Properties

Label 5.35.c
Level $5$
Weight $35$
Character orbit 5.c
Rep. character $\chi_{5}(2,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $32$
Newform subspaces $1$
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: \(\Q(i)\)
Newform subspaces: \( 1 \)
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

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

Decomposition of \(S_{35}^{\mathrm{new}}(5, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
5.35.c.a 5.c 5.c $32$ $36.613$ None \(131070\) \(-78988260\) \(-730721770860\) \(53\!\cdots\!00\) $\mathrm{SU}(2)[C_{4}]$