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Properties

Label 63.10
Level 63
Weight 10
Dimension 961
Nonzero newspaces 10
Newform subspaces 22
Sturm bound 2880
Trace bound 2

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Defining parameters

Level: \( N \) = \( 63 = 3^{2} \cdot 7 \)
Weight: \( k \) = \( 10 \)
Nonzero newspaces: \( 10 \)
Newform subspaces: \( 22 \)
Sturm bound: \(2880\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_1(63))\).

Total New Old
Modular forms 1344 1005 339
Cusp forms 1248 961 287
Eisenstein series 96 44 52

Trace form

\( 961 q - 75 q^{2} - 6 q^{3} + 3409 q^{4} - 5751 q^{5} - 4890 q^{6} + 9634 q^{7} + 35103 q^{8} + 31326 q^{9} + O(q^{10}) \) \( 961 q - 75 q^{2} - 6 q^{3} + 3409 q^{4} - 5751 q^{5} - 4890 q^{6} + 9634 q^{7} + 35103 q^{8} + 31326 q^{9} - 91770 q^{10} - 79005 q^{11} + 485484 q^{12} - 37756 q^{13} - 808485 q^{14} - 652710 q^{15} + 1295245 q^{16} - 960099 q^{17} + 678540 q^{18} + 1977965 q^{19} + 4525662 q^{20} + 2453583 q^{21} - 7530054 q^{22} - 12489885 q^{23} - 5097270 q^{24} + 12021061 q^{25} + 20479014 q^{26} + 24428256 q^{27} - 14114543 q^{28} - 18709500 q^{29} - 63988350 q^{30} - 5343127 q^{31} - 9137481 q^{32} + 71455404 q^{33} + 52946310 q^{34} - 2401227 q^{35} + 14912622 q^{36} - 28562233 q^{37} - 156496380 q^{38} - 138670902 q^{39} + 92936754 q^{40} + 51663492 q^{41} + 132958512 q^{42} + 133774340 q^{43} + 601946910 q^{44} + 91184130 q^{45} - 482632002 q^{46} - 502200129 q^{47} - 725124438 q^{48} - 188080340 q^{49} + 627319959 q^{50} + 277356894 q^{51} + 836518058 q^{52} + 429138093 q^{53} + 339563676 q^{54} - 80973906 q^{55} + 627554319 q^{56} - 628465002 q^{57} - 1412126652 q^{58} - 758248707 q^{59} + 119193150 q^{60} + 1049707409 q^{61} + 1072631700 q^{62} - 424628511 q^{63} + 1542998029 q^{64} - 896217726 q^{65} - 2600541486 q^{66} - 1108453813 q^{67} - 1025477958 q^{68} + 1129671450 q^{69} + 123633810 q^{70} + 3675957252 q^{71} + 2516102160 q^{72} + 1068062135 q^{73} - 1035687414 q^{74} - 4544874246 q^{75} - 5544183646 q^{76} - 2904875256 q^{77} - 239101224 q^{78} - 855628129 q^{79} + 3754659054 q^{80} + 4070282346 q^{81} + 5693296602 q^{82} + 1638929250 q^{83} + 3425088990 q^{84} + 3057900066 q^{85} + 376698216 q^{86} - 4349701182 q^{87} - 14951865420 q^{88} - 3720878823 q^{89} - 4063899846 q^{90} - 145316482 q^{91} + 7060533696 q^{92} + 4921287126 q^{93} + 16477810236 q^{94} + 7260586923 q^{95} - 711876792 q^{96} - 3436439380 q^{97} - 16937674737 q^{98} - 10536467562 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_1(63))\)

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 available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
63.10.a \(\chi_{63}(1, \cdot)\) 63.10.a.a 1 1
63.10.a.b 2
63.10.a.c 2
63.10.a.d 2
63.10.a.e 3
63.10.a.f 3
63.10.a.g 4
63.10.a.h 6
63.10.c \(\chi_{63}(62, \cdot)\) 63.10.c.a 4 1
63.10.c.b 20
63.10.e \(\chi_{63}(37, \cdot)\) 63.10.e.a 10 2
63.10.e.b 10
63.10.e.c 14
63.10.e.d 24
63.10.f \(\chi_{63}(22, \cdot)\) 63.10.f.a 54 2
63.10.f.b 54
63.10.g \(\chi_{63}(4, \cdot)\) 63.10.g.a 140 2
63.10.h \(\chi_{63}(25, \cdot)\) 63.10.h.a 140 2
63.10.i \(\chi_{63}(5, \cdot)\) 63.10.i.a 140 2
63.10.o \(\chi_{63}(20, \cdot)\) 63.10.o.a 140 2
63.10.p \(\chi_{63}(17, \cdot)\) 63.10.p.a 48 2
63.10.s \(\chi_{63}(47, \cdot)\) 63.10.s.a 140 2

Decomposition of \(S_{10}^{\mathrm{old}}(\Gamma_1(63))\) into lower level spaces

\( S_{10}^{\mathrm{old}}(\Gamma_1(63)) \cong \) \(S_{10}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 3}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 2}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 2}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(63))\)\(^{\oplus 1}\)