Properties

Label 4.35.b
Level 4
Weight 35
Character orbit b
Rep. character \(\chi_{4}(3,\cdot)\)
Character field \(\Q\)
Dimension 16
Newforms 1
Sturm bound 17
Trace bound 0

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Defining parameters

Level: \( N \) = \( 4 = 2^{2} \)
Weight: \( k \) = \( 35 \)
Character orbit: \([\chi]\) = 4.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 4 \)
Character field: \(\Q\)
Newforms: \( 1 \)
Sturm bound: \(17\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{35}(4, [\chi])\).

Total New Old
Modular forms 18 18 0
Cusp forms 16 16 0
Eisenstein series 2 2 0

Trace form

\(16q \) \(\mathstrut -\mathstrut 27372q^{2} \) \(\mathstrut -\mathstrut 20032875248q^{4} \) \(\mathstrut -\mathstrut 21372255840q^{5} \) \(\mathstrut +\mathstrut 20836736461728q^{6} \) \(\mathstrut +\mathstrut 2284358011394112q^{8} \) \(\mathstrut -\mathstrut 67828545645364080q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(16q \) \(\mathstrut -\mathstrut 27372q^{2} \) \(\mathstrut -\mathstrut 20032875248q^{4} \) \(\mathstrut -\mathstrut 21372255840q^{5} \) \(\mathstrut +\mathstrut 20836736461728q^{6} \) \(\mathstrut +\mathstrut 2284358011394112q^{8} \) \(\mathstrut -\mathstrut 67828545645364080q^{9} \) \(\mathstrut -\mathstrut 45113792455239160q^{10} \) \(\mathstrut +\mathstrut 2389205919902175360q^{12} \) \(\mathstrut -\mathstrut 5233507036411659616q^{13} \) \(\mathstrut -\mathstrut 78584294183795706432q^{14} \) \(\mathstrut +\mathstrut 495182112183820124416q^{16} \) \(\mathstrut -\mathstrut 603670905919309938144q^{17} \) \(\mathstrut -\mathstrut 3049682100893194226508q^{18} \) \(\mathstrut -\mathstrut 33058393758449688290400q^{20} \) \(\mathstrut +\mathstrut 51436061805005728413696q^{21} \) \(\mathstrut +\mathstrut 71660876143050404765280q^{22} \) \(\mathstrut +\mathstrut 216144869785928938234368q^{24} \) \(\mathstrut +\mathstrut 1224730607199300816400560q^{25} \) \(\mathstrut -\mathstrut 2068583291215840445568696q^{26} \) \(\mathstrut +\mathstrut 891252510406495618671360q^{28} \) \(\mathstrut -\mathstrut 4086289565288128397679456q^{29} \) \(\mathstrut +\mathstrut 29601064663371600024444480q^{30} \) \(\mathstrut +\mathstrut 20026414012547463259849728q^{32} \) \(\mathstrut +\mathstrut 73954448514753271238568960q^{33} \) \(\mathstrut +\mathstrut 46288216238217191722231976q^{34} \) \(\mathstrut +\mathstrut 569062048300724903070378384q^{36} \) \(\mathstrut +\mathstrut 950385175701396416644593056q^{37} \) \(\mathstrut -\mathstrut 123498782719680108073563360q^{38} \) \(\mathstrut -\mathstrut 3250024485723791435879459200q^{40} \) \(\mathstrut +\mathstrut 469238845433510127731349792q^{41} \) \(\mathstrut +\mathstrut 2352670327884382399711157760q^{42} \) \(\mathstrut +\mathstrut 7327222247557584897899214720q^{44} \) \(\mathstrut -\mathstrut 24427097188106605438098250080q^{45} \) \(\mathstrut -\mathstrut 19562783684402230406331003072q^{46} \) \(\mathstrut +\mathstrut 10576141603633237485164267520q^{48} \) \(\mathstrut -\mathstrut 5662649722408510114314091760q^{49} \) \(\mathstrut +\mathstrut 20191932196464263485504736220q^{50} \) \(\mathstrut -\mathstrut 299155663662273783907276503904q^{52} \) \(\mathstrut -\mathstrut 287274278887575172234950512736q^{53} \) \(\mathstrut +\mathstrut 6047252470624543429578889536q^{54} \) \(\mathstrut +\mathstrut 957626384837555513184792726528q^{56} \) \(\mathstrut +\mathstrut 2791286265941381406754467578880q^{57} \) \(\mathstrut -\mathstrut 314499391713380785247660833336q^{58} \) \(\mathstrut +\mathstrut 1103184540481814815474103512320q^{60} \) \(\mathstrut -\mathstrut 7360215904797065436447249778528q^{61} \) \(\mathstrut +\mathstrut 6668101684324825273374014288640q^{62} \) \(\mathstrut -\mathstrut 4672502276277215477475812569088q^{64} \) \(\mathstrut +\mathstrut 7390500022468645317433010287680q^{65} \) \(\mathstrut -\mathstrut 12460359580334220374288279205120q^{66} \) \(\mathstrut +\mathstrut 3201090312765007118305938045984q^{68} \) \(\mathstrut -\mathstrut 20909099675706939600670541666304q^{69} \) \(\mathstrut -\mathstrut 13302319794857519494110175324800q^{70} \) \(\mathstrut -\mathstrut 776423968147266229824274003392q^{72} \) \(\mathstrut -\mathstrut 21322365514881309087265291408096q^{73} \) \(\mathstrut +\mathstrut 60200090281780873185690769101576q^{74} \) \(\mathstrut -\mathstrut 104909582027053727863743869884800q^{76} \) \(\mathstrut +\mathstrut 31510097566037837419459121448960q^{77} \) \(\mathstrut +\mathstrut 173718506967281862717403400063040q^{78} \) \(\mathstrut +\mathstrut 360511559214548868760655536888320q^{80} \) \(\mathstrut -\mathstrut 262819454584631237298859074129648q^{81} \) \(\mathstrut -\mathstrut 127799686177535642546403976474264q^{82} \) \(\mathstrut -\mathstrut 481860976739335096182940424300544q^{84} \) \(\mathstrut +\mathstrut 2066519418228326883252673443837760q^{85} \) \(\mathstrut +\mathstrut 680164732953303409567751182232928q^{86} \) \(\mathstrut -\mathstrut 1868588957981221169228370505105920q^{88} \) \(\mathstrut -\mathstrut 2487774705888249186282098457137376q^{89} \) \(\mathstrut +\mathstrut 2710136859758550244207319911170120q^{90} \) \(\mathstrut -\mathstrut 5719642193953545223478177490435840q^{92} \) \(\mathstrut -\mathstrut 4648987096869411453766406983557120q^{93} \) \(\mathstrut -\mathstrut 174301665834847119752293250078592q^{94} \) \(\mathstrut -\mathstrut 1356265248520894619800195113541632q^{96} \) \(\mathstrut +\mathstrut 7119191713926779638291321673063456q^{97} \) \(\mathstrut +\mathstrut 16929214407930779244441537548523732q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{35}^{\mathrm{new}}(4, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
4.35.b.a \(16\) \(29.290\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(-27372\) \(0\) \(-21372255840\) \(0\) \(q+(-1711+\beta _{1})q^{2}+(19-76\beta _{1}-\beta _{2}+\cdots)q^{3}+\cdots\)