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Properties

Label 21.17
Level 21
Weight 17
Dimension 178
Nonzero newspaces 4
Newform subspaces 6
Sturm bound 544
Trace bound 1

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Defining parameters

Level: \( N \) = \( 21 = 3 \cdot 7 \)
Weight: \( k \) = \( 17 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 6 \)
Sturm bound: \(544\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{17}(\Gamma_1(21))\).

Total New Old
Modular forms 268 186 82
Cusp forms 244 178 66
Eisenstein series 24 8 16

Trace form

\( 178 q - 2460 q^{3} + 287066 q^{4} - 483786 q^{5} + 806106 q^{6} + 1376762 q^{7} - 39355182 q^{8} - 141395958 q^{9} + O(q^{10}) \) \( 178 q - 2460 q^{3} + 287066 q^{4} - 483786 q^{5} + 806106 q^{6} + 1376762 q^{7} - 39355182 q^{8} - 141395958 q^{9} + 1172452716 q^{10} - 1323491382 q^{11} + 1096126086 q^{12} + 1891998054 q^{13} - 8022479112 q^{14} - 1524023340 q^{15} + 32804733442 q^{16} - 22499945856 q^{17} - 35339656620 q^{18} + 118798378314 q^{19} - 53528524794 q^{21} + 273658173060 q^{22} + 243318078720 q^{23} - 432772226790 q^{24} - 411160625048 q^{25} + 1993445161722 q^{26} - 258342758232 q^{27} - 4637646582902 q^{28} + 901947131388 q^{29} + 5411754891816 q^{30} - 4671130286178 q^{31} - 3520346136570 q^{32} + 8775135926124 q^{33} + 5148079250496 q^{34} + 1144413832086 q^{35} - 45027488009706 q^{36} - 5705962660052 q^{37} + 49187858126670 q^{38} - 36144753811146 q^{39} - 65927809992576 q^{40} + 62717088928464 q^{42} + 49220685396868 q^{43} - 141253299612936 q^{44} - 67100741446212 q^{45} + 141918395917044 q^{46} - 99722691667386 q^{47} + 165071402394774 q^{48} + 120435483261148 q^{49} - 324146604554586 q^{50} - 128091253925382 q^{51} + 236270558645784 q^{52} + 318674824212996 q^{53} + 221036655139188 q^{54} - 874521600843996 q^{55} - 1258563600346734 q^{56} + 790103701815120 q^{57} + 1439412206837472 q^{58} + 200025707250348 q^{59} - 984126255672684 q^{60} + 33038977020390 q^{61} + 1594003659732 q^{63} + 733703983978406 q^{64} + 102759594348438 q^{65} - 3328712589389616 q^{66} - 334575461339362 q^{67} + 2737335888109044 q^{68} + 2496647290129020 q^{69} + 2206995742901316 q^{70} - 6365829183153768 q^{71} - 4749037545552810 q^{72} - 1355382842715864 q^{73} + 10505879919682578 q^{74} + 3174046804112244 q^{75} + 9333793605951852 q^{76} - 4825701467542296 q^{77} - 9300072898859304 q^{78} - 11001536994462862 q^{79} + 26493033994360560 q^{80} + 4378849526503062 q^{81} + 8067376608232572 q^{82} - 6341706240432174 q^{84} - 39121857338405616 q^{85} - 12442317702337278 q^{86} + 21273287071416528 q^{87} + 82284104854301160 q^{88} + 17556190527992796 q^{89} - 41272342882243116 q^{90} - 44075332304601732 q^{91} - 86515359167178900 q^{92} + 32686935311895294 q^{93} + 3597304152944652 q^{94} + 51659302406397534 q^{95} + 9342066112678326 q^{96} + 45653982481143528 q^{97} - 103242652145628678 q^{98} - 31000140944600580 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{17}^{\mathrm{new}}(\Gamma_1(21))\)

We only show spaces with odd parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
21.17.b \(\chi_{21}(8, \cdot)\) 21.17.b.a 32 1
21.17.d \(\chi_{21}(13, \cdot)\) 21.17.d.a 22 1
21.17.f \(\chi_{21}(10, \cdot)\) 21.17.f.a 20 2
21.17.f.b 22
21.17.h \(\chi_{21}(2, \cdot)\) 21.17.h.a 2 2
21.17.h.b 80

Decomposition of \(S_{17}^{\mathrm{old}}(\Gamma_1(21))\) into lower level spaces

\( S_{17}^{\mathrm{old}}(\Gamma_1(21)) \cong \) \(S_{17}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 2}\)\(\oplus\)\(S_{17}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 2}\)