Properties

Label 63.9
Level 63
Weight 9
Dimension 853
Nonzero newspaces 10
Newform subspaces 18
Sturm bound 2592
Trace bound 3

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Defining parameters

Level: \( N \) = \( 63 = 3^{2} \cdot 7 \)
Weight: \( k \) = \( 9 \)
Nonzero newspaces: \( 10 \)
Newform subspaces: \( 18 \)
Sturm bound: \(2592\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(\Gamma_1(63))\).

Total New Old
Modular forms 1200 899 301
Cusp forms 1104 853 251
Eisenstein series 96 46 50

Trace form

\( 853 q - 3 q^{2} + 174 q^{3} - 1983 q^{4} - 1722 q^{5} + 4506 q^{6} - 543 q^{7} - 4059 q^{8} - 35958 q^{9} + O(q^{10}) \) \( 853 q - 3 q^{2} + 174 q^{3} - 1983 q^{4} - 1722 q^{5} + 4506 q^{6} - 543 q^{7} - 4059 q^{8} - 35958 q^{9} + 23580 q^{10} + 50118 q^{11} + 108672 q^{12} - 21290 q^{13} + 271605 q^{14} + 23028 q^{15} - 555803 q^{16} - 14562 q^{17} + 90876 q^{18} + 765424 q^{19} - 1078926 q^{20} - 943728 q^{21} - 1841016 q^{22} + 1296348 q^{23} + 2840838 q^{24} + 2180581 q^{25} + 2134170 q^{26} + 1952430 q^{27} - 1144607 q^{28} - 9705126 q^{29} - 8048886 q^{30} + 7143862 q^{31} + 24730497 q^{32} + 10688214 q^{33} - 19735080 q^{34} - 14210046 q^{35} - 31316418 q^{36} + 4170918 q^{37} + 9592644 q^{38} + 6200388 q^{39} + 28284462 q^{40} + 20478876 q^{41} + 17432658 q^{42} - 13080000 q^{43} - 69137388 q^{44} - 75523896 q^{45} - 14995902 q^{46} - 33184110 q^{47} + 33335262 q^{48} + 28229383 q^{49} + 155358039 q^{50} + 63212010 q^{51} - 30297830 q^{52} - 33248970 q^{53} - 25418004 q^{54} - 85672488 q^{55} - 84606747 q^{56} - 104948898 q^{57} + 18805824 q^{58} + 144023334 q^{59} + 9377490 q^{60} + 179570800 q^{61} + 42391056 q^{63} - 151894563 q^{64} - 71026428 q^{65} + 129010662 q^{66} - 129285364 q^{67} + 338586480 q^{68} + 244382544 q^{69} + 404843262 q^{70} - 135833850 q^{71} - 787143576 q^{72} - 53732648 q^{73} - 440284308 q^{74} - 57120798 q^{75} - 293599640 q^{76} + 244624872 q^{77} + 386506956 q^{78} + 330005510 q^{79} + 837901926 q^{80} + 347007978 q^{81} - 267276036 q^{82} + 397831974 q^{83} - 71499066 q^{84} - 533804880 q^{85} - 1660715382 q^{86} - 608391858 q^{87} - 339099882 q^{88} - 44280414 q^{89} + 515040558 q^{90} + 488610568 q^{91} + 676690158 q^{92} + 32174070 q^{93} + 315910602 q^{94} - 685699566 q^{95} - 1263062424 q^{96} - 41361488 q^{97} + 139460787 q^{98} + 727593048 q^{99} + O(q^{100}) \)

Decomposition of \(S_{9}^{\mathrm{new}}(\Gamma_1(63))\)

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
63.9.b \(\chi_{63}(8, \cdot)\) 63.9.b.a 16 1
63.9.d \(\chi_{63}(55, \cdot)\) 63.9.d.a 1 1
63.9.d.b 2
63.9.d.c 4
63.9.d.d 8
63.9.d.e 10
63.9.j \(\chi_{63}(11, \cdot)\) 63.9.j.a 124 2
63.9.k \(\chi_{63}(31, \cdot)\) 63.9.k.a 124 2
63.9.l \(\chi_{63}(13, \cdot)\) 63.9.l.a 124 2
63.9.m \(\chi_{63}(10, \cdot)\) 63.9.m.a 2 2
63.9.m.b 8
63.9.m.c 10
63.9.m.d 12
63.9.m.e 20
63.9.n \(\chi_{63}(2, \cdot)\) 63.9.n.a 124 2
63.9.q \(\chi_{63}(44, \cdot)\) 63.9.q.a 44 2
63.9.r \(\chi_{63}(29, \cdot)\) 63.9.r.a 96 2
63.9.t \(\chi_{63}(40, \cdot)\) 63.9.t.a 124 2

Decomposition of \(S_{9}^{\mathrm{old}}(\Gamma_1(63))\) into lower level spaces

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