Properties

Label 63.3
Level 63
Weight 3
Dimension 197
Nonzero newspaces 10
Newform subspaces 18
Sturm bound 864
Trace bound 3

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Defining parameters

Level: \( N \) = \( 63 = 3^{2} \cdot 7 \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 10 \)
Newform subspaces: \( 18 \)
Sturm bound: \(864\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(63))\).

Total New Old
Modular forms 336 243 93
Cusp forms 240 197 43
Eisenstein series 96 46 50

Trace form

\( 197 q - 3 q^{2} - 6 q^{3} + q^{4} - 18 q^{5} - 30 q^{6} - 11 q^{7} - 15 q^{8} + 6 q^{9} + O(q^{10}) \) \( 197 q - 3 q^{2} - 6 q^{3} + q^{4} - 18 q^{5} - 30 q^{6} - 11 q^{7} - 15 q^{8} + 6 q^{9} - 6 q^{11} - 48 q^{12} - 42 q^{13} - 135 q^{14} - 84 q^{15} - 199 q^{16} - 114 q^{17} - 60 q^{18} - 96 q^{19} - 6 q^{20} + 12 q^{21} + 96 q^{22} + 216 q^{23} + 222 q^{24} + 185 q^{25} + 234 q^{26} + 6 q^{27} + 257 q^{28} - 6 q^{29} - 78 q^{30} - 138 q^{31} - 363 q^{32} - 222 q^{33} - 456 q^{34} - 438 q^{35} - 306 q^{36} - 118 q^{37} - 300 q^{38} - 36 q^{39} - 234 q^{40} + 24 q^{41} + 54 q^{42} + 20 q^{43} + 408 q^{44} + 288 q^{45} + 330 q^{46} + 594 q^{47} + 774 q^{48} + 203 q^{49} + 1203 q^{50} + 582 q^{51} + 378 q^{52} + 834 q^{53} + 1092 q^{54} + 168 q^{55} + 993 q^{56} + 282 q^{57} + 72 q^{58} - 90 q^{59} + 282 q^{60} + 60 q^{61} - 132 q^{63} + 241 q^{64} - 480 q^{65} - 522 q^{66} - 212 q^{67} - 1332 q^{68} - 936 q^{69} - 786 q^{70} - 1266 q^{71} - 2208 q^{72} - 900 q^{73} - 2040 q^{74} - 1290 q^{75} - 432 q^{76} - 1104 q^{77} - 1284 q^{78} - 302 q^{79} - 1266 q^{80} - 18 q^{81} - 300 q^{82} + 150 q^{83} - 114 q^{84} + 384 q^{85} + 450 q^{86} + 438 q^{87} - 258 q^{88} + 102 q^{89} + 6 q^{90} + 264 q^{91} - 234 q^{92} - 138 q^{93} + 450 q^{94} + 726 q^{95} + 384 q^{96} + 492 q^{97} + 963 q^{98} + 504 q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(63))\)

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
63.3.b \(\chi_{63}(8, \cdot)\) 63.3.b.a 4 1
63.3.d \(\chi_{63}(55, \cdot)\) 63.3.d.a 1 1
63.3.d.b 2
63.3.d.c 2
63.3.j \(\chi_{63}(11, \cdot)\) 63.3.j.a 6 2
63.3.j.b 22
63.3.k \(\chi_{63}(31, \cdot)\) 63.3.k.a 28 2
63.3.l \(\chi_{63}(13, \cdot)\) 63.3.l.a 28 2
63.3.m \(\chi_{63}(10, \cdot)\) 63.3.m.a 2 2
63.3.m.b 2
63.3.m.c 2
63.3.m.d 2
63.3.m.e 4
63.3.n \(\chi_{63}(2, \cdot)\) 63.3.n.a 6 2
63.3.n.b 22
63.3.q \(\chi_{63}(44, \cdot)\) 63.3.q.a 12 2
63.3.r \(\chi_{63}(29, \cdot)\) 63.3.r.a 24 2
63.3.t \(\chi_{63}(40, \cdot)\) 63.3.t.a 28 2

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(63))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(63)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 2}\)