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Properties

Label 63.8
Level 63
Weight 8
Dimension 741
Nonzero newspaces 10
Newform subspaces 23
Sturm bound 2304
Trace bound 2

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Defining parameters

Level: \( N \) = \( 63 = 3^{2} \cdot 7 \)
Weight: \( k \) = \( 8 \)
Nonzero newspaces: \( 10 \)
Newform subspaces: \( 23 \)
Sturm bound: \(2304\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(63))\).

Total New Old
Modular forms 1056 785 271
Cusp forms 960 741 219
Eisenstein series 96 44 52

Trace form

\( 741 q + 21 q^{2} - 60 q^{3} - 367 q^{4} + 1128 q^{5} + 2454 q^{6} - 49 q^{7} - 16329 q^{8} - 1992 q^{9} + O(q^{10}) \) \( 741 q + 21 q^{2} - 60 q^{3} - 367 q^{4} + 1128 q^{5} + 2454 q^{6} - 49 q^{7} - 16329 q^{8} - 1992 q^{9} + 8742 q^{10} + 16266 q^{11} - 15348 q^{12} + 17648 q^{13} - 44973 q^{14} - 8148 q^{15} + 60909 q^{16} + 87132 q^{17} - 72132 q^{18} - 251956 q^{19} - 190866 q^{20} + 66270 q^{21} + 280626 q^{22} + 124266 q^{23} + 103578 q^{24} + 162309 q^{25} - 520098 q^{26} - 857730 q^{27} - 901839 q^{28} + 179058 q^{29} + 2848962 q^{30} + 492290 q^{31} - 128913 q^{32} - 457944 q^{33} - 1091466 q^{34} + 656652 q^{35} - 1951506 q^{36} + 2744074 q^{37} + 4772940 q^{38} + 3183264 q^{39} - 3455574 q^{40} - 3367428 q^{41} - 4743936 q^{42} - 4626656 q^{43} - 7777794 q^{44} - 2986164 q^{45} + 11345502 q^{46} + 9661350 q^{47} + 18001386 q^{48} + 2084193 q^{49} + 7729959 q^{50} - 2021340 q^{51} - 23902198 q^{52} - 14443530 q^{53} - 22723620 q^{54} + 583560 q^{55} - 4716657 q^{56} - 559860 q^{57} + 21151572 q^{58} + 9328356 q^{59} + 18712830 q^{60} - 5806786 q^{61} + 2740116 q^{62} + 21268740 q^{63} - 14293123 q^{64} + 4668312 q^{65} - 14645214 q^{66} + 11242056 q^{67} - 24928806 q^{68} - 31955220 q^{69} - 14506062 q^{70} - 36266124 q^{71} - 4366560 q^{72} + 34110566 q^{73} + 41871978 q^{74} + 31179552 q^{75} + 21971426 q^{76} + 51871944 q^{77} + 40058328 q^{78} - 5264592 q^{79} + 5389566 q^{80} + 25124436 q^{81} - 61795854 q^{82} - 78860982 q^{83} - 87895482 q^{84} - 38081568 q^{85} - 75120384 q^{86} - 18502338 q^{87} + 46814004 q^{88} + 42374004 q^{89} + 59804394 q^{90} + 44643062 q^{91} + 33357216 q^{92} + 16669806 q^{93} + 50282580 q^{94} + 74383254 q^{95} + 51168984 q^{96} + 47727560 q^{97} + 54792135 q^{98} + 32862960 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(63))\)

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
63.8.a \(\chi_{63}(1, \cdot)\) 63.8.a.a 1 1
63.8.a.b 1
63.8.a.c 2
63.8.a.d 2
63.8.a.e 2
63.8.a.f 2
63.8.a.g 3
63.8.a.h 4
63.8.c \(\chi_{63}(62, \cdot)\) 63.8.c.a 4 1
63.8.c.b 16
63.8.e \(\chi_{63}(37, \cdot)\) 63.8.e.a 2 2
63.8.e.b 8
63.8.e.c 8
63.8.e.d 10
63.8.e.e 16
63.8.f \(\chi_{63}(22, \cdot)\) 63.8.f.a 42 2
63.8.f.b 42
63.8.g \(\chi_{63}(4, \cdot)\) 63.8.g.a 108 2
63.8.h \(\chi_{63}(25, \cdot)\) 63.8.h.a 108 2
63.8.i \(\chi_{63}(5, \cdot)\) 63.8.i.a 108 2
63.8.o \(\chi_{63}(20, \cdot)\) 63.8.o.a 108 2
63.8.p \(\chi_{63}(17, \cdot)\) 63.8.p.a 36 2
63.8.s \(\chi_{63}(47, \cdot)\) 63.8.s.a 108 2

Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_1(63))\) into lower level spaces

\( S_{8}^{\mathrm{old}}(\Gamma_1(63)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 3}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(63))\)\(^{\oplus 1}\)