# Properties

 Label 105.3.o Level 105 Weight 3 Character orbit o Rep. character $$\chi_{105}(44,\cdot)$$ Character field $$\Q(\zeta_{6})$$ Dimension 56 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.o (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$105$$ 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 72 0
Cusp forms 56 56 0
Eisenstein series 16 16 0

## Trace form

 $$56q - 52q^{4} + 4q^{9} + O(q^{10})$$ $$56q - 52q^{4} + 4q^{9} + 22q^{10} + 4q^{15} - 84q^{16} - 8q^{19} + 28q^{21} - 12q^{24} - 6q^{25} + 20q^{30} - 100q^{31} + 176q^{34} - 192q^{36} + 136q^{39} + 174q^{40} - 120q^{45} + 184q^{46} - 52q^{49} + 116q^{51} + 60q^{54} - 500q^{55} - 90q^{60} - 104q^{61} - 72q^{64} + 460q^{66} - 512q^{69} - 50q^{70} - 324q^{75} + 64q^{76} + 268q^{79} - 328q^{81} + 152q^{84} + 336q^{85} + 1436q^{90} + 432q^{91} - 80q^{94} + 72q^{96} + 144q^{99} + O(q^{100})$$

## 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.o.a $$16$$ $$2.861$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{6}q^{2}+(-\beta _{3}-\beta _{9}+\beta _{13})q^{3}+(-1+\cdots)q^{4}+\cdots$$
105.3.o.b $$40$$ $$2.861$$ None $$0$$ $$0$$ $$0$$ $$0$$

## Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ ($$( 1 - 6 T^{2} + 10 T^{4} + 36 T^{6} - 156 T^{8} + 576 T^{10} + 2560 T^{12} - 24576 T^{14} + 65536 T^{16} )^{2}$$)
$3$ ($$1 + 4 T^{2} + 90 T^{4} - 944 T^{6} - 2381 T^{8} - 76464 T^{10} + 590490 T^{12} + 2125764 T^{14} + 43046721 T^{16}$$)
$5$ ($$1 + 250 T^{4} - 328125 T^{8} + 97656250 T^{12} + 152587890625 T^{16}$$)
$7$ ($$( 1 + 52 T^{2} + 4263 T^{4} + 124852 T^{6} + 5764801 T^{8} )^{2}$$)
$11$ ($$( 1 + 334 T^{2} + 57760 T^{4} + 8187676 T^{6} + 1046359339 T^{8} + 119875764316 T^{10} + 12381368966560 T^{12} + 1048235077824814 T^{14} + 45949729863572161 T^{16} )^{2}$$)
$13$ ($$( 1 - 188 T^{2} + 20583 T^{4} - 5369468 T^{6} + 815730721 T^{8} )^{4}$$)
$17$ ($$( 1 - 906 T^{2} + 463000 T^{4} - 172859364 T^{6} + 52513801899 T^{8} - 14437386940644 T^{10} + 3229775695183000 T^{12} - 527855746930163466 T^{14} + 48661191875666868481 T^{16} )^{2}$$)
$19$ ($$( 1 - 12 T - 599 T^{2} - 252 T^{3} + 369744 T^{4} - 90972 T^{5} - 78062279 T^{6} - 564550572 T^{7} + 16983563041 T^{8} )^{4}$$)
$23$ ($$( 1 - 1066 T^{2} + 315400 T^{4} - 278518084 T^{6} + 277658769259 T^{8} - 77940779144644 T^{10} + 24699284757627400 T^{12} - 23360989644533662186 T^{14} +$$$$61\!\cdots\!61$$$$T^{16} )^{2}$$)
$29$ ($$( 1 - 2394 T^{2} + 2753756 T^{4} - 1693230714 T^{6} + 500246412961 T^{8} )^{4}$$)
$31$ ($$( 1 - 86 T + 3685 T^{2} - 153854 T^{3} + 5740444 T^{4} - 147853694 T^{5} + 3403174885 T^{6} - 76325316566 T^{7} + 852891037441 T^{8} )^{4}$$)
$37$ ($$( 1 + 2468 T^{2} + 1780081 T^{4} + 1388548628 T^{6} + 3656190464464 T^{8} + 2602363685201108 T^{10} + 6252497938815147601 T^{12} +$$$$16\!\cdots\!08$$$$T^{14} +$$$$12\!\cdots\!41$$$$T^{16} )^{2}$$)
$41$ ($$( 1 - 3054 T^{2} + 6815636 T^{4} - 8629874094 T^{6} + 7984925229121 T^{8} )^{4}$$)
$43$ ($$( 1 - 4124 T^{2} + 11073111 T^{4} - 14099135324 T^{6} + 11688200277601 T^{8} )^{4}$$)
$47$ ($$( 1 - 7336 T^{2} + 31122250 T^{4} - 94893243424 T^{6} + 228626385513379 T^{8} - 463048756964467744 T^{10} +$$$$74\!\cdots\!50$$$$T^{12} -$$$$85\!\cdots\!76$$$$T^{14} +$$$$56\!\cdots\!21$$$$T^{16} )^{2}$$)
$53$ ($$( 1 - 7636 T^{2} + 28650250 T^{4} - 105966940624 T^{6} + 357269785558579 T^{8} - 836130131621800144 T^{10} +$$$$17\!\cdots\!50$$$$T^{12} -$$$$37\!\cdots\!76$$$$T^{14} +$$$$38\!\cdots\!21$$$$T^{16} )^{2}$$)
$59$ ($$( 1 + 474 T^{2} + 12860200 T^{4} - 17476496604 T^{6} + 10103548950219 T^{8} - 211769018365942044 T^{10} +$$$$18\!\cdots\!00$$$$T^{12} +$$$$84\!\cdots\!94$$$$T^{14} +$$$$21\!\cdots\!41$$$$T^{16} )^{2}$$)
$61$ ($$( 1 + 98 T + 136 T^{2} + 198548 T^{3} + 40060699 T^{4} + 738797108 T^{5} + 1883034376 T^{6} + 5048996687378 T^{7} + 191707312997281 T^{8} )^{4}$$)
$67$ ($$( 1 + 12548 T^{2} + 81642721 T^{4} + 445546114868 T^{6} + 2168184767444464 T^{8} + 8978253671784967028 T^{10} +$$$$33\!\cdots\!61$$$$T^{12} +$$$$10\!\cdots\!28$$$$T^{14} +$$$$16\!\cdots\!81$$$$T^{16} )^{2}$$)
$71$ ($$( 1 - 13674 T^{2} + 87943916 T^{4} - 347479325994 T^{6} + 645753531245761 T^{8} )^{4}$$)
$73$ ($$( 1 + 10828 T^{2} + 58596841 T^{4} + 20056282108 T^{6} - 696353387031776 T^{8} + 569563132866972028 T^{10} +$$$$47\!\cdots\!21$$$$T^{12} +$$$$24\!\cdots\!88$$$$T^{14} +$$$$65\!\cdots\!61$$$$T^{16} )^{2}$$)
$79$ ($$( 1 - 152 T + 4981 T^{2} - 857432 T^{3} + 145300984 T^{4} - 5351233112 T^{5} + 194010353461 T^{6} - 36949293239192 T^{7} + 1517108809906561 T^{8} )^{4}$$)
$83$ ($$( 1 + 7386 T^{2} + 83632076 T^{4} + 350527158906 T^{6} + 2252292232139041 T^{8} )^{4}$$)
$89$ ($$( 1 - 1586 T^{2} - 121555520 T^{4} + 2241915676 T^{6} + 11299181809334539 T^{8} + 140662813645269916 T^{10} -$$$$47\!\cdots\!20$$$$T^{12} -$$$$39\!\cdots\!06$$$$T^{14} +$$$$15\!\cdots\!61$$$$T^{16} )^{2}$$)
$97$ ($$( 1 - 37448 T^{2} + 527638098 T^{4} - 3315244514888 T^{6} + 7837433594376961 T^{8} )^{4}$$)