Properties

 Label 16.28.e Level $16$ Weight $28$ Character orbit 16.e Rep. character $\chi_{16}(5,\cdot)$ Character field $\Q(\zeta_{4})$ Dimension $106$ Newform subspaces $1$ Sturm bound $56$ Trace bound $0$

Related objects

Defining parameters

 Level: $$N$$ $$=$$ $$16 = 2^{4}$$ Weight: $$k$$ $$=$$ $$28$$ Character orbit: $$[\chi]$$ $$=$$ 16.e (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$16$$ Character field: $$\Q(i)$$ Newform subspaces: $$1$$ Sturm bound: $$56$$ Trace bound: $$0$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{28}(16, [\chi])$$.

Total New Old
Modular forms 110 110 0
Cusp forms 106 106 0
Eisenstein series 4 4 0

Trace form

 $$106 q - 2 q^{2} - 2 q^{3} + 125095688 q^{4} - 2 q^{5} - 59499919472 q^{6} - 287180933804 q^{8} + O(q^{10})$$ $$106 q - 2 q^{2} - 2 q^{3} + 125095688 q^{4} - 2 q^{5} - 59499919472 q^{6} - 287180933804 q^{8} + 8247210235372 q^{10} - 34039821810222 q^{11} + 1748989708884580 q^{12} - 2 q^{13} - 7155218316814660 q^{14} - 15569560546875004 q^{15} - 11277270898466024 q^{16} - 4 q^{17} - 142926567667036386 q^{18} - 361273435637780378 q^{19} + 442470438134323004 q^{20} + 15251194969972 q^{21} - 1169169681057307068 q^{22} + 10984755246449911984 q^{24} + 17037255844415508360 q^{26} - 16968259081125930056 q^{27} - 60190300783057535720 q^{28} - 27121773564864273802 q^{29} - 676957577616991436364 q^{30} + 293010555569340511088 q^{31} - 1166901104384201893432 q^{32} - 4 q^{33} - 290590654320714186380 q^{34} - 1483431258098321642404 q^{35} + 2272823118258680645548 q^{36} - 470486119578222882250 q^{37} - 7667804020978176078752 q^{38} - 13361029860556314821176 q^{40} - 46808273599641292573640 q^{42} + 30832447383975033909242 q^{43} + 78151525061974584923236 q^{44} + 14901145942652686274 q^{45} - 30741189488837489213204 q^{46} - 109219994122411663546544 q^{47} - 189351174993879449193752 q^{48} - 882423151738888904731010 q^{49} + 548328807383867462419206 q^{50} - 115559869623218432212572 q^{51} - 870962460180776269413356 q^{52} - 5971340109916911897018 q^{53} + 1136059014139929162305056 q^{54} + 1200724087407057566405656 q^{56} - 2828993593282901350448872 q^{58} - 34394779779101149275670 q^{59} + 7255680995179605171006528 q^{60} - 2475467954128860415560434 q^{61} - 3746979776437258967395280 q^{62} + 5188426743337460248956228 q^{63} - 998638142638832585325568 q^{64} + 2911521903927484929681108 q^{65} + 19080130794608880088211092 q^{66} + 19927279436319849143450902 q^{67} - 8373829219145321982498160 q^{68} - 11740592568211854067772156 q^{69} - 5132370883366275255574400 q^{70} + 19086224804727807421919172 q^{72} + 42828123668533070044258924 q^{74} - 81164500905568543837973834 q^{75} - 105896749199037309084347596 q^{76} + 43639762623313421635882292 q^{77} - 98604570863977418199548932 q^{78} - 27720061020991987308873792 q^{79} - 62182770892870708184304728 q^{80} - 581497370030400596903901694 q^{81} - 341107120874158685100150464 q^{82} + 26201266111333778096099838 q^{83} + 507935364828252675231522472 q^{84} + 224109171520266208496093748 q^{85} - 704077428371873697577134268 q^{86} - 681166827660725136677389832 q^{88} + 482826168478152776777239896 q^{90} + 67827511015091818004015876 q^{91} - 83646902794933560160672648 q^{92} + 886600140227681407873186288 q^{93} - 168289477479668477956229936 q^{94} + 239338208955746404979764980 q^{95} - 752456785864472227742519632 q^{96} - 4 q^{97} - 1043862744854197068838248646 q^{98} + 1641925710538879681648895966 q^{99} + O(q^{100})$$

Decomposition of $$S_{28}^{\mathrm{new}}(16, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
16.28.e.a $106$ $73.897$ None $$-2$$ $$-2$$ $$-2$$ $$0$$