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Properties

Label 21.10
Level 21
Weight 10
Dimension 98
Nonzero newspaces 4
Newform subspaces 9
Sturm bound 320
Trace bound 1

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Defining parameters

Level: \( N \) = \( 21 = 3 \cdot 7 \)
Weight: \( k \) = \( 10 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 9 \)
Sturm bound: \(320\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_1(21))\).

Total New Old
Modular forms 156 110 46
Cusp forms 132 98 34
Eisenstein series 24 12 12

Trace form

\( 98 q + 36 q^{2} - 165 q^{3} - 1198 q^{4} + 3984 q^{5} - 972 q^{6} - 7390 q^{7} - 57114 q^{8} + 24447 q^{9} + O(q^{10}) \) \( 98 q + 36 q^{2} - 165 q^{3} - 1198 q^{4} + 3984 q^{5} - 972 q^{6} - 7390 q^{7} - 57114 q^{8} + 24447 q^{9} + 60816 q^{10} - 193392 q^{11} + 73032 q^{12} + 777964 q^{13} + 6072 q^{14} - 804582 q^{15} - 1249678 q^{16} + 166116 q^{17} + 2531682 q^{18} - 975026 q^{19} - 677052 q^{20} - 1902687 q^{21} + 4851696 q^{22} - 40584 q^{23} + 622872 q^{24} - 8024206 q^{25} - 5592630 q^{26} + 2125764 q^{27} + 36460490 q^{28} - 1442304 q^{29} - 18021042 q^{30} - 53538302 q^{31} - 42431010 q^{32} - 565533 q^{33} + 103018020 q^{34} + 72736692 q^{35} + 100034394 q^{36} - 99897170 q^{37} - 114008058 q^{38} - 34117188 q^{39} + 38176248 q^{40} + 61439352 q^{41} + 3310326 q^{42} - 49446032 q^{43} - 232746792 q^{44} + 105366411 q^{45} + 98011332 q^{46} + 133604856 q^{47} + 130012128 q^{48} + 42288938 q^{49} - 221439150 q^{50} - 265707405 q^{51} - 347503400 q^{52} - 196886868 q^{53} + 410463666 q^{54} + 509470932 q^{55} + 85364850 q^{56} + 421245450 q^{57} + 352123464 q^{58} + 291494352 q^{59} - 615514356 q^{60} - 533295350 q^{61} - 1137678492 q^{62} - 550876773 q^{63} - 465830938 q^{64} + 459625608 q^{65} + 1379156994 q^{66} + 777988870 q^{67} + 472762896 q^{68} + 672641496 q^{69} + 540777744 q^{70} + 131491572 q^{71} - 1834381242 q^{72} - 431625614 q^{73} - 2578991514 q^{74} - 347823384 q^{75} - 1301542904 q^{76} + 63994212 q^{77} + 4145078160 q^{78} + 2627235058 q^{79} + 3089728584 q^{80} - 3059671221 q^{81} - 2139679800 q^{82} + 227089704 q^{83} - 5060061492 q^{84} - 1511014980 q^{85} + 1609139286 q^{86} + 2211977448 q^{87} + 5719474092 q^{88} + 879649008 q^{89} + 527976792 q^{90} - 1373054348 q^{91} - 1614694368 q^{92} - 3089271597 q^{93} - 5912472648 q^{94} + 1203940032 q^{95} + 260186436 q^{96} + 1793848732 q^{97} + 7812444678 q^{98} + 8253694242 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_1(21))\)

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
21.10.a \(\chi_{21}(1, \cdot)\) 21.10.a.a 1 1
21.10.a.b 2
21.10.a.c 2
21.10.a.d 3
21.10.c \(\chi_{21}(20, \cdot)\) 21.10.c.a 2 1
21.10.c.b 20
21.10.e \(\chi_{21}(4, \cdot)\) 21.10.e.a 10 2
21.10.e.b 14
21.10.g \(\chi_{21}(5, \cdot)\) 21.10.g.a 44 2

Decomposition of \(S_{10}^{\mathrm{old}}(\Gamma_1(21))\) into lower level spaces

\( S_{10}^{\mathrm{old}}(\Gamma_1(21)) \cong \) \(S_{10}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 2}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 2}\)