LMFDB - Newform orbit 875.2.bb.a

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [875,2,Mod(82,875)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("875.82"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(875, base_ring=CyclotomicField(60)) chi = DirichletCharacter(H, H._module([27, 50])) N = Newforms(chi, 2, names="a")

Level:	$N$	$=$	$875 = 5^{3} \cdot 7$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	875.bb (of order $60$ , degree $16$ , not minimal)

Newform invariants

comment:select newform

sage:traces = [288,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.98691017686$
Analytic rank:	$0$
Dimension:	$288$
Relative dimension:	$18$ over $\Q(\zeta_{60})$
Twist minimal:	no (minimal twist has level 175)
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

$q$ -expansion

The algebraic $q$ -expansion of this newform has not been computed, but we have computed the trace expansion.

\operatorname{Tr}(f)(q) =

288 q - 2 q^{2} - 6 q^{3} + 10 q^{4} + 10 q^{7} - 64 q^{8} + 10 q^{9} - 6 q^{11} + 6 q^{12} + 20 q^{14} - 30 q^{16} + 12 q^{17} + 14 q^{18} + 30 q^{19} - 12 q^{21} + 8 q^{22} - 30 q^{23} - 48 q^{26} + 58 q^{28}+ \cdots - 62 q^{98}+O(q^{100})

288 * q - 2 * q^2 - 6 * q^3 + 10 * q^4 + 10 * q^7 - 64 * q^8 + 10 * q^9 - 6 * q^11 + 6 * q^12 + 20 * q^14 - 30 * q^16 + 12 * q^17 + 14 * q^18 + 30 * q^19 - 12 * q^21 + 8 * q^22 - 30 * q^23 - 48 * q^26 + 58 * q^28 - 18 * q^31 - 8 * q^32 + 150 * q^33 + 40 * q^36 - 12 * q^38 - 30 * q^39 - 166 * q^42 + 108 * q^43 + 10 * q^44 - 6 * q^46 + 24 * q^47 - 16 * q^51 + 24 * q^52 + 40 * q^53 + 30 * q^54 + 4 * q^56 + 216 * q^57 + 114 * q^58 - 90 * q^59 - 18 * q^61 + 16 * q^63 + 100 * q^64 - 90 * q^66 - 74 * q^67 - 342 * q^68 - 24 * q^71 + 222 * q^72 + 216 * q^73 - 90 * q^77 + 32 * q^78 + 10 * q^79 - 10 * q^81 - 216 * q^82 - 20 * q^84 - 6 * q^86 + 18 * q^87 - 58 * q^88 - 120 * q^89 - 12 * q^91 + 24 * q^92 - 106 * q^93 + 30 * q^94 - 90 * q^96 - 62 * 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.

comment:embeddings in the coefficient field

gp:mfembed(f)

Label	$a_{2}$			$a_{3}$			$a_{4}$				$a_{6}$			$a_{7}$			$a_{8}$			$a_{9}$
82.1	−2.53114	−	0.971615i	0.977922	−	0.0512507i	3.97637	+	3.58034i	0	−2.52506	−	0.820441i	2.54155	−	0.735207i	−4.12431	−	8.09441i	−2.02986	+	0.213347i	0
82.2	−2.18349	−	0.838165i	−1.19738	+	0.0627519i	2.57884	+	2.32200i	0	2.66706	+	0.866582i	−2.62853	+	0.301393i	−1.56104	−	3.06372i	−1.55379	+	0.163310i	0
82.3	−2.07887	−	0.798002i	−2.97775	+	0.156057i	2.19859	+	1.97962i	0	6.31487	+	2.05183i	1.33917	−	2.28180i	−0.968973	−	1.90172i	5.85905	−	0.615811i	0
82.4	−1.81626	−	0.697196i	2.40177	−	0.125871i	1.32642	+	1.19431i	0	−4.44999	−	1.44589i	2.13721	−	1.55960i	0.190005	+	0.372906i	2.76909	−	0.291043i	0
82.5	−1.47859	−	0.567578i	−0.936069	+	0.0490573i	0.377800	+	0.340173i	0	1.41191	+	0.458757i	0.0623449	+	2.64502i	1.07251	+	2.10492i	−2.10975	+	0.221743i	0
82.6	−0.782618	−	0.300419i	2.02474	−	0.106112i	−0.964050	−	0.868035i	0	−1.61648	−	0.525226i	0.522392	+	2.59367i	1.25487	+	2.46282i	1.10477	−	0.116116i	0
82.7	−0.596349	−	0.228917i	0.0491972	−	0.00257832i	−1.18306	−	1.06523i	0	−0.0299289	−	0.00972449i	−1.82620	−	1.91442i	1.04166	+	2.04438i	−2.98115	+	0.313332i	0
82.8	−0.278809	−	0.107025i	−3.11927	+	0.163474i	−1.42001	−	1.27858i	0	0.887175	+	0.288261i	−2.59603	+	0.510505i	0.530235	+	1.04064i	6.71954	−	0.706252i	0
82.9	0.00521563	+	0.00200209i	−2.07789	+	0.108898i	−1.48627	−	1.33824i	0	−0.0110555	−	0.00359216i	1.62930	+	2.08455i	−0.0101452	−	0.0199110i	1.32220	−	0.138969i	0
82.10	0.252007	+	0.0967363i	1.95874	−	0.102653i	−1.43214	−	1.28950i	0	0.503546	+	0.163612i	2.64466	+	0.0759508i	−0.481263	−	0.944532i	0.842568	−	0.0885574i	0
82.11	0.766047	+	0.294058i	−0.140222	+	0.00734873i	−0.985932	−	0.887737i	0	−0.109578	−	0.0356039i	1.23154	−	2.34165i	−1.23927	−	2.43220i	−2.96396	+	0.311524i	0
82.12	0.957274	+	0.367463i	1.16281	−	0.0609404i	−0.704945	−	0.634736i	0	1.13552	+	0.368954i	−2.47964	+	0.922709i	−1.37261	−	2.69390i	−1.63515	+	0.171861i	0
82.13	1.30359	+	0.500401i	3.22509	−	0.169020i	−0.0373446	−	0.0336253i	0	4.28878	+	1.39351i	−2.37511	−	1.16570i	−1.29970	−	2.55081i	7.38909	−	0.776624i	0
82.14	1.67005	+	0.641073i	−0.719894	+	0.0377280i	0.891813	+	0.802992i	0	−1.22645	−	0.398497i	−1.50450	+	2.17635i	−0.649660	−	1.27503i	−2.46674	+	0.259265i	0
82.15	1.78057	+	0.683496i	−1.92325	+	0.100793i	1.21696	+	1.09576i	0	−3.49337	−	1.13506i	2.62152	+	0.357251i	−0.313803	−	0.615873i	0.705160	−	0.0741153i	0
82.16	2.09413	+	0.803861i	−2.97123	+	0.155716i	2.25290	+	2.02852i	0	−6.34732	−	2.06237i	−1.16740	−	2.37427i	1.05050	+	2.06173i	5.82041	−	0.611750i	0
82.17	2.32523	+	0.892573i	1.91879	−	0.100560i	3.12372	+	2.81261i	0	4.55139	+	1.47884i	0.589885	−	2.57915i	2.49145	+	4.88974i	0.688086	−	0.0723207i	0
82.18	2.43619	+	0.935166i	0.773359	−	0.0405301i	3.57420	+	3.21822i	0	1.92195	+	0.624480i	0.425622	+	2.61129i	3.32847	+	6.53248i	−2.38712	+	0.250897i	0
143.1	−0.145421	−	2.77479i	−1.03115	−	0.835009i	−5.68928	+	0.597968i	0	−2.16703	+	2.98265i	1.54641	+	2.14677i	1.61724	+	10.2108i	−0.257705	−	1.21240i	0
143.2	−0.127179	−	2.42673i	1.58931	+	1.28700i	−3.88379	+	0.408202i	0	2.92107	−	4.02051i	−1.28591	−	2.31224i	0.724243	+	4.57269i	0.245810	+	1.15644i	0

See next 80 embeddings (of 288 total)

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
7.d	odd	6	1	inner
25.f	odd	20	1	inner
175.x	even	60	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	875.2.bb.a		288
5.b	even	2	1		875.2.bb.b		288
5.c	odd	4	1		175.2.x.a	✓	288
5.c	odd	4	1		875.2.bb.c		288
7.d	odd	6	1	inner	875.2.bb.a		288
25.d	even	5	1		875.2.bb.c		288
25.e	even	10	1		175.2.x.a	✓	288
25.f	odd	20	1	inner	875.2.bb.a		288
25.f	odd	20	1		875.2.bb.b		288
35.i	odd	6	1		875.2.bb.b		288
35.k	even	12	1		175.2.x.a	✓	288
35.k	even	12	1		875.2.bb.c		288
175.u	odd	30	1		175.2.x.a	✓	288
175.v	odd	30	1		875.2.bb.c		288
175.x	even	60	1	inner	875.2.bb.a		288
175.x	even	60	1		875.2.bb.b		288

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
175.2.x.a	✓	288	5.c	odd	4	1
175.2.x.a	✓	288	25.e	even	10	1
175.2.x.a	✓	288	35.k	even	12	1
175.2.x.a	✓	288	175.u	odd	30	1
875.2.bb.a		288	1.a	even	1	1	trivial
875.2.bb.a		288	7.d	odd	6	1	inner
875.2.bb.a		288	25.f	odd	20	1	inner
875.2.bb.a		288	175.x	even	60	1	inner
875.2.bb.b		288	5.b	even	2	1
875.2.bb.b		288	25.f	odd	20	1
875.2.bb.b		288	35.i	odd	6	1
875.2.bb.b		288	175.x	even	60	1
875.2.bb.c		288	5.c	odd	4	1
875.2.bb.c		288	25.d	even	5	1
875.2.bb.c		288	35.k	even	12	1
875.2.bb.c		288	175.v	odd	30	1

This newform subspace can be constructed as the kernel of the linear operator $T_{2}^{288} + 2 T_{2}^{287} - 3 T_{2}^{286} + 18 T_{2}^{285} + 184 T_{2}^{284} + 184 T_{2}^{283} + \cdots + 1$ T2^288 + 2*T2^287 - 3*T2^286 + 18*T2^285 + 184*T2^284 + 184*T2^283 - 293*T2^282 + 2820*T2^281 + 12053*T2^280 + 7744*T2^279 + 4917*T2^278 + 159070*T2^277 + 269724*T2^276 + 427462*T2^275 + 2100813*T2^274 + 1393636*T2^273 - 12123602*T2^272 + 35338738*T2^271 + 147103533*T2^270 - 382347228*T2^269 - 1494227904*T2^268 + 1872518244*T2^267 + 5484017547*T2^266 - 33437453800*T2^265 - 77148917693*T2^264 + 69703288954*T2^263 + 37063247822*T2^262 - 1507623825020*T2^261 - 1315975421565*T2^260 + 1001395570196*T2^259 - 12463281858793*T2^258 - 21157226792798*T2^257 + 91289486648636*T2^256 - 115198544510812*T2^255 - 911106924429346*T2^254 + 1954136640845380*T2^253 + 7050476747856215*T2^252 - 10665160100228564*T2^251 - 26168213794713957*T2^250 + 140743566228831560*T2^249 + 190431355899233748*T2^248 - 348804327008391716*T2^247 + 185865120707903982*T2^246 + 3676209165603794680*T2^245 + 133469869595431705*T2^244 + 1521172136807480272*T2^243 + 39088900926058446982*T2^242 - 23665521115071170442*T2^241 - 184009299436427651460*T2^240 + 534272055935002834184*T2^239 + 1345196575764686533525*T2^238 - 5258493890443124306986*T2^237 - 8158472171167470653911*T2^236 + 18800809420924474491132*T2^235 + 18449112920126175089667*T2^234 - 186056552247890903250812*T2^233 - 186159109172126238427811*T2^232 + 180473341619348734132866*T2^231 - 403511041916750174882640*T2^230 - 2350841536044410199502844*T2^229 + 467039001130622963061163*T2^228 - 8092135288135789568261082*T2^227 - 37157040824569710238975272*T2^226 + 56811171909509331093946972*T2^225 + 194900545152535169108511687*T2^224 - 322198030636495157655222098*T2^223 - 1125269816279733746371424947*T2^222 + 3299074554568297546172290776*T2^221 + 6016104020015523238870127112*T2^220 - 2759360733190106204519614348*T2^219 - 7536217720208158580065953176*T2^218 + 68477923028361645791784660114*T2^217 + 44308717711447658662910653017*T2^216 + 123262016424626012728772412536*T2^215 + 555567555074183777354098911153*T2^214 + 495563170322540983695145617640*T2^213 - 1700948888087317894201836391085*T2^212 + 3943949466960393196343931101782*T2^211 + 16924314362424440466132777459586*T2^210 - 15530675842032109513725755631280*T2^209 - 45477354397595831819099669780832*T2^208 + 26154681456365720645095054983302*T2^207 + 151589827030490223765630237202288*T2^206 - 732088703320222488024159606797364*T2^205 - 378829945922739820173423685349822*T2^204 - 1489266294100923088872548970952878*T2^203 - 1750383530587701057058283669979597*T2^202 - 14722060949551102065750213978607234*T2^201 + 4947085572624993514177461917906406*T2^200 - 54598530887363290403543511938565284*T2^199 - 65512425240595587873254505886960266*T2^198 - 141095865466435785190505919491569872*T2^197 + 276156292050458352871328097128359576*T2^196 - 807029535701138287634271892051732282*T2^195 - 702443103467382696115895609171670370*T2^194 + 685743988178414758659968496489363588*T2^193 + 6301124426405970620174168484437186709*T2^192 - 2587168651502764968803746718108989492*T2^191 + 7063795008480259850665139324423686221*T2^190 + 48872558326741085514918759562638580686*T2^189 + 78276191971282884428956382264453474502*T2^188 + 133007966046829605775992011175558427322*T2^187 + 396372449220737648026539959017951517703*T2^186 + 876116940080137207432399236750643205266*T2^185 + 444068660200389859278181120857764221119*T2^184 + 3467400826696605152880341905586578178408*T2^183 + 6851718663185136813276012439278861191043*T2^182 + 8042853220837085920876565922837758916902*T2^181 - 958277541997521272924627798920309386369*T2^180 + 45347683205883209679117580699802981457692*T2^179 + 56521535104833110490141224041205283515120*T2^178 + 19415203086663042206543816730276467189422*T2^177 - 45706116648676478814065355795597760039008*T2^176 + 210470400974931814414780834016999532174756*T2^175 - 16206829788308932781690692537787577820619*T2^174 - 605122375662464433901398184998832164983166*T2^173 - 905640283713692219381698227125921386865493*T2^172 - 3542952342137874068511165957979152104925572*T2^171 - 6739959563088001563327992331595143210676990*T2^170 - 10862623475168070867396823372953294707355042*T2^169 - 13454536481482032264515648117665118598860907*T2^168 - 76004389683834781920734199768000180849857398*T2^167 - 91739193427972941716759743188237528031279403*T2^166 - 92096291416688566187833532855998144993921962*T2^165 - 109961961760305799988884478884154495537084768*T2^164 - 609730966106637111932302029781327796948663608*T2^163 - 617597166360901809556840106968594518401993863*T2^162 - 207713628300893419247177951485555883689224032*T2^161 + 3501651605734236823750133454904947011876333*T2^160 - 1158465763741589384550988393664887902215918678*T2^159 - 550787863632407958794959070472922486335689860*T2^158 + 5330938713691518348365802795185190516714967202*T2^157 + 11399636017540014414066696007332780943902551017*T2^156 + 29615546626827239792096874608515969372081164826*T2^155 + 45949017927940986713498643884394112829937249481*T2^154 + 100154648773649141436864370535382985431483887924*T2^153 + 191002150866162847041152399242358509338356835802*T2^152 + 464404483695668935990079615569656992423230849858*T2^151 + 666795890050703234245693374847308162487306138055*T2^150 + 950098522906272063933673175741977342111036771488*T2^149 + 1593335370411930592004668308627017747839577109128*T2^148 + 3278578140220550434273394313561654298366011569942*T2^147 + 4183137606415825086752474687198610376833217452797*T2^146 + 3861289618725898703343481143689106351837052081378*T2^145 + 4775060539857248162964287548016990644026535791137*T2^144 + 7452723077492316583790842135789111326576486353402*T2^143 + 6625972680856950885344342630303701795753194029227*T2^142 - 7060376381498874931915354461517991285257877129472*T2^141 - 22222601984737213398112298691373870887549577735187*T2^140 - 52757077000237306055793647064761276249195262905768*T2^139 - 70591399850389722554762309081478066379942476712835*T2^138 - 128375771866537497634955755298199883954065002478328*T2^137 - 204293974050851784945811177970841111813902775479888*T2^136 - 417125751056483241577964973679431596829356137429594*T2^135 - 418079853181929422482948240418381760514451874811594*T2^134 - 259601078732859415128195714710072808909360940587096*T2^133 - 246176916802395017378408698398382487143941030960333*T2^132 - 879387635911799069331410500979867758315340501837522*T2^131 - 869178671354000790657286940773000643659800565853725*T2^130 + 1290561558037990614211426765544860855809104749087788*T2^129 + 2168274883515229938131632261139309255028674958813853*T2^128 + 657102270936597264108578508822828447042820071144942*T2^127 - 1715216687156591579538993681015454970288615611983418*T2^126 + 6383389222420391182079871470912674854238587229890008*T2^125 + 10666658732454687317619080527072936712881919628541522*T2^124 + 6383397292596697610682802936361606927382033627850942*T2^123 - 5077659862090278456909345565160242045662195186810643*T2^122 + 14711754455870288410391343654409722281313293640662458*T2^121 + 51167821982438649398488187830428713037967084828145213*T2^120 + 59480131278228582678389420613934814414047891106057492*T2^119 + 46628699717337262128962628016368371430624551172037005*T2^118 + 54720601497662248367009706125092637638085057896368842*T2^117 + 156519479731678694268660841279919725010731034391790957*T2^116 + 146432688123725527391426938464955711682083949148958646*T2^115 - 8634304661523108385067356759898942126295799368274314*T2^114 - 357961740995003223811951150941118959741624581259178696*T2^113 - 477980078801012977890879731462063992930863180698103833*T2^112 - 560069851750595951152407685348503569990630621430588522*T2^111 - 789525718219743322956160807519508266851912384128473780*T2^110 - 1353945523754612043182095304306662870259963190453934782*T2^109 - 1456176336300746752074619652618470283488520778176432329*T2^108 - 559079718808600237415828678475416848091091444689854762*T2^107 + 472381449875829904783433681052059150648008439751369118*T2^106 + 779728047233688876627989699151506554198278076881704612*T2^105 + 204270475297739998391931334906178620549664764339329029*T2^104 + 680968245460917928450155908023311216121360877323359014*T2^103 + 1642893629842330446412773010674782761010746663515579603*T2^102 + 2430702812911803857513268903306735899656803738419623848*T2^101 + 1756651158274482253000130494236603073698797458356519537*T2^100 + 1617681517034822236465690711242232306768994951206955634*T2^99 + 2788492612918178561960659149680087008192789354989976671*T2^98 + 4725074245717220741826385595639256782673446952544824712*T2^97 + 5919462329873509727494991711881062424411627262622551694*T2^96 + 5563565344568994495967145127040166442432481425506457522*T2^95 + 5389055638242475299920976509713965946279588566468570050*T2^94 + 5607861253403039922092953100987731587137177841871101672*T2^93 + 7002330435426448446089200941362593171472865957533160531*T2^92 + 7302693008582114276404066159360797590203040082457734492*T2^91 + 7072332047261980926130793277060520027204128601852706514*T2^90 + 6120653679666801376799353323978131007055994407565176734*T2^89 + 6018930409640539375240524536953325912849759791115369526*T2^88 + 5983383015759344638451680457947727767754775113244355844*T2^87 + 5652558327672361970273419338990935684336066868574492148*T2^86 + 4781363894606637783300383219576015516195457457295938988*T2^85 + 3858963728084717620664770188621840548967507176017664018*T2^84 + 3420703316643663667748674088995521341395144018141239364*T2^83 + 3074619292715097903768107186816864132529753233778069273*T2^82 + 2847233000609967914678962483308082194786649106602595898*T2^81 + 2206118337600052879385000455228201634611820513896586873*T2^80 + 1677423105036672908553607509685508491690749620102634360*T2^79 + 1196872473113029461136012893637446986194265277804279986*T2^78 + 1095075422078073964120298571637652420720847375808305498*T2^77 + 887736240798494003002797720298692073825182800105924615*T2^76 + 720252221231590664783425837931326271295447152153203360*T2^75 + 489040528752885349411933294176674723084855552770749083*T2^74 + 340148977095702625836301684417005178948786558214495814*T2^73 + 226283532653538350191360496986455547915059333045872077*T2^72 + 183813358284697583789531235541797593342704053266037426*T2^71 + 140164755945131799766693279477329705212747467184591109*T2^70 + 82134502368719666550349283519053178400881107381941868*T2^69 + 58023013511504137558640355975235690692005452149511712*T2^68 + 26410679709567293191022715080436320815068678192174864*T2^67 + 24461958562516275517445421688002947065559493157426218*T2^66 + 6024509802530499354028398028715984552474257823285598*T2^65 + 12237240879455538838572336026312566450743874202617192*T2^64 - 1935112398968555199137295582170832741257586866950492*T2^63 + 5225475338402387498925252531557765547406169960637268*T2^62 - 3168186077179707815737153112514995624328299918788348*T2^61 + 2726989635072008662262010883895821905586033322940548*T2^60 - 2408815413322071596486343764688554893922938614025516*T2^59 + 1507991294477688151736174089963289440983019174825385*T2^58 - 1350982245680910276093615439513789013359400600916466*T2^57 + 849988036892321046464180060095649354276228695519229*T2^56 - 731168148108304511215277567310083917054200688767128*T2^55 + 377588271861228439140840962998666319391624792348022*T2^54 - 306291786047242595797082600893648208564788030494342*T2^53 + 196968246409571401209954334258035550359504160880774*T2^52 - 120199127025892067192101963733614126663093200346884*T2^51 + 74148098300769906567645857276567675312511523447270*T2^50 - 45636421954765915835651610462997719660984005825584*T2^49 + 25987797041451385833750966910563418562014418046690*T2^48 - 16465396689779443896779436264123518580482523550948*T2^47 + 12207914094836138953511022278226557394391978145402*T2^46 - 6361918425911163575782972566921735738911862752572*T2^45 + 3533174941059807035228544585970776902362263342500*T2^44 - 2149217846897424302568113835862302845384553757760*T2^43 + 1162516638654933257083961329611941368964140046637*T2^42 - 540457517533520353796621296004456332884396621164*T2^41 + 227661013726099056910925036129445881225693628963*T2^40 - 105889742538587992009825273127882440919196705980*T2^39 + 44855890706819040949007584153934329433563587863*T2^38 - 15874481236342348415887608509647217729661756446*T2^37 + 5190629157654078564267124659844115162202091395*T2^36 - 1865767510763852378553813697884320588794190480*T2^35 + 705289580232926389278550391022348634147896509*T2^34 - 183171436826033219576003500774491288584864148*T2^33 + 42266092665516474006381044720891117025119421*T2^32 - 18580579461702792850805817198836753885526722*T2^31 + 6436738527511481678379919917709467186914312*T2^30 - 1141377739700178457134467281459498742037306*T2^29 + 322329359769516677285911373651087715545145*T2^28 - 174665434354067740669803793282492657239340*T2^27 + 49381705035082405048839888136089831268042*T2^26 - 8411364833481100479308253611375993137704*T2^25 + 2329873093480047950285338963294119901452*T2^24 - 902338945163330827604620614742374939370*T2^23 + 237213721456105126191396452022864482902*T2^22 - 41773908568820382650540538129451497944*T2^21 + 7729912702650919674391400153597463981*T2^20 - 2246266651824792358497711636323963202*T2^19 + 530096651551127682372410236582092923*T2^18 - 72526639855281283350764177152561498*T2^17 + 3872991686007015727116394281434143*T2^16 + 204766029686853405171418967511784*T2^15 + 10396974102166050539609074917953*T2^14 + 202840600086322090351079155368*T2^13 + 4040430825569262683028075079*T2^12 - 328231016787717384610485730*T2^11 - 882092219492276467798388*T2^10 - 10290414294607450257444*T2^9 + 1424688688239083176288*T2^8 - 4175034085957858940*T2^7 - 31107058404449968*T2^6 - 37249488804574*T2^5 + 1348809076009*T2^4 - 2245668848*T2^3 + 2552172*T2^2 - 1962*T2 + 1 acting on $S_{2}^{\mathrm{new}}(875, [\chi])$ .

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

$n$ :		e.g. 2-40 or 990-1000
Embeddings:		e.g. 1-3 or 82.18
Significant digits:
Format:

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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