↑

Properties

Label 99.9
Level 99
Weight 9
Dimension 2203
Nonzero newspaces 8
Newform subspaces 14
Sturm bound 6480
Trace bound 2

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 99 = 3^{2} \cdot 11 \)
Weight: \( k \) = \( 9 \)
Nonzero newspaces: \( 8 \)
Newform subspaces: \( 14 \)
Sturm bound: \(6480\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(\Gamma_1(99))\).

Total New Old
Modular forms 2960 2285 675
Cusp forms 2800 2203 597
Eisenstein series 160 82 78

Trace form

\( 2203 q - 9 q^{2} + 166 q^{3} - 2501 q^{4} - 891 q^{5} + 4498 q^{6} - 2992 q^{7} - 3855 q^{8} - 35966 q^{9} + O(q^{10}) \) \( 2203 q - 9 q^{2} + 166 q^{3} - 2501 q^{4} - 891 q^{5} + 4498 q^{6} - 2992 q^{7} - 3855 q^{8} - 35966 q^{9} + 17768 q^{10} + 49557 q^{11} + 110180 q^{12} + 89210 q^{13} - 324972 q^{14} + 150532 q^{15} + 365543 q^{16} + 368190 q^{17} - 486668 q^{18} - 90025 q^{19} - 1785738 q^{20} - 708128 q^{21} + 893868 q^{22} + 1804839 q^{23} + 5691646 q^{24} + 1697969 q^{25} - 8415600 q^{26} - 1634318 q^{27} - 5124140 q^{28} - 2049114 q^{29} + 4232776 q^{30} + 6222595 q^{31} + 16923732 q^{32} - 891249 q^{33} - 19768068 q^{34} - 15127050 q^{35} - 34446034 q^{36} + 443225 q^{37} + 7715028 q^{38} + 6636118 q^{39} + 27578582 q^{40} + 9101124 q^{41} + 50745076 q^{42} - 30813984 q^{43} - 19946490 q^{44} - 32761746 q^{45} + 30654494 q^{46} - 40594506 q^{47} - 33521038 q^{48} + 6295892 q^{49} + 78047691 q^{50} + 48069686 q^{51} + 34109644 q^{52} + 98986200 q^{53} - 9151290 q^{54} - 33402869 q^{55} - 364154988 q^{56} - 202489614 q^{57} - 154644970 q^{58} + 166459320 q^{59} + 339386580 q^{60} + 179521968 q^{61} + 365324490 q^{62} + 58941036 q^{63} + 81186891 q^{64} - 138466014 q^{65} - 180020356 q^{66} - 90957709 q^{67} - 190614264 q^{68} - 85115220 q^{69} - 440451950 q^{70} - 77123835 q^{71} - 43678112 q^{72} + 42591212 q^{73} + 711083160 q^{74} + 278665958 q^{75} + 619089588 q^{76} + 284526420 q^{77} - 257493420 q^{78} - 215569212 q^{79} - 502589910 q^{80} + 34512682 q^{81} - 35469515 q^{82} + 202195347 q^{83} - 404162942 q^{84} - 503414658 q^{85} - 104546913 q^{86} + 490192668 q^{87} - 290656946 q^{88} + 553451235 q^{89} + 953358080 q^{90} + 1343482024 q^{91} + 69136578 q^{92} - 882527088 q^{93} + 106383702 q^{94} - 2053827366 q^{95} - 3571469326 q^{96} - 231448216 q^{97} + 1116465372 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{9}^{\mathrm{new}}(\Gamma_1(99))\)

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 available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
99.9.b \(\chi_{99}(89, \cdot)\) 99.9.b.a 28 1
99.9.c \(\chi_{99}(10, \cdot)\) 99.9.c.a 1 1
99.9.c.b 6
99.9.c.c 16
99.9.c.d 16
99.9.h \(\chi_{99}(43, \cdot)\) 99.9.h.a 4 2
99.9.h.b 184
99.9.i \(\chi_{99}(23, \cdot)\) 99.9.i.a 160 2
99.9.k \(\chi_{99}(19, \cdot)\) 99.9.k.a 28 4
99.9.k.b 64
99.9.k.c 64
99.9.l \(\chi_{99}(26, \cdot)\) 99.9.l.a 128 4
99.9.n \(\chi_{99}(5, \cdot)\) 99.9.n.a 752 8
99.9.o \(\chi_{99}(7, \cdot)\) 99.9.o.a 752 8

Decomposition of \(S_{9}^{\mathrm{old}}(\Gamma_1(99))\) into lower level spaces

\( S_{9}^{\mathrm{old}}(\Gamma_1(99)) \cong \) \(S_{9}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 2}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 3}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 2}\)