Properties

Label 5.35.c
Level 5
Weight 35
Character orbit c
Rep. character \(\chi_{5}(2,\cdot)\)
Character field \(\Q(\zeta_{4})\)
Dimension 32
Newforms 1
Sturm bound 17
Trace bound 0

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Defining parameters

Level: \( N \) = \( 5 \)
Weight: \( k \) = \( 35 \)
Character orbit: \([\chi]\) = 5.c (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 5 \)
Character field: \(\Q(i)\)
Newforms: \( 1 \)
Sturm bound: \(17\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{35}(5, [\chi])\).

Total New Old
Modular forms 36 36 0
Cusp forms 32 32 0
Eisenstein series 4 4 0

Trace form

\(32q \) \(\mathstrut +\mathstrut 131070q^{2} \) \(\mathstrut -\mathstrut 78988260q^{3} \) \(\mathstrut -\mathstrut 730721770860q^{5} \) \(\mathstrut -\mathstrut 44043049959816q^{6} \) \(\mathstrut +\mathstrut 5337954235100q^{7} \) \(\mathstrut -\mathstrut 4536119823236220q^{8} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(32q \) \(\mathstrut +\mathstrut 131070q^{2} \) \(\mathstrut -\mathstrut 78988260q^{3} \) \(\mathstrut -\mathstrut 730721770860q^{5} \) \(\mathstrut -\mathstrut 44043049959816q^{6} \) \(\mathstrut +\mathstrut 5337954235100q^{7} \) \(\mathstrut -\mathstrut 4536119823236220q^{8} \) \(\mathstrut +\mathstrut 141196165961877590q^{10} \) \(\mathstrut +\mathstrut 365981602487621544q^{11} \) \(\mathstrut -\mathstrut 5313878568511975560q^{12} \) \(\mathstrut -\mathstrut 11000397968713344520q^{13} \) \(\mathstrut +\mathstrut 208604390017026786780q^{15} \) \(\mathstrut -\mathstrut 1456002327393916605448q^{16} \) \(\mathstrut +\mathstrut 496656489553605410760q^{17} \) \(\mathstrut +\mathstrut 1956191845428178111890q^{18} \) \(\mathstrut +\mathstrut 21729462132767742779220q^{20} \) \(\mathstrut -\mathstrut 142103646776097180182616q^{21} \) \(\mathstrut +\mathstrut 204776256011020418595040q^{22} \) \(\mathstrut -\mathstrut 436662638834307282633780q^{23} \) \(\mathstrut +\mathstrut 1269373145455066350614600q^{25} \) \(\mathstrut -\mathstrut 5758044909260756123220396q^{26} \) \(\mathstrut +\mathstrut 7995615376341697400032560q^{27} \) \(\mathstrut +\mathstrut 884081328441809235881080q^{28} \) \(\mathstrut +\mathstrut 16906131495392963185393680q^{30} \) \(\mathstrut +\mathstrut 84491420536973998188491704q^{31} \) \(\mathstrut -\mathstrut 184975661677973569185317880q^{32} \) \(\mathstrut +\mathstrut 73478673331281977814021480q^{33} \) \(\mathstrut -\mathstrut 332848603752554511148164660q^{35} \) \(\mathstrut +\mathstrut 1137988291793068131741823932q^{36} \) \(\mathstrut -\mathstrut 333379985446943362532279920q^{37} \) \(\mathstrut -\mathstrut 1419101265678050265971769480q^{38} \) \(\mathstrut +\mathstrut 4641604844152767517723905900q^{40} \) \(\mathstrut +\mathstrut 3652223875741628991126246984q^{41} \) \(\mathstrut -\mathstrut 4739529391137459161391231840q^{42} \) \(\mathstrut +\mathstrut 16353372323322642143796902300q^{43} \) \(\mathstrut -\mathstrut 54286650153199422028483226820q^{45} \) \(\mathstrut +\mathstrut 131432785549604658942769746424q^{46} \) \(\mathstrut -\mathstrut 164755893091890118218758986260q^{47} \) \(\mathstrut +\mathstrut 267416366563859197412890248720q^{48} \) \(\mathstrut -\mathstrut 497290949765735966798667321150q^{50} \) \(\mathstrut +\mathstrut 879726622206121123479191444184q^{51} \) \(\mathstrut -\mathstrut 1364297502096066356787005826100q^{52} \) \(\mathstrut +\mathstrut 827578466548898383340593310640q^{53} \) \(\mathstrut -\mathstrut 1221257473238015705547088196120q^{55} \) \(\mathstrut +\mathstrut 2582027089558247357967654389520q^{56} \) \(\mathstrut -\mathstrut 3021243382907908474517658024480q^{57} \) \(\mathstrut +\mathstrut 2354096772250584899097633644880q^{58} \) \(\mathstrut -\mathstrut 4980359145024739517552715163560q^{60} \) \(\mathstrut +\mathstrut 10984341568764658290951563973544q^{61} \) \(\mathstrut -\mathstrut 17271108259627677777618202511160q^{62} \) \(\mathstrut +\mathstrut 8610875544094751042813983810860q^{63} \) \(\mathstrut -\mathstrut 3889653492316185824736749428320q^{65} \) \(\mathstrut -\mathstrut 27230920485870501670249585219872q^{66} \) \(\mathstrut +\mathstrut 23820125360634701614572823748060q^{67} \) \(\mathstrut -\mathstrut 16651918880901511226895130538460q^{68} \) \(\mathstrut +\mathstrut 102445984984636060085153989346040q^{70} \) \(\mathstrut -\mathstrut 162839011061674956057132387035976q^{71} \) \(\mathstrut +\mathstrut 414631921651932227241773986664580q^{72} \) \(\mathstrut -\mathstrut 290761010682860591477846798111680q^{73} \) \(\mathstrut +\mathstrut 254021604564596224038530548706700q^{75} \) \(\mathstrut -\mathstrut 588265232627198985506540939882160q^{76} \) \(\mathstrut +\mathstrut 319978294665614883220802415073800q^{77} \) \(\mathstrut +\mathstrut 251541126280658548479082634723400q^{78} \) \(\mathstrut -\mathstrut 119374410596579550068027983848960q^{80} \) \(\mathstrut +\mathstrut 46998375893846038447057289461032q^{81} \) \(\mathstrut -\mathstrut 480327268957748332277390888075360q^{82} \) \(\mathstrut -\mathstrut 987023986692010851073141552006740q^{83} \) \(\mathstrut +\mathstrut 541698100211230692020622872942840q^{85} \) \(\mathstrut +\mathstrut 2563129008649864341703296140749464q^{86} \) \(\mathstrut -\mathstrut 3601816973758507596709087426821120q^{87} \) \(\mathstrut +\mathstrut 4467012425011508421563596255937760q^{88} \) \(\mathstrut -\mathstrut 12012751049536233233863224473584170q^{90} \) \(\mathstrut +\mathstrut 9733965316721903607010024138955704q^{91} \) \(\mathstrut -\mathstrut 5821741665997247478385288152437640q^{92} \) \(\mathstrut +\mathstrut 1188287280403911040224754269765480q^{93} \) \(\mathstrut +\mathstrut 1357322148200915652339912426951600q^{95} \) \(\mathstrut +\mathstrut 24207915861230982937605202170100704q^{96} \) \(\mathstrut -\mathstrut 29449480417814037063188176022138560q^{97} \) \(\mathstrut +\mathstrut 25177080070348305002521179770557470q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{35}^{\mathrm{new}}(5, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
5.35.c.a \(32\) \(36.613\) None \(131070\) \(-78988260\) \(-730721770860\) \(53\!\cdots\!00\)