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Properties

Label 63.16
Level 63
Weight 16
Dimension 1615
Nonzero newspaces 10
Sturm bound 4608
Trace bound 2

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Defining parameters

Level: \( N \) = \( 63 = 3^{2} \cdot 7 \)
Weight: \( k \) = \( 16 \)
Nonzero newspaces: \( 10 \)
Sturm bound: \(4608\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{16}(\Gamma_1(63))\).

Total New Old
Modular forms 2208 1659 549
Cusp forms 2112 1615 497
Eisenstein series 96 44 52

Trace form

\( 1615 q + 69 q^{2} - 6702 q^{3} + 126481 q^{4} + 294453 q^{5} - 4416474 q^{6} + 618970 q^{7} - 37439529 q^{8} + 31193970 q^{9} + O(q^{10}) \) \( 1615 q + 69 q^{2} - 6702 q^{3} + 126481 q^{4} + 294453 q^{5} - 4416474 q^{6} + 618970 q^{7} - 37439529 q^{8} + 31193970 q^{9} - 153402378 q^{10} + 376985859 q^{11} - 363829620 q^{12} - 101390332 q^{13} - 250842381 q^{14} + 2531161482 q^{15} - 3751340819 q^{16} + 6643266645 q^{17} - 1764546468 q^{18} - 4543728187 q^{19} - 17719994706 q^{20} - 16177772913 q^{21} + 36005589378 q^{22} + 141980480163 q^{23} - 136066360998 q^{24} - 9398067941 q^{25} + 136155648942 q^{26} - 348525189120 q^{27} - 198681992399 q^{28} + 136360356360 q^{29} - 977924575518 q^{30} + 721246736153 q^{31} + 407878841487 q^{32} + 750568142712 q^{33} + 3094244322246 q^{34} - 1750673498283 q^{35} - 4905461596050 q^{36} - 2266750673809 q^{37} + 17532541410348 q^{38} - 3595982254470 q^{39} - 15715627620534 q^{40} - 7009398225756 q^{41} + 6343342724160 q^{42} - 1019602644772 q^{43} + 6337671169662 q^{44} - 6567441718374 q^{45} - 20431498248354 q^{46} - 15862151195409 q^{47} - 26239551494166 q^{48} + 7956276241186 q^{49} - 22881933188841 q^{50} + 3278384901366 q^{51} - 111141867822838 q^{52} + 2125416703845 q^{53} + 7497855642252 q^{54} + 3467339882430 q^{55} + 130439981965839 q^{56} + 65055321938010 q^{57} + 171262672722804 q^{58} - 104559662587323 q^{59} - 434072110355970 q^{60} - 90277746541915 q^{61} + 715112594644788 q^{62} + 152475197785905 q^{63} - 324603070467779 q^{64} - 311739234154878 q^{65} - 59682465159966 q^{66} + 112940079114059 q^{67} + 706852778282970 q^{68} + 327068859511674 q^{69} - 289866749729502 q^{70} - 835217295267900 q^{71} - 893373386511648 q^{72} - 359746740511921 q^{73} + 1078652779313514 q^{74} + 1193184428664642 q^{75} + 465635127460322 q^{76} - 1122604269905100 q^{77} + 1116690628063800 q^{78} - 581805444601537 q^{79} - 2032594651446594 q^{80} - 440538970726890 q^{81} + 772360416385554 q^{82} - 790003939400550 q^{83} - 1915423150179930 q^{84} - 1554008987001078 q^{85} + 4075598473420656 q^{86} + 5206883436798162 q^{87} + 3399516681260340 q^{88} - 6764999283036471 q^{89} - 10855991113354326 q^{90} - 2896766156627458 q^{91} + 6915121125509664 q^{92} + 3904330295147118 q^{93} - 585637575734796 q^{94} + 11397849600935019 q^{95} - 5469406056869736 q^{96} - 713367317845492 q^{97} - 12578809829294265 q^{98} - 8311558635141786 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{16}^{\mathrm{new}}(\Gamma_1(63))\)

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
63.16.a \(\chi_{63}(1, \cdot)\) 63.16.a.a 3 1
63.16.a.b 3
63.16.a.c 4
63.16.a.d 4
63.16.a.e 4
63.16.a.f 5
63.16.a.g 6
63.16.a.h 8
63.16.c \(\chi_{63}(62, \cdot)\) 63.16.c.a 4 1
63.16.c.b 36
63.16.e \(\chi_{63}(37, \cdot)\) 63.16.e.a 18 2
63.16.e.b 18
63.16.e.c 22
63.16.e.d 40
63.16.f \(\chi_{63}(22, \cdot)\) n/a 180 2
63.16.g \(\chi_{63}(4, \cdot)\) n/a 236 2
63.16.h \(\chi_{63}(25, \cdot)\) n/a 236 2
63.16.i \(\chi_{63}(5, \cdot)\) n/a 236 2
63.16.o \(\chi_{63}(20, \cdot)\) n/a 236 2
63.16.p \(\chi_{63}(17, \cdot)\) 63.16.p.a 80 2
63.16.s \(\chi_{63}(47, \cdot)\) n/a 236 2

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{16}^{\mathrm{old}}(\Gamma_1(63))\) into lower level spaces

\( S_{16}^{\mathrm{old}}(\Gamma_1(63)) \cong \) \(S_{16}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 3}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 2}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 2}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(\Gamma_1(63))\)\(^{\oplus 1}\)