↑

Properties

Label 33.9
Level 33
Weight 9
Dimension 226
Nonzero newspaces 4
Newform subspaces 4
Sturm bound 720
Trace bound 1

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 33 = 3 \cdot 11 \)
Weight: \( k \) = \( 9 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 4 \)
Sturm bound: \(720\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(\Gamma_1(33))\).

Total New Old
Modular forms 340 242 98
Cusp forms 300 226 74
Eisenstein series 40 16 24

Trace form

\( 226 q - 185 q^{3} + 982 q^{4} - 1573 q^{6} - 3960 q^{7} + 7680 q^{8} + 31629 q^{9} + O(q^{10}) \) \( 226 q - 185 q^{3} + 982 q^{4} - 1573 q^{6} - 3960 q^{7} + 7680 q^{8} + 31629 q^{9} - 20180 q^{10} - 41790 q^{11} - 44970 q^{12} - 77940 q^{13} + 166050 q^{14} + 315765 q^{15} - 616210 q^{16} - 736410 q^{17} - 326395 q^{18} + 809598 q^{19} + 1405950 q^{20} + 314990 q^{21} - 1960510 q^{22} - 1186080 q^{23} - 3062619 q^{24} - 849550 q^{25} + 4205250 q^{26} + 3426910 q^{27} + 1985540 q^{28} - 1580160 q^{29} - 10565990 q^{30} - 2226898 q^{31} + 7601130 q^{33} + 16754596 q^{34} - 4634880 q^{35} - 11511677 q^{36} - 17141970 q^{37} - 3659250 q^{38} - 3377610 q^{39} + 26632660 q^{40} + 25477920 q^{41} + 35880240 q^{42} + 33146680 q^{43} - 4620330 q^{44} - 34583195 q^{45} - 119450336 q^{46} - 43405530 q^{47} - 11143610 q^{48} + 41809504 q^{49} + 87583650 q^{50} + 68667127 q^{51} + 149493800 q^{52} + 30428850 q^{53} - 74092602 q^{54} - 108418050 q^{55} - 182775480 q^{56} + 35930775 q^{57} + 20936020 q^{58} - 23533650 q^{59} - 79222210 q^{60} - 8754848 q^{61} + 128970240 q^{62} - 10366050 q^{63} + 164039158 q^{64} - 37077410 q^{66} - 173756290 q^{67} - 330224640 q^{68} + 181018703 q^{69} + 151381740 q^{70} - 21898920 q^{71} + 159729880 q^{72} + 331953540 q^{73} + 256186830 q^{74} - 181393865 q^{75} - 270136004 q^{76} - 342739890 q^{77} - 452196760 q^{78} - 312587072 q^{79} - 498053730 q^{80} + 160862121 q^{81} + 266302770 q^{82} + 525506730 q^{83} + 167938370 q^{84} + 669713540 q^{85} + 612727920 q^{86} + 235224900 q^{87} + 354781590 q^{88} - 264501180 q^{89} - 313947870 q^{90} - 1227676940 q^{91} - 545571570 q^{92} - 150293625 q^{93} - 377026564 q^{94} + 643261830 q^{95} - 98284764 q^{96} - 438770340 q^{97} - 206669885 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{9}^{\mathrm{new}}(\Gamma_1(33))\)

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
33.9.b \(\chi_{33}(23, \cdot)\) 33.9.b.a 26 1
33.9.c \(\chi_{33}(10, \cdot)\) 33.9.c.a 16 1
33.9.g \(\chi_{33}(7, \cdot)\) 33.9.g.a 64 4
33.9.h \(\chi_{33}(5, \cdot)\) 33.9.h.a 120 4

Decomposition of \(S_{9}^{\mathrm{old}}(\Gamma_1(33))\) into lower level spaces

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