Properties

Label 63.2
Level 63
Weight 2
Dimension 87
Nonzero newspaces 10
Newforms 17
Sturm bound 576
Trace bound 4

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Defining parameters

Level: \( N \) = \( 63 = 3^{2} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 10 \)
Newforms: \( 17 \)
Sturm bound: \(576\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(63))\).

Total New Old
Modular forms 192 131 61
Cusp forms 97 87 10
Eisenstein series 95 44 51

Trace form

\(87q \) \(\mathstrut -\mathstrut 9q^{2} \) \(\mathstrut -\mathstrut 12q^{3} \) \(\mathstrut -\mathstrut 13q^{4} \) \(\mathstrut -\mathstrut 12q^{5} \) \(\mathstrut -\mathstrut 12q^{6} \) \(\mathstrut -\mathstrut 13q^{7} \) \(\mathstrut -\mathstrut 27q^{8} \) \(\mathstrut -\mathstrut 12q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(87q \) \(\mathstrut -\mathstrut 9q^{2} \) \(\mathstrut -\mathstrut 12q^{3} \) \(\mathstrut -\mathstrut 13q^{4} \) \(\mathstrut -\mathstrut 12q^{5} \) \(\mathstrut -\mathstrut 12q^{6} \) \(\mathstrut -\mathstrut 13q^{7} \) \(\mathstrut -\mathstrut 27q^{8} \) \(\mathstrut -\mathstrut 12q^{9} \) \(\mathstrut -\mathstrut 42q^{10} \) \(\mathstrut -\mathstrut 18q^{11} \) \(\mathstrut -\mathstrut 16q^{13} \) \(\mathstrut -\mathstrut 3q^{14} \) \(\mathstrut -\mathstrut 12q^{15} \) \(\mathstrut +\mathstrut 3q^{16} \) \(\mathstrut +\mathstrut 12q^{17} \) \(\mathstrut +\mathstrut 12q^{18} \) \(\mathstrut -\mathstrut 16q^{19} \) \(\mathstrut +\mathstrut 36q^{20} \) \(\mathstrut +\mathstrut 6q^{21} \) \(\mathstrut +\mathstrut 6q^{23} \) \(\mathstrut +\mathstrut 24q^{24} \) \(\mathstrut -\mathstrut 9q^{25} \) \(\mathstrut +\mathstrut 24q^{26} \) \(\mathstrut +\mathstrut 6q^{27} \) \(\mathstrut -\mathstrut 33q^{28} \) \(\mathstrut -\mathstrut 18q^{29} \) \(\mathstrut +\mathstrut 30q^{30} \) \(\mathstrut -\mathstrut 10q^{31} \) \(\mathstrut +\mathstrut 39q^{32} \) \(\mathstrut +\mathstrut 12q^{33} \) \(\mathstrut +\mathstrut 12q^{34} \) \(\mathstrut +\mathstrut 24q^{35} \) \(\mathstrut +\mathstrut 36q^{36} \) \(\mathstrut -\mathstrut 14q^{37} \) \(\mathstrut +\mathstrut 54q^{38} \) \(\mathstrut +\mathstrut 24q^{39} \) \(\mathstrut +\mathstrut 48q^{40} \) \(\mathstrut +\mathstrut 60q^{41} \) \(\mathstrut +\mathstrut 54q^{42} \) \(\mathstrut -\mathstrut 8q^{43} \) \(\mathstrut +\mathstrut 66q^{44} \) \(\mathstrut +\mathstrut 36q^{45} \) \(\mathstrut +\mathstrut 24q^{46} \) \(\mathstrut +\mathstrut 18q^{47} \) \(\mathstrut -\mathstrut 24q^{48} \) \(\mathstrut +\mathstrut 3q^{49} \) \(\mathstrut -\mathstrut 9q^{50} \) \(\mathstrut -\mathstrut 12q^{51} \) \(\mathstrut +\mathstrut 8q^{52} \) \(\mathstrut -\mathstrut 42q^{53} \) \(\mathstrut -\mathstrut 42q^{54} \) \(\mathstrut -\mathstrut 48q^{55} \) \(\mathstrut -\mathstrut 87q^{56} \) \(\mathstrut -\mathstrut 72q^{57} \) \(\mathstrut -\mathstrut 36q^{58} \) \(\mathstrut -\mathstrut 96q^{59} \) \(\mathstrut -\mathstrut 114q^{60} \) \(\mathstrut -\mathstrut 22q^{61} \) \(\mathstrut -\mathstrut 156q^{62} \) \(\mathstrut -\mathstrut 96q^{63} \) \(\mathstrut -\mathstrut 127q^{64} \) \(\mathstrut -\mathstrut 72q^{65} \) \(\mathstrut -\mathstrut 54q^{66} \) \(\mathstrut -\mathstrut 12q^{67} \) \(\mathstrut -\mathstrut 120q^{68} \) \(\mathstrut -\mathstrut 36q^{69} \) \(\mathstrut +\mathstrut 24q^{70} \) \(\mathstrut -\mathstrut 12q^{71} \) \(\mathstrut -\mathstrut 66q^{72} \) \(\mathstrut +\mathstrut 14q^{73} \) \(\mathstrut +\mathstrut 12q^{74} \) \(\mathstrut +\mathstrut 38q^{76} \) \(\mathstrut +\mathstrut 36q^{77} \) \(\mathstrut +\mathstrut 12q^{78} \) \(\mathstrut +\mathstrut 36q^{79} \) \(\mathstrut +\mathstrut 36q^{80} \) \(\mathstrut +\mathstrut 72q^{81} \) \(\mathstrut +\mathstrut 18q^{82} \) \(\mathstrut +\mathstrut 66q^{83} \) \(\mathstrut +\mathstrut 132q^{84} \) \(\mathstrut +\mathstrut 24q^{85} \) \(\mathstrut +\mathstrut 126q^{86} \) \(\mathstrut +\mathstrut 78q^{87} \) \(\mathstrut +\mathstrut 78q^{88} \) \(\mathstrut +\mathstrut 132q^{89} \) \(\mathstrut +\mathstrut 150q^{90} \) \(\mathstrut +\mathstrut 38q^{91} \) \(\mathstrut +\mathstrut 132q^{92} \) \(\mathstrut +\mathstrut 102q^{93} \) \(\mathstrut +\mathstrut 90q^{94} \) \(\mathstrut +\mathstrut 114q^{95} \) \(\mathstrut +\mathstrut 168q^{96} \) \(\mathstrut +\mathstrut 56q^{97} \) \(\mathstrut +\mathstrut 123q^{98} \) \(\mathstrut +\mathstrut 72q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(63))\)

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
63.2.a \(\chi_{63}(1, \cdot)\) 63.2.a.a 1 1
63.2.a.b 2
63.2.c \(\chi_{63}(62, \cdot)\) 63.2.c.a 4 1
63.2.e \(\chi_{63}(37, \cdot)\) 63.2.e.a 2 2
63.2.e.b 2
63.2.f \(\chi_{63}(22, \cdot)\) 63.2.f.a 6 2
63.2.f.b 6
63.2.g \(\chi_{63}(4, \cdot)\) 63.2.g.a 2 2
63.2.g.b 10
63.2.h \(\chi_{63}(25, \cdot)\) 63.2.h.a 2 2
63.2.h.b 10
63.2.i \(\chi_{63}(5, \cdot)\) 63.2.i.a 2 2
63.2.i.b 10
63.2.o \(\chi_{63}(20, \cdot)\) 63.2.o.a 12 2
63.2.p \(\chi_{63}(17, \cdot)\) 63.2.p.a 4 2
63.2.s \(\chi_{63}(47, \cdot)\) 63.2.s.a 2 2
63.2.s.b 10

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(63))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(63)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 2}\)