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Properties

Label 21.15
Level 21
Weight 15
Dimension 154
Nonzero newspaces 4
Newform subspaces 6
Sturm bound 480
Trace bound 1

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Defining parameters

Level: \( N \) = \( 21 = 3 \cdot 7 \)
Weight: \( k \) = \( 15 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 6 \)
Sturm bound: \(480\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{15}(\Gamma_1(21))\).

Total New Old
Modular forms 236 162 74
Cusp forms 212 154 58
Eisenstein series 24 8 16

Trace form

\( 154 q - 6582 q^{3} + 13050 q^{4} + 3354 q^{5} + 628986 q^{6} + 345018 q^{7} - 13758654 q^{8} + 13973472 q^{9} + O(q^{10}) \) \( 154 q - 6582 q^{3} + 13050 q^{4} + 3354 q^{5} + 628986 q^{6} + 345018 q^{7} - 13758654 q^{8} + 13973472 q^{9} - 86100852 q^{10} + 36508422 q^{11} + 245877582 q^{12} - 439849070 q^{13} + 650648568 q^{14} + 495218928 q^{15} - 3590607422 q^{16} + 986359632 q^{17} + 5315705988 q^{18} - 3593130206 q^{19} + 931678920 q^{21} - 13898137356 q^{22} + 4833070944 q^{23} - 3932529198 q^{24} - 977684732 q^{25} - 48382543062 q^{26} - 2669974620 q^{27} + 92326115626 q^{28} + 19454387988 q^{29} + 15976202784 q^{30} - 45372982106 q^{31} - 109670294922 q^{32} + 47463538434 q^{33} - 395535053856 q^{34} - 110236786590 q^{35} - 128335754778 q^{36} + 264293086080 q^{37} - 505985559906 q^{38} + 83888773866 q^{39} + 646656691056 q^{40} - 1159414885512 q^{42} + 1483360056276 q^{43} - 1215722363016 q^{44} + 988206939522 q^{45} + 1020945705492 q^{46} - 4247813731278 q^{47} - 6970720047402 q^{48} + 5957327652688 q^{49} + 9566287954566 q^{50} + 549430465080 q^{51} - 10198930132616 q^{52} - 7514538988668 q^{53} + 4765099162236 q^{54} + 15412352432556 q^{55} + 8394417099954 q^{56} + 4199091489900 q^{57} - 13374064230912 q^{58} - 8948260942572 q^{59} + 4049231418636 q^{60} + 4851398817286 q^{61} - 581071957290 q^{63} + 33608226047046 q^{64} + 23025167408898 q^{65} - 3900498895224 q^{66} - 40219769063338 q^{67} - 58981699756188 q^{68} + 34875739863504 q^{69} + 78025481200740 q^{70} + 9780881327448 q^{71} - 62113856863794 q^{72} + 49688002968652 q^{73} - 76224162542382 q^{74} - 107705055409140 q^{75} - 98319080862740 q^{76} + 86523049466856 q^{77} + 105828287911656 q^{78} + 86477967655538 q^{79} + 30283583206848 q^{80} + 69490390949136 q^{81} - 365949567260820 q^{82} + 293915218093074 q^{84} + 311506186751832 q^{85} - 62539607652942 q^{86} - 143599264831500 q^{87} - 857876857540440 q^{88} - 130028954604924 q^{89} + 237078352564068 q^{90} + 215784333691324 q^{91} + 565804333641036 q^{92} + 405891050580048 q^{93} - 822000908234340 q^{94} - 786633835853478 q^{95} - 401579276944506 q^{96} + 76618002292360 q^{97} + 654317775813978 q^{98} + 457266163590720 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{15}^{\mathrm{new}}(\Gamma_1(21))\)

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
21.15.b \(\chi_{21}(8, \cdot)\) 21.15.b.a 28 1
21.15.d \(\chi_{21}(13, \cdot)\) 21.15.d.a 18 1
21.15.f \(\chi_{21}(10, \cdot)\) 21.15.f.a 18 2
21.15.f.b 20
21.15.h \(\chi_{21}(2, \cdot)\) 21.15.h.a 2 2
21.15.h.b 68

Decomposition of \(S_{15}^{\mathrm{old}}(\Gamma_1(21))\) into lower level spaces

\( S_{15}^{\mathrm{old}}(\Gamma_1(21)) \cong \) \(S_{15}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 2}\)\(\oplus\)\(S_{15}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 2}\)