↑

Properties

Label 21.20
Level 21
Weight 20
Dimension 216
Nonzero newspaces 4
Newform subspaces 9
Sturm bound 640
Trace bound 1

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 21 = 3 \cdot 7 \)
Weight: \( k \) = \( 20 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 9 \)
Sturm bound: \(640\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{20}(\Gamma_1(21))\).

Total New Old
Modular forms 316 228 88
Cusp forms 292 216 76
Eisenstein series 24 12 12

Trace form

\( 216 q + 804 q^{2} + 19680 q^{3} - 836878 q^{4} - 14078574 q^{5} + 10628820 q^{6} + 374685818 q^{7} - 2774565642 q^{8} - 2775986502 q^{9} + O(q^{10}) \) \( 216 q + 804 q^{2} + 19680 q^{3} - 836878 q^{4} - 14078574 q^{5} + 10628820 q^{6} + 374685818 q^{7} - 2774565642 q^{8} - 2775986502 q^{9} - 3120763152 q^{10} + 11000491842 q^{11} + 54783461616 q^{12} - 38134367230 q^{13} + 259137503592 q^{14} + 198225312732 q^{15} - 856504365774 q^{16} + 2495037906888 q^{17} - 3207052486926 q^{18} + 6136906738406 q^{19} - 12839265602076 q^{20} - 5636667752844 q^{21} + 27178849770240 q^{22} + 392775948072 q^{23} - 5702851532592 q^{24} + 147262455391554 q^{25} - 130309852139334 q^{26} - 15251194969974 q^{27} + 141284752148010 q^{28} - 70634017759056 q^{29} - 370158907001850 q^{30} - 841768704691594 q^{31} + 2012381271167982 q^{32} + 52179816048678 q^{33} - 4175805804589500 q^{34} + 739797208790274 q^{35} + 8870537006946186 q^{36} - 2351597019387236 q^{37} + 463593504128694 q^{38} - 4389763534705806 q^{39} - 6342980164100664 q^{40} + 155908743228 q^{41} - 6215939589226482 q^{42} + 2698964877421600 q^{43} + 6508415289526488 q^{44} + 20720548577611926 q^{45} + 46666107114528228 q^{46} - 34164973016283282 q^{47} - 18882656270343072 q^{48} + 22206556236530706 q^{49} - 86450085282109038 q^{50} - 34587228747623004 q^{51} - 2674767257845192 q^{52} + 45711724933562676 q^{53} - 47833169657839398 q^{54} + 63540219488639160 q^{55} - 195080523769591278 q^{56} + 157285092372477732 q^{57} + 586384889080693608 q^{58} - 241786426439863284 q^{59} - 691555334397448140 q^{60} - 77950929719603734 q^{61} + 1486457358059496708 q^{62} + 351617098636204242 q^{63} - 1512665990271750586 q^{64} - 861392179016755566 q^{65} - 810731122103804742 q^{66} + 1414223150801683098 q^{67} + 2582507642453939712 q^{68} - 950536959338746440 q^{69} - 3783694955815590384 q^{70} - 587998065931528308 q^{71} + 4205266812332939790 q^{72} + 5398101368961972944 q^{73} + 1357298266273093830 q^{74} - 7004896155906644454 q^{75} - 4189440215764874296 q^{76} + 3950228440107193152 q^{77} + 5228015606617843872 q^{78} - 1048684531243427826 q^{79} - 11842349839559255784 q^{80} - 4794447335648398218 q^{81} - 753969961494486216 q^{82} - 479028174092951076 q^{83} + 7540396078827243180 q^{84} - 989831272039406592 q^{85} + 5801235581200613766 q^{86} - 4932614997804786876 q^{87} + 32091278421840121068 q^{88} - 13183232551622448144 q^{89} - 8353002961759772520 q^{90} - 17604530944351115320 q^{91} - 13168451760833625984 q^{92} + 26817111008120036964 q^{93} + 57900494628539649672 q^{94} - 33359370713793875766 q^{95} - 32642932787876297484 q^{96} - 7282556970221754172 q^{97} - 22509130625744441178 q^{98} + 18402092995325976972 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{20}^{\mathrm{new}}(\Gamma_1(21))\)

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
21.20.a \(\chi_{21}(1, \cdot)\) 21.20.a.a 4 1
21.20.a.b 5
21.20.a.c 5
21.20.a.d 6
21.20.c \(\chi_{21}(20, \cdot)\) 21.20.c.a 48 1
21.20.e \(\chi_{21}(4, \cdot)\) 21.20.e.a 24 2
21.20.e.b 26
21.20.g \(\chi_{21}(5, \cdot)\) 21.20.g.a 2 2
21.20.g.b 96

Decomposition of \(S_{20}^{\mathrm{old}}(\Gamma_1(21))\) into lower level spaces

\( S_{20}^{\mathrm{old}}(\Gamma_1(21)) \cong \) \(S_{20}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{20}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 2}\)\(\oplus\)\(S_{20}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 2}\)