Properties

Label 63.6
Level 63
Weight 6
Dimension 525
Nonzero newspaces 10
Newform subspaces 25
Sturm bound 1728
Trace bound 2

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Defining parameters

Level: \( N \) = \( 63 = 3^{2} \cdot 7 \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 10 \)
Newform subspaces: \( 25 \)
Sturm bound: \(1728\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(63))\).

Total New Old
Modular forms 768 569 199
Cusp forms 672 525 147
Eisenstein series 96 44 52

Trace form

\( 525 q - 27 q^{2} + 12 q^{3} + 145 q^{4} - 186 q^{5} - 354 q^{6} - 113 q^{7} + 1647 q^{8} + 816 q^{9} + O(q^{10}) \) \( 525 q - 27 q^{2} + 12 q^{3} + 145 q^{4} - 186 q^{5} - 354 q^{6} - 113 q^{7} + 1647 q^{8} + 816 q^{9} + 1470 q^{10} - 1818 q^{11} - 5268 q^{12} - 620 q^{13} - 3381 q^{14} + 780 q^{15} - 3795 q^{16} + 9690 q^{17} + 19164 q^{18} + 4720 q^{19} + 10782 q^{20} - 1860 q^{21} + 2706 q^{22} - 15846 q^{23} - 12630 q^{24} - 13119 q^{25} + 4638 q^{26} + 5190 q^{27} - 18639 q^{28} - 10242 q^{29} - 2670 q^{30} + 34978 q^{31} - 14457 q^{32} - 9996 q^{33} - 75426 q^{34} - 45312 q^{35} - 17586 q^{36} + 12644 q^{37} + 54468 q^{38} + 22032 q^{39} + 200994 q^{40} + 128136 q^{41} + 98064 q^{42} + 40136 q^{43} - 14754 q^{44} - 80280 q^{45} - 174642 q^{46} - 106362 q^{47} - 119574 q^{48} - 110745 q^{49} - 218601 q^{50} - 32628 q^{51} - 142838 q^{52} + 170700 q^{53} + 348420 q^{54} + 131544 q^{55} + 312495 q^{56} + 227820 q^{57} + 151140 q^{58} - 80256 q^{59} - 586050 q^{60} - 9632 q^{61} - 727836 q^{62} - 451140 q^{63} + 128653 q^{64} + 14364 q^{65} + 111474 q^{66} + 295692 q^{67} + 779610 q^{68} + 524592 q^{69} - 592710 q^{70} - 164652 q^{71} + 282480 q^{72} - 761612 q^{73} - 247206 q^{74} - 69096 q^{75} - 289310 q^{76} - 183132 q^{77} - 853080 q^{78} + 664872 q^{79} + 319374 q^{80} + 81684 q^{81} + 1371642 q^{82} + 809898 q^{83} + 673230 q^{84} + 779916 q^{85} + 1375056 q^{86} + 830526 q^{87} + 553908 q^{88} + 617538 q^{89} + 461274 q^{90} - 977354 q^{91} - 2770368 q^{92} - 1333578 q^{93} - 3026628 q^{94} - 2712642 q^{95} - 1430616 q^{96} - 773204 q^{97} - 606201 q^{98} + 43272 q^{99} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(63))\)

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
63.6.a \(\chi_{63}(1, \cdot)\) 63.6.a.a 1 1
63.6.a.b 1
63.6.a.c 1
63.6.a.d 1
63.6.a.e 1
63.6.a.f 2
63.6.a.g 2
63.6.a.h 4
63.6.c \(\chi_{63}(62, \cdot)\) 63.6.c.a 4 1
63.6.c.b 8
63.6.e \(\chi_{63}(37, \cdot)\) 63.6.e.a 2 2
63.6.e.b 2
63.6.e.c 4
63.6.e.d 4
63.6.e.e 8
63.6.e.f 12
63.6.f \(\chi_{63}(22, \cdot)\) 63.6.f.a 30 2
63.6.f.b 30
63.6.g \(\chi_{63}(4, \cdot)\) 63.6.g.a 76 2
63.6.h \(\chi_{63}(25, \cdot)\) 63.6.h.a 76 2
63.6.i \(\chi_{63}(5, \cdot)\) 63.6.i.a 76 2
63.6.o \(\chi_{63}(20, \cdot)\) 63.6.o.a 76 2
63.6.p \(\chi_{63}(17, \cdot)\) 63.6.p.a 4 2
63.6.p.b 24
63.6.s \(\chi_{63}(47, \cdot)\) 63.6.s.a 76 2

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(63))\) into lower level spaces

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