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

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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

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