Properties

Label 5.35
Level 5
Weight 35
Dimension 32
Nonzero newspaces 1
Newform subspaces 1
Sturm bound 70
Trace bound 0

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Defining parameters

Level: \( N \) = \( 5 \)
Weight: \( k \) = \( 35 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 1 \)
Sturm bound: \(70\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{35}(\Gamma_1(5))\).

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

Trace form

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

Decomposition of \(S_{35}^{\mathrm{new}}(\Gamma_1(5))\)

We only show spaces with odd parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
5.35.c \(\chi_{5}(2, \cdot)\) 5.35.c.a 32 2

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database