↑

Properties

Label 33.5
Level 33
Weight 5
Dimension 110
Nonzero newspaces 4
Newform subspaces 4
Sturm bound 400
Trace bound 1

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 33 = 3 \cdot 11 \)
Weight: \( k \) = \( 5 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 4 \)
Sturm bound: \(400\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(33))\).

Total New Old
Modular forms 180 126 54
Cusp forms 140 110 30
Eisenstein series 40 16 24

Trace form

\( 110 q - 5 q^{3} - 10 q^{4} - 85 q^{6} + 140 q^{7} + 480 q^{8} + 165 q^{9} + O(q^{10}) \) \( 110 q - 5 q^{3} - 10 q^{4} - 85 q^{6} + 140 q^{7} + 480 q^{8} + 165 q^{9} - 20 q^{10} - 210 q^{11} - 810 q^{12} - 520 q^{13} - 2430 q^{14} - 615 q^{15} + 1870 q^{16} + 2490 q^{17} + 1925 q^{18} + 2030 q^{19} + 1950 q^{20} - 10 q^{21} - 2590 q^{22} - 1680 q^{23} - 1515 q^{24} - 5450 q^{25} - 6750 q^{26} - 2180 q^{27} - 2460 q^{28} + 960 q^{29} + 10 q^{30} + 7590 q^{31} - 3480 q^{33} - 4700 q^{34} + 1920 q^{35} + 14275 q^{36} + 9110 q^{37} + 12750 q^{38} + 12960 q^{39} + 12340 q^{40} + 9360 q^{41} - 5760 q^{42} - 7720 q^{43} - 10890 q^{44} - 13745 q^{45} - 8320 q^{46} - 3030 q^{47} - 6410 q^{48} - 4080 q^{49} - 11550 q^{50} - 5 q^{51} + 5640 q^{52} + 750 q^{53} + 11430 q^{54} + 11950 q^{55} + 12360 q^{56} - 5085 q^{57} - 15660 q^{58} - 13950 q^{59} - 56770 q^{60} - 35900 q^{61} - 39360 q^{62} - 22200 q^{63} - 29930 q^{64} + 24190 q^{66} + 23170 q^{67} + 68160 q^{68} + 48545 q^{69} + 50540 q^{70} - 13080 q^{71} + 68440 q^{72} - 29680 q^{73} - 2130 q^{74} + 26335 q^{75} + 27260 q^{76} + 27810 q^{77} + 19880 q^{78} + 61780 q^{79} + 27870 q^{80} - 35895 q^{81} + 82930 q^{82} + 35430 q^{83} - 18910 q^{84} + 7400 q^{85} - 29520 q^{86} - 29160 q^{87} - 96650 q^{88} - 23220 q^{89} - 80430 q^{90} - 167320 q^{91} - 106770 q^{92} - 81465 q^{93} - 147940 q^{94} - 71670 q^{95} - 38220 q^{96} - 54400 q^{97} + 43915 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(33))\)

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
33.5.b \(\chi_{33}(23, \cdot)\) 33.5.b.a 14 1
33.5.c \(\chi_{33}(10, \cdot)\) 33.5.c.a 8 1
33.5.g \(\chi_{33}(7, \cdot)\) 33.5.g.a 32 4
33.5.h \(\chi_{33}(5, \cdot)\) 33.5.h.a 56 4

Decomposition of \(S_{5}^{\mathrm{old}}(\Gamma_1(33))\) into lower level spaces

\( S_{5}^{\mathrm{old}}(\Gamma_1(33)) \cong \) \(S_{5}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 2}\)