Properties

Label 21.2
Level 21
Weight 2
Dimension 5
Nonzero newspaces 3
Newforms 3
Sturm bound 64
Trace bound 2

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Defining parameters

Level: \( N \) = \( 21 = 3 \cdot 7 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 3 \)
Newforms: \( 3 \)
Sturm bound: \(64\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(21))\).

Total New Old
Modular forms 28 17 11
Cusp forms 5 5 0
Eisenstein series 23 12 11

Trace form

\(5q \) \(\mathstrut -\mathstrut 3q^{2} \) \(\mathstrut -\mathstrut 3q^{3} \) \(\mathstrut -\mathstrut 5q^{4} \) \(\mathstrut +\mathstrut 3q^{6} \) \(\mathstrut -\mathstrut 5q^{7} \) \(\mathstrut +\mathstrut 3q^{8} \) \(\mathstrut +\mathstrut 3q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(5q \) \(\mathstrut -\mathstrut 3q^{2} \) \(\mathstrut -\mathstrut 3q^{3} \) \(\mathstrut -\mathstrut 5q^{4} \) \(\mathstrut +\mathstrut 3q^{6} \) \(\mathstrut -\mathstrut 5q^{7} \) \(\mathstrut +\mathstrut 3q^{8} \) \(\mathstrut +\mathstrut 3q^{9} \) \(\mathstrut +\mathstrut 6q^{10} \) \(\mathstrut +\mathstrut 6q^{11} \) \(\mathstrut +\mathstrut 3q^{12} \) \(\mathstrut +\mathstrut 3q^{14} \) \(\mathstrut -\mathstrut 6q^{15} \) \(\mathstrut -\mathstrut q^{16} \) \(\mathstrut -\mathstrut 6q^{17} \) \(\mathstrut -\mathstrut 3q^{18} \) \(\mathstrut -\mathstrut 6q^{19} \) \(\mathstrut -\mathstrut 6q^{20} \) \(\mathstrut -\mathstrut 3q^{21} \) \(\mathstrut -\mathstrut 12q^{22} \) \(\mathstrut +\mathstrut 3q^{24} \) \(\mathstrut +\mathstrut 5q^{25} \) \(\mathstrut +\mathstrut 3q^{27} \) \(\mathstrut +\mathstrut 17q^{28} \) \(\mathstrut +\mathstrut 6q^{29} \) \(\mathstrut +\mathstrut 6q^{30} \) \(\mathstrut +\mathstrut 6q^{31} \) \(\mathstrut +\mathstrut 3q^{32} \) \(\mathstrut +\mathstrut 6q^{33} \) \(\mathstrut +\mathstrut 6q^{34} \) \(\mathstrut -\mathstrut 9q^{36} \) \(\mathstrut +\mathstrut 2q^{37} \) \(\mathstrut -\mathstrut 6q^{38} \) \(\mathstrut -\mathstrut 6q^{40} \) \(\mathstrut -\mathstrut 18q^{41} \) \(\mathstrut -\mathstrut 9q^{42} \) \(\mathstrut -\mathstrut 4q^{43} \) \(\mathstrut +\mathstrut 6q^{47} \) \(\mathstrut -\mathstrut 9q^{48} \) \(\mathstrut -\mathstrut q^{49} \) \(\mathstrut -\mathstrut 3q^{50} \) \(\mathstrut -\mathstrut 6q^{51} \) \(\mathstrut -\mathstrut 6q^{52} \) \(\mathstrut -\mathstrut 6q^{53} \) \(\mathstrut -\mathstrut 3q^{54} \) \(\mathstrut -\mathstrut 3q^{56} \) \(\mathstrut +\mathstrut 24q^{57} \) \(\mathstrut -\mathstrut 6q^{58} \) \(\mathstrut +\mathstrut 24q^{59} \) \(\mathstrut +\mathstrut 6q^{60} \) \(\mathstrut +\mathstrut 36q^{62} \) \(\mathstrut +\mathstrut 15q^{63} \) \(\mathstrut +\mathstrut 7q^{64} \) \(\mathstrut +\mathstrut 6q^{65} \) \(\mathstrut -\mathstrut 2q^{67} \) \(\mathstrut +\mathstrut 6q^{68} \) \(\mathstrut -\mathstrut 18q^{70} \) \(\mathstrut -\mathstrut 12q^{71} \) \(\mathstrut +\mathstrut 3q^{72} \) \(\mathstrut -\mathstrut 30q^{73} \) \(\mathstrut -\mathstrut 12q^{74} \) \(\mathstrut -\mathstrut 15q^{75} \) \(\mathstrut -\mathstrut 12q^{77} \) \(\mathstrut +\mathstrut 6q^{78} \) \(\mathstrut -\mathstrut 2q^{79} \) \(\mathstrut -\mathstrut 6q^{80} \) \(\mathstrut -\mathstrut 9q^{81} \) \(\mathstrut +\mathstrut 18q^{82} \) \(\mathstrut -\mathstrut 3q^{84} \) \(\mathstrut +\mathstrut 12q^{85} \) \(\mathstrut -\mathstrut 6q^{86} \) \(\mathstrut -\mathstrut 6q^{87} \) \(\mathstrut +\mathstrut 12q^{88} \) \(\mathstrut -\mathstrut 30q^{89} \) \(\mathstrut -\mathstrut 6q^{90} \) \(\mathstrut +\mathstrut 6q^{91} \) \(\mathstrut -\mathstrut 24q^{93} \) \(\mathstrut +\mathstrut 12q^{94} \) \(\mathstrut -\mathstrut 6q^{95} \) \(\mathstrut +\mathstrut 3q^{96} \) \(\mathstrut +\mathstrut 6q^{97} \) \(\mathstrut +\mathstrut 3q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
21.2.a \(\chi_{21}(1, \cdot)\) 21.2.a.a 1 1
21.2.c \(\chi_{21}(20, \cdot)\) None 0 1
21.2.e \(\chi_{21}(4, \cdot)\) 21.2.e.a 2 2
21.2.g \(\chi_{21}(5, \cdot)\) 21.2.g.a 2 2