Properties

Label 21.3
Level 21
Weight 3
Dimension 18
Nonzero newspaces 4
Newforms 7
Sturm bound 96
Trace bound 2

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Defining parameters

Level: \( N \) = \( 21 = 3 \cdot 7 \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 4 \)
Newforms: \( 7 \)
Sturm bound: \(96\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(21))\).

Total New Old
Modular forms 44 26 18
Cusp forms 20 18 2
Eisenstein series 24 8 16

Trace form

\(18q \) \(\mathstrut -\mathstrut 6q^{3} \) \(\mathstrut -\mathstrut 22q^{4} \) \(\mathstrut -\mathstrut 6q^{5} \) \(\mathstrut -\mathstrut 6q^{6} \) \(\mathstrut +\mathstrut 2q^{7} \) \(\mathstrut -\mathstrut 6q^{8} \) \(\mathstrut -\mathstrut 24q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(18q \) \(\mathstrut -\mathstrut 6q^{3} \) \(\mathstrut -\mathstrut 22q^{4} \) \(\mathstrut -\mathstrut 6q^{5} \) \(\mathstrut -\mathstrut 6q^{6} \) \(\mathstrut +\mathstrut 2q^{7} \) \(\mathstrut -\mathstrut 6q^{8} \) \(\mathstrut -\mathstrut 24q^{9} \) \(\mathstrut -\mathstrut 12q^{10} \) \(\mathstrut +\mathstrut 6q^{11} \) \(\mathstrut +\mathstrut 18q^{12} \) \(\mathstrut +\mathstrut 2q^{13} \) \(\mathstrut +\mathstrut 24q^{14} \) \(\mathstrut +\mathstrut 48q^{15} \) \(\mathstrut +\mathstrut 90q^{16} \) \(\mathstrut +\mathstrut 48q^{17} \) \(\mathstrut +\mathstrut 96q^{18} \) \(\mathstrut +\mathstrut 2q^{19} \) \(\mathstrut -\mathstrut 24q^{21} \) \(\mathstrut -\mathstrut 108q^{22} \) \(\mathstrut -\mathstrut 96q^{23} \) \(\mathstrut -\mathstrut 150q^{24} \) \(\mathstrut -\mathstrut 132q^{25} \) \(\mathstrut -\mathstrut 126q^{26} \) \(\mathstrut -\mathstrut 132q^{27} \) \(\mathstrut -\mathstrut 102q^{28} \) \(\mathstrut -\mathstrut 12q^{29} \) \(\mathstrut +\mathstrut 24q^{30} \) \(\mathstrut +\mathstrut 86q^{31} \) \(\mathstrut +\mathstrut 78q^{32} \) \(\mathstrut +\mathstrut 186q^{33} \) \(\mathstrut +\mathstrut 240q^{34} \) \(\mathstrut +\mathstrut 210q^{35} \) \(\mathstrut +\mathstrut 198q^{36} \) \(\mathstrut +\mathstrut 160q^{37} \) \(\mathstrut +\mathstrut 174q^{38} \) \(\mathstrut +\mathstrut 66q^{39} \) \(\mathstrut +\mathstrut 96q^{40} \) \(\mathstrut -\mathstrut 72q^{42} \) \(\mathstrut -\mathstrut 188q^{43} \) \(\mathstrut -\mathstrut 168q^{44} \) \(\mathstrut -\mathstrut 198q^{45} \) \(\mathstrut -\mathstrut 204q^{46} \) \(\mathstrut -\mathstrut 222q^{47} \) \(\mathstrut -\mathstrut 210q^{48} \) \(\mathstrut -\mathstrut 120q^{49} \) \(\mathstrut -\mathstrut 114q^{50} \) \(\mathstrut -\mathstrut 168q^{51} \) \(\mathstrut +\mathstrut 152q^{52} \) \(\mathstrut -\mathstrut 12q^{53} \) \(\mathstrut -\mathstrut 84q^{54} \) \(\mathstrut +\mathstrut 156q^{55} \) \(\mathstrut +\mathstrut 18q^{56} \) \(\mathstrut +\mathstrut 108q^{57} \) \(\mathstrut +\mathstrut 84q^{59} \) \(\mathstrut +\mathstrut 96q^{60} \) \(\mathstrut +\mathstrut 38q^{61} \) \(\mathstrut +\mathstrut 78q^{63} \) \(\mathstrut -\mathstrut 34q^{64} \) \(\mathstrut +\mathstrut 18q^{65} \) \(\mathstrut -\mathstrut 36q^{66} \) \(\mathstrut +\mathstrut 102q^{67} \) \(\mathstrut +\mathstrut 36q^{68} \) \(\mathstrut +\mathstrut 288q^{69} \) \(\mathstrut -\mathstrut 60q^{70} \) \(\mathstrut +\mathstrut 120q^{71} \) \(\mathstrut +\mathstrut 174q^{72} \) \(\mathstrut -\mathstrut 100q^{73} \) \(\mathstrut +\mathstrut 90q^{74} \) \(\mathstrut +\mathstrut 180q^{75} \) \(\mathstrut -\mathstrut 292q^{76} \) \(\mathstrut +\mathstrut 72q^{77} \) \(\mathstrut +\mathstrut 24q^{78} \) \(\mathstrut +\mathstrut 162q^{79} \) \(\mathstrut +\mathstrut 48q^{80} \) \(\mathstrut +\mathstrut 108q^{82} \) \(\mathstrut +\mathstrut 102q^{84} \) \(\mathstrut -\mathstrut 168q^{85} \) \(\mathstrut +\mathstrut 210q^{86} \) \(\mathstrut +\mathstrut 12q^{87} \) \(\mathstrut -\mathstrut 24q^{88} \) \(\mathstrut -\mathstrut 60q^{89} \) \(\mathstrut -\mathstrut 132q^{90} \) \(\mathstrut -\mathstrut 148q^{91} \) \(\mathstrut -\mathstrut 84q^{92} \) \(\mathstrut -\mathstrut 264q^{93} \) \(\mathstrut -\mathstrut 324q^{94} \) \(\mathstrut -\mathstrut 438q^{95} \) \(\mathstrut -\mathstrut 402q^{96} \) \(\mathstrut -\mathstrut 376q^{97} \) \(\mathstrut -\mathstrut 270q^{98} \) \(\mathstrut -\mathstrut 432q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(21))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
21.3.b \(\chi_{21}(8, \cdot)\) 21.3.b.a 4 1
21.3.d \(\chi_{21}(13, \cdot)\) 21.3.d.a 2 1
21.3.f \(\chi_{21}(10, \cdot)\) 21.3.f.a 2 2
21.3.f.b 2
21.3.f.c 2
21.3.h \(\chi_{21}(2, \cdot)\) 21.3.h.a 2 2
21.3.h.b 4

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(21))\) into lower level spaces

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