# Properties

 Label 105.3.t Level 105 Weight 3 Character orbit t Rep. character $$\chi_{105}(11,\cdot)$$ Character field $$\Q(\zeta_{6})$$ Dimension 44 Newform subspaces 2 Sturm bound 48 Trace bound 1

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$105 = 3 \cdot 5 \cdot 7$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 105.t (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$21$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$2$$ Sturm bound: $$48$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(105, [\chi])$$.

Total New Old
Modular forms 72 44 28
Cusp forms 56 44 12
Eisenstein series 16 0 16

## Trace form

 $$44q + 48q^{4} + 8q^{6} - 2q^{7} + 6q^{9} + O(q^{10})$$ $$44q + 48q^{4} + 8q^{6} - 2q^{7} + 6q^{9} + 10q^{12} - 92q^{13} - 20q^{15} - 96q^{16} - 66q^{18} + 86q^{19} - 40q^{21} + 184q^{22} - 116q^{24} + 110q^{25} + 60q^{27} + 36q^{28} + 20q^{30} - 58q^{31} - 148q^{33} - 368q^{34} + 24q^{36} - 38q^{37} - 34q^{39} + 126q^{42} - 156q^{43} + 60q^{45} - 120q^{46} + 860q^{48} + 10q^{49} + 44q^{51} - 188q^{52} - 204q^{54} - 40q^{55} - 100q^{57} + 64q^{58} - 150q^{60} - 60q^{61} - 202q^{63} - 112q^{64} - 128q^{66} + 146q^{67} - 24q^{69} + 60q^{70} + 26q^{72} + 98q^{73} + 912q^{76} - 608q^{78} - 10q^{79} + 158q^{81} - 248q^{82} + 444q^{84} + 120q^{85} + 482q^{87} + 216q^{88} + 180q^{90} + 102q^{91} + 162q^{93} + 272q^{94} + 412q^{96} + 1168q^{97} + 312q^{99} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(105, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
105.3.t.a $$8$$ $$2.861$$ 8.0.3317760000.8 None $$0$$ $$-4$$ $$0$$ $$56$$ $$q+(\beta _{2}-\beta _{4}-\beta _{5})q^{2}+(-1+\beta _{3}+\beta _{5}+\cdots)q^{3}+\cdots$$
105.3.t.b $$36$$ $$2.861$$ None $$0$$ $$4$$ $$0$$ $$-58$$

## Decomposition of $$S_{3}^{\mathrm{old}}(105, [\chi])$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(105, [\chi]) \cong$$ $$S_{3}^{\mathrm{new}}(21, [\chi])$$$$^{\oplus 2}$$

## Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ ($$1 + 2 T^{2} + 11 T^{4} - 78 T^{6} - 271 T^{8} - 1248 T^{10} + 2816 T^{12} + 8192 T^{14} + 65536 T^{16}$$)
$3$ ($$1 + 4 T + 4 T^{2} - 24 T^{3} - 81 T^{4} - 216 T^{5} + 324 T^{6} + 2916 T^{7} + 6561 T^{8}$$)
$5$ ($$( 1 - 5 T^{2} + 25 T^{4} )^{2}$$)
$7$ ($$( 1 - 7 T )^{8}$$)
$11$ ($$1 + 358 T^{2} + 70081 T^{4} + 10310758 T^{6} + 1282826884 T^{8} + 150959807878 T^{10} + 15022484739361 T^{12} + 1123557358866118 T^{14} + 45949729863572161 T^{16}$$)
$13$ ($$( 1 - 2 T + 89 T^{2} - 338 T^{3} + 28561 T^{4} )^{4}$$)
$17$ ($$1 + 512 T^{2} + 32126 T^{4} + 32243712 T^{6} + 24037993859 T^{8} + 2693027069952 T^{10} + 224103183549566 T^{12} + 298302585461637632 T^{14} + 48661191875666868481 T^{16}$$)
$19$ ($$( 1 - 18 T + 11 T^{2} + 7362 T^{3} - 149316 T^{4} + 2657682 T^{5} + 1433531 T^{6} - 846825858 T^{7} + 16983563041 T^{8} )^{2}$$)
$23$ ($$1 + 1082 T^{2} + 328601 T^{4} + 305601162 T^{6} + 303243586964 T^{8} + 85519734775242 T^{10} + 25733068074321881 T^{12} + 23711623635445987322 T^{14} +$$$$61\!\cdots\!61$$$$T^{16}$$)
$29$ ($$( 1 - 2624 T^{2} + 3071906 T^{4} - 1855905344 T^{6} + 500246412961 T^{8} )^{2}$$)
$31$ ($$( 1 - 12 T - 1324 T^{2} + 5448 T^{3} + 1093119 T^{4} + 5235528 T^{5} - 1222741804 T^{6} - 10650044172 T^{7} + 852891037441 T^{8} )^{2}$$)
$37$ ($$( 1 + 6 T - 1021 T^{2} - 10086 T^{3} - 806196 T^{4} - 13807734 T^{5} - 1913518381 T^{6} + 15394358454 T^{7} + 3512479453921 T^{8} )^{2}$$)
$41$ ($$( 1 - 2957 T^{2} + 2825761 T^{4} )^{4}$$)
$43$ ($$( 1 - 12 T + 3484 T^{2} - 22188 T^{3} + 3418801 T^{4} )^{4}$$)
$47$ ($$1 + 4442 T^{2} + 9608921 T^{4} + 1612805802 T^{6} - 17630196388396 T^{8} + 7869977828709162 T^{10} +$$$$22\!\cdots\!81$$$$T^{12} +$$$$51\!\cdots\!22$$$$T^{14} +$$$$56\!\cdots\!21$$$$T^{16}$$)
$53$ ($$1 + 4982 T^{2} + 12556241 T^{4} - 17521091178 T^{6} - 107696253516316 T^{8} - 138249837039276618 T^{10} +$$$$78\!\cdots\!01$$$$T^{12} +$$$$24\!\cdots\!62$$$$T^{14} +$$$$38\!\cdots\!21$$$$T^{16}$$)
$59$ ($$1 + 428 T^{2} - 23559094 T^{4} - 210766032 T^{6} + 414645620367539 T^{8} - 2553928096281552 T^{10} -$$$$34\!\cdots\!74$$$$T^{12} +$$$$76\!\cdots\!68$$$$T^{14} +$$$$21\!\cdots\!41$$$$T^{16}$$)
$61$ ($$( 1 - 132 T + 7586 T^{2} - 316272 T^{3} + 18105699 T^{4} - 1176848112 T^{5} + 105034549826 T^{6} - 6800689415652 T^{7} + 191707312997281 T^{8} )^{2}$$)
$67$ ($$( 1 - 144 T + 6734 T^{2} - 723456 T^{3} + 82820979 T^{4} - 3247593984 T^{5} + 135697648814 T^{6} - 13026007032336 T^{7} + 406067677556641 T^{8} )^{2}$$)
$71$ ($$( 1 - 17824 T^{2} + 128951106 T^{4} - 452937802144 T^{6} + 645753531245761 T^{8} )^{2}$$)
$73$ ($$( 1 + 144 T + 5384 T^{2} + 675936 T^{3} + 96783519 T^{4} + 3602062944 T^{5} + 152896129544 T^{6} + 21792128585616 T^{7} + 806460091894081 T^{8} )^{2}$$)
$79$ ($$( 1 + 172 T + 9796 T^{2} + 1256632 T^{3} + 167981119 T^{4} + 7842640312 T^{5} + 381554993476 T^{6} + 41811042349612 T^{7} + 1517108809906561 T^{8} )^{2}$$)
$83$ ($$( 1 - 14396 T^{2} + 103463846 T^{4} - 683209989116 T^{6} + 2252292232139041 T^{8} )^{2}$$)
$89$ ($$1 + 28948 T^{2} + 504871786 T^{4} + 6010485861328 T^{6} + 54451796051280979 T^{8} +$$$$37\!\cdots\!48$$$$T^{10} +$$$$19\!\cdots\!66$$$$T^{12} +$$$$71\!\cdots\!08$$$$T^{14} +$$$$15\!\cdots\!61$$$$T^{16}$$)
$97$ ($$( 1 + 112 T + 21704 T^{2} + 1053808 T^{3} + 88529281 T^{4} )^{4}$$)