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Properties

Label 21.21
Level 21
Weight 21
Dimension 222
Nonzero newspaces 4
Newform subspaces 6
Sturm bound 672
Trace bound 1

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Defining parameters

Level: \( N \) = \( 21 = 3 \cdot 7 \)
Weight: \( k \) = \( 21 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 6 \)
Sturm bound: \(672\)
Trace bound: \(1\)

Dimensions

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

Total New Old
Modular forms 332 230 102
Cusp forms 308 222 86
Eisenstein series 24 8 16

Trace form

\( 222 q + 67290 q^{3} + 56090 q^{4} - 26337366 q^{5} + 192802458 q^{6} - 25688458 q^{7} - 2463173262 q^{8} + 11731545468 q^{9} + O(q^{10}) \) \( 222 q + 67290 q^{3} + 56090 q^{4} - 26337366 q^{5} + 192802458 q^{6} - 25688458 q^{7} - 2463173262 q^{8} + 11731545468 q^{9} - 51183020244 q^{10} + 54489250710 q^{11} - 186100268874 q^{12} - 351000554566 q^{13} - 832749144840 q^{14} + 1425514261440 q^{15} - 6383558731134 q^{16} + 4343544700704 q^{17} - 9316118700300 q^{18} - 8667944603374 q^{19} + 17464184405784 q^{21} - 117044145029340 q^{22} + 166971843086400 q^{23} - 389277739026582 q^{24} + 148530498052392 q^{25} + 381717168592410 q^{26} - 1382098409018952 q^{27} - 1322878818853302 q^{28} + 825911569671012 q^{29} - 3439808715669384 q^{30} - 1401060057946642 q^{31} - 4691750676802650 q^{32} + 629562468476454 q^{33} + 10274886370364928 q^{34} - 19853637216390054 q^{35} - 69093561597601290 q^{36} - 2367512006548112 q^{37} - 4598537247421650 q^{38} - 2886169247444178 q^{39} + 11302097245380384 q^{40} + 115126009494531264 q^{42} - 134662291439995652 q^{43} + 236094321431679480 q^{44} - 47964116650785642 q^{45} - 71915704774706508 q^{46} + 82471337499706794 q^{47} - 268220012006169066 q^{48} + 441402889458069300 q^{49} + 302053488981459174 q^{50} + 426387839539364400 q^{51} - 184380726076922536 q^{52} + 124314755788179756 q^{53} + 993275963443516452 q^{54} + 980494477465645524 q^{55} + 1587507371528871762 q^{56} - 4114874104257002580 q^{57} + 3387495940696036512 q^{58} + 5199860463039384660 q^{59} - 6144511500371110044 q^{60} - 3906226862008910410 q^{61} + 7549465225694313762 q^{63} - 1267326366216802714 q^{64} - 8865691642455240582 q^{65} - 10752139161682439904 q^{66} + 2926171011247945998 q^{67} + 17009022950342802324 q^{68} - 4834316207954786040 q^{69} - 18011519621517449724 q^{70} - 7388609176964983608 q^{71} - 7317921923476725210 q^{72} - 7319219607866904604 q^{73} + 7179649498533847698 q^{74} + 42654087283161965064 q^{75} - 121843465711406709652 q^{76} - 30799954708115897736 q^{77} + 62436178376406768696 q^{78} + 35590235151736983450 q^{79} - 27401758927873827120 q^{80} + 3235143142821832344 q^{81} + 165010701061992253212 q^{82} - 7058669324357238318 q^{84} + 78703820911272811224 q^{85} + 189088096250459111202 q^{86} - 208212784243811844072 q^{87} + 121342988346502783080 q^{88} + 97030577737796339556 q^{89} + 275086193442741957684 q^{90} + 7316370575037393092 q^{91} - 771036986920281801300 q^{92} - 428261090252153249076 q^{93} + 1336419617113721938284 q^{94} + 389312810556898473234 q^{95} - 277750474990521074538 q^{96} - 734654400869706533752 q^{97} - 330199456243066087878 q^{98} + 204075444868219575432 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

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
21.21.b \(\chi_{21}(8, \cdot)\) 21.21.b.a 40 1
21.21.d \(\chi_{21}(13, \cdot)\) 21.21.d.a 26 1
21.21.f \(\chi_{21}(10, \cdot)\) 21.21.f.a 26 2
21.21.f.b 28
21.21.h \(\chi_{21}(2, \cdot)\) 21.21.h.a 2 2
21.21.h.b 100

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

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