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Properties

Label 21.16
Level 21
Weight 16
Dimension 170
Nonzero newspaces 4
Newform subspaces 9
Sturm bound 512
Trace bound 1

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Defining parameters

Level: \( N \) = \( 21 = 3 \cdot 7 \)
Weight: \( k \) = \( 16 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 9 \)
Sturm bound: \(512\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{16}(\Gamma_1(21))\).

Total New Old
Modular forms 252 182 70
Cusp forms 228 170 58
Eisenstein series 24 12 12

Trace form

\( 170 q + 612 q^{2} + 4371 q^{3} + 11186 q^{4} + 348576 q^{5} - 2388204 q^{6} + 9951986 q^{7} - 8348202 q^{8} - 17220669 q^{9} + O(q^{10}) \) \( 170 q + 612 q^{2} + 4371 q^{3} + 11186 q^{4} + 348576 q^{5} - 2388204 q^{6} + 9951986 q^{7} - 8348202 q^{8} - 17220669 q^{9} + 114958128 q^{10} - 286279632 q^{11} + 810909600 q^{12} - 1210132748 q^{13} + 610510344 q^{14} + 3103241562 q^{15} - 4600798798 q^{16} - 8937198708 q^{17} + 7409942802 q^{18} + 5956244542 q^{19} - 69604912476 q^{20} + 29046842409 q^{21} + 21238267104 q^{22} - 74253478152 q^{23} + 89568156384 q^{24} + 127931485034 q^{25} + 26833287642 q^{26} - 41841412812 q^{27} + 237508681322 q^{28} + 591616991088 q^{29} - 500520376170 q^{30} - 625359137630 q^{31} + 79702300110 q^{32} + 536788148967 q^{33} + 1988302984068 q^{34} - 731750112156 q^{35} + 8146033401642 q^{36} + 2317673022406 q^{37} + 674954366166 q^{38} - 4153237622700 q^{39} + 2881837938216 q^{40} + 1625529383736 q^{41} + 7469865359262 q^{42} - 8090237295872 q^{43} - 2457772578600 q^{44} - 8380174312809 q^{45} + 23580488529060 q^{46} + 2931648021432 q^{47} - 21233890159776 q^{48} - 14599168426270 q^{49} + 22496682665682 q^{50} + 41713906607163 q^{51} + 63195208248952 q^{52} + 31339411515156 q^{53} - 89165609023734 q^{54} - 137522310618540 q^{55} + 98955490130130 q^{56} + 67200904801386 q^{57} - 120425226467544 q^{58} + 16879643729616 q^{59} - 19220505034140 q^{60} + 44192021809498 q^{61} - 152216683079484 q^{62} + 56060307399867 q^{63} - 46434320707450 q^{64} - 38475782466696 q^{65} + 159294301668810 q^{66} - 39736951330634 q^{67} - 423370612957152 q^{68} - 48573874889208 q^{69} - 366963323956464 q^{70} - 107551526916972 q^{71} - 7597497531906 q^{72} + 571614157845490 q^{73} + 49760455849734 q^{74} + 545860956973296 q^{75} - 2203549086900152 q^{76} - 937061792928756 q^{77} - 802967580322560 q^{78} + 1949263483212562 q^{79} + 3342409124349816 q^{80} + 533883626139159 q^{81} - 2119493220297768 q^{82} - 3563641475926008 q^{83} - 1124165069919636 q^{84} + 3159528282283308 q^{85} + 3353454073248678 q^{86} + 51622010541792 q^{87} - 184854527929236 q^{88} - 1872411259501632 q^{89} - 98157429049320 q^{90} - 1917531280678028 q^{91} + 5656165491044544 q^{92} + 1173394130298015 q^{93} + 10897347454460136 q^{94} + 1378059432379584 q^{95} - 829359072066924 q^{96} - 8197213925316236 q^{97} - 8509025872586586 q^{98} - 2796695610288894 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{16}^{\mathrm{new}}(\Gamma_1(21))\)

We only show spaces with even 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
21.16.a \(\chi_{21}(1, \cdot)\) 21.16.a.a 3 1
21.16.a.b 4
21.16.a.c 4
21.16.a.d 5
21.16.c \(\chi_{21}(20, \cdot)\) 21.16.c.a 2 1
21.16.c.b 36
21.16.e \(\chi_{21}(4, \cdot)\) 21.16.e.a 18 2
21.16.e.b 22
21.16.g \(\chi_{21}(5, \cdot)\) 21.16.g.a 76 2

Decomposition of \(S_{16}^{\mathrm{old}}(\Gamma_1(21))\) into lower level spaces

\( S_{16}^{\mathrm{old}}(\Gamma_1(21)) \cong \) \(S_{16}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 2}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 2}\)