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Properties

Label 4.35.b
Level $4$
Weight $35$
Character orbit 4.b
Rep. character $\chi_{4}(3,\cdot)$
Character field $\Q$
Dimension $16$
Newform subspaces $1$
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: \(\Q\)
Newform subspaces: \( 1 \)
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

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

Display 100 coefficients 10 coefficients

Decomposition of \(S_{35}^{\mathrm{new}}(4, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
4.35.b.a 4.b 4.b $16$ $29.290$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(-27372\) \(0\) \(-21372255840\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1711+\beta _{1})q^{2}+(19-76\beta _{1}-\beta _{2}+\cdots)q^{3}+\cdots\)