486502924970 * q^10 - 60046450487712 * q^11 + 474303804173880 * q^12 - 175933888149240 * q^13 + 8120813383152960 * q^15 - 33177982875701256 * q^16 + 13120603958605320 * q^17 + 30866287060816530 * q^18 - 155387715501860460 * q^20 + 711072085237596768 * q^21 - 1230085358274609120 * q^22 - 95943648493582560 * q^23 - 2199572636699820600 * q^25 + 5610652365807815508 * q^26 - 4182554138103802080 * q^27 + 9022697066815419960 * q^28 - 73497992102613921840 * q^30 + 136536207174201936768 * q^31 - 313156508993493901560 * q^32 + 310679334418782310560 * q^33 - 294265004156402368320 * q^35 + 1280456324930471178684 * q^36 - 813771390050070972840 * q^37 - 241574669977239410760 * q^38 - 634199087129857022100 * q^40 - 1209719584341877336992 * q^41 + 3329982079791874237920 * q^42 - 2155184970418473088800 * q^43 + 8900452148996849486760 * q^45 - 9558960779134484923272 * q^46 + 14032272766974133560480 * q^47 - 23339469323152065294960 * q^48 - 5039825198339566324350 * q^50 - 34517174933375733238272 * q^51 + 89834235163276703786700 * q^52 - 76996005973852456719720 * q^53 + 61786508697335020764960 * q^55 + 140965426896397798196880 * q^56 - 373196499625490096640960 * q^57 + 527990314981987315382160 * q^58 - 985009875968846023801320 * q^60 + 711008904295257078187488 * q^61 - 106522048356410497848120 * q^62 + 129194443701484657698720 * q^63 + 810043281159028896596760 * q^65 - 243183023298774209168544 * q^66 + 475247161241828436325920 * q^67 - 1328735440043135338553820 * q^68 - 1284031520218999793566920 * q^70 - 5316544531031301273526272 * q^71 + 6424730229084419392336260 * q^72 + 368145928043753098041240 * q^73 - 1071958391540662870531200 * q^75 - 193843537989214188398640 * q^76 + 10746086757941471790823200 * q^77 - 2877347849192885454991800 * q^78 - 155629044348497668149120 * q^80 - 13389238123125713812551096 * q^81 - 11578218915296284645122720 * q^82 + 25615096518304734510222720 * q^83 - 60208098774533809021022520 * q^85 + 56773655020233836832486168 * q^86 - 25953487917103015108688640 * q^87 + 117068604801345686184349920 * q^88 - 128643549677224721883790890 * q^90 - 19525332839000266679349312 * q^91 + 18999183544674712785412920 * q^92 + 207592489093568143530468960 * q^93 - 172205668812635374982450400 * q^95 - 605527074895544071145393952 * q^96 + 347025186458821372557867480 * q^97 + 372096096878694378037335390 * q^98

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 −9199.72 9199.72i 1.92148e6 1.92148e6i 1.02161e8i 1.20945e9 + 1.65366e8i −3.53542e10 2.78396e10 + 2.78396e10i 3.22468e11 3.22468e11i 4.84231e12i −9.60528e12 1.26479e13i
2.2 −8967.06 8967.06i −1.25875e6 + 1.25875e6i 9.37076e7i 2.09822e8 + 1.20254e9i 2.25746e10 5.31741e10 + 5.31741e10i 2.38512e11 2.38512e11i 6.27038e11i 8.90172e12 1.26647e13i
2.3 −8964.00 8964.00i −84346.8 + 84346.8i 9.35978e7i −6.90551e8 1.00661e9i 1.51217e9 −8.97185e10 8.97185e10i 2.37446e11 2.37446e11i 2.52764e12i −2.83311e12 + 1.52133e13i
2.4 −3781.13 3781.13i 1.14164e6 1.14164e6i 3.85150e7i −1.21579e9 + 1.09366e8i −8.63336e9 1.09895e11 + 1.09895e11i −3.99377e11 + 3.99377e11i 6.48110e10i 5.01060e12 + 4.18355e12i
2.5 −2621.08 2621.08i −823115. + 823115.i 5.33688e7i 9.07026e8 8.16957e8i 4.31489e9 3.09387e10 + 3.09387e10i −3.15781e11 + 3.15781e11i 1.18683e12i −4.51869e12 2.36078e11i
2.6 −1256.27 1256.27i 745542. 745542.i 6.39524e7i 1.73270e8 + 1.20834e9i −1.87321e9 −1.19717e11 1.19717e11i −1.64649e11 + 1.64649e11i 1.43020e12i 1.30034e12 1.73568e12i
2.7 584.877 + 584.877i −2.17135e6 + 2.17135e6i 6.64247e7i −1.21727e9 + 9.14507e7i −2.53995e9 −4.74948e10 4.74948e10i 7.81007e10 7.81007e10i 6.88765e12i −7.65443e11 6.58468e11i
2.8 4190.94 + 4190.94i 1.61385e6 1.61385e6i 3.19809e7i 6.93244e8 1.00475e9i 1.35270e10 −1.14147e10 1.14147e10i 4.15279e11 4.15279e11i 2.66713e12i 7.11620e12 1.30552e12i
2.9 6254.19 + 6254.19i −748889. + 748889.i 1.11210e7i 7.43869e8 + 9.67872e8i −9.36739e9 5.67260e10 + 5.67260e10i 3.50159e11 3.50159e11i 1.42020e12i −1.40096e12 + 1.07056e13i
2.10 6346.94 + 6346.94i 105171. 105171.i 1.34583e7i −1.17280e9 3.38608e8i 1.33503e9 1.02411e10 + 1.02411e10i 3.40516e11 3.40516e11i 2.51974e12i −5.29457e12 9.59281e12i
2.11 10388.0 + 10388.0i −1.27015e6 + 1.27015e6i 1.48710e8i 4.12302e8 1.14897e9i −2.63886e10 −8.34659e10 8.34659e10i −8.47671e11 + 8.47671e11i 6.84708e11i 1.62184e13 7.65243e12i
2.12 11119.4 + 11119.4i 1.76277e6 1.76277e6i 1.80172e8i −1.23038e8 + 1.21449e9i 3.92017e10 1.33787e10 + 1.33787e10i −1.25719e12 + 1.25719e12i 3.67282e12i −1.48724e13 + 1.21362e13i
3.1 −9199.72 + 9199.72i 1.92148e6 + 1.92148e6i 1.02161e8i 1.20945e9 1.65366e8i −3.53542e10 2.78396e10 2.78396e10i 3.22468e11 + 3.22468e11i 4.84231e12i −9.60528e12 + 1.26479e13i
3.2 −8967.06 + 8967.06i −1.25875e6 1.25875e6i 9.37076e7i 2.09822e8 1.20254e9i 2.25746e10 5.31741e10 5.31741e10i 2.38512e11 + 2.38512e11i 6.27038e11i 8.90172e12 + 1.26647e13i
3.3 −8964.00 + 8964.00i −84346.8 84346.8i 9.35978e7i −6.90551e8 + 1.00661e9i 1.51217e9 −8.97185e10 + 8.97185e10i 2.37446e11 + 2.37446e11i 2.52764e12i −2.83311e12 1.52133e13i
3.4 −3781.13 + 3781.13i 1.14164e6 + 1.14164e6i 3.85150e7i −1.21579e9 1.09366e8i −8.63336e9 1.09895e11 1.09895e11i −3.99377e11 3.99377e11i 6.48110e10i 5.01060e12 4.18355e12i
3.5 −2621.08 + 2621.08i −823115. 823115.i 5.33688e7i 9.07026e8 + 8.16957e8i 4.31489e9 3.09387e10 3.09387e10i −3.15781e11 3.15781e11i 1.18683e12i −4.51869e12 + 2.36078e11i
3.6 −1256.27 + 1256.27i 745542. + 745542.i 6.39524e7i 1.73270e8 1.20834e9i −1.87321e9 −1.19717e11 + 1.19717e11i −1.64649e11 1.64649e11i 1.43020e12i 1.30034e12 + 1.73568e12i
3.7 584.877 584.877i −2.17135e6 2.17135e6i 6.64247e7i −1.21727e9 9.14507e7i −2.53995e9 −4.74948e10 + 4.74948e10i 7.81007e10 + 7.81007e10i 6.88765e12i −7.65443e11 + 6.58468e11i
3.8 4190.94 4190.94i 1.61385e6 + 1.61385e6i 3.19809e7i 6.93244e8 + 1.00475e9i 1.35270e10 −1.14147e10 + 1.14147e10i 4.15279e11 + 4.15279e11i 2.66713e12i 7.11620e12 + 1.30552e12i
See all 24 embeddings
 $$n$$: e.g. 2-40 or 990-1000 Embeddings: e.g. 1-3 or 3.12 Significant digits: Format: Complex embeddings Normalized embeddings Satake parameters Satake angles

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
5.c odd 4 1 inner

Twists

By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 5.27.c.a 24
5.b even 2 1 25.27.c.b 24
5.c odd 4 1 inner 5.27.c.a 24
5.c odd 4 1 25.27.c.b 24

By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
5.27.c.a 24 1.a even 1 1 trivial
5.27.c.a 24 5.c odd 4 1 inner
25.27.c.b 24 5.b even 2 1
25.27.c.b 24 5.c odd 4 1

Hecke kernels

This newform subspace is the entire newspace $$S_{27}^{\mathrm{new}}(5, [\chi])$$.