Properties

Label 33.6
Level 33
Weight 6
Dimension 138
Nonzero newspaces 4
Newform subspaces 10
Sturm bound 480
Trace bound 1

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Defining parameters

Level: \( N \) = \( 33 = 3 \cdot 11 \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 10 \)
Sturm bound: \(480\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(33))\).

Total New Old
Modular forms 220 158 62
Cusp forms 180 138 42
Eisenstein series 40 20 20

Trace form

\( 138 q + 12 q^{2} - 23 q^{3} - 18 q^{4} - 12 q^{5} + 123 q^{6} - 520 q^{7} - 656 q^{8} + 383 q^{9} + O(q^{10}) \) \( 138 q + 12 q^{2} - 23 q^{3} - 18 q^{4} - 12 q^{5} + 123 q^{6} - 520 q^{7} - 656 q^{8} + 383 q^{9} + 2072 q^{10} + 1454 q^{11} + 238 q^{12} - 2296 q^{13} + 510 q^{14} - 3853 q^{15} - 14018 q^{16} - 5274 q^{17} + 4977 q^{18} + 5572 q^{19} + 17002 q^{20} + 9540 q^{21} + 21746 q^{22} + 7060 q^{23} - 3559 q^{24} - 6592 q^{25} - 24794 q^{26} + 8602 q^{27} - 46240 q^{28} - 21896 q^{29} - 11402 q^{30} + 24410 q^{31} + 78100 q^{32} - 1869 q^{33} - 11236 q^{34} - 55480 q^{35} - 58293 q^{36} - 48430 q^{37} - 45722 q^{38} + 11876 q^{39} + 50284 q^{40} + 86040 q^{41} + 145940 q^{42} + 72292 q^{43} + 78046 q^{44} + 35213 q^{45} - 47720 q^{46} - 23266 q^{47} - 84942 q^{48} - 97746 q^{49} - 194258 q^{50} - 168726 q^{51} - 5984 q^{52} - 111610 q^{53} + 37908 q^{54} + 117854 q^{55} + 344040 q^{56} + 312018 q^{57} + 270916 q^{58} + 26598 q^{59} + 9958 q^{60} - 61616 q^{61} + 10320 q^{62} - 161640 q^{63} - 576714 q^{64} - 291396 q^{65} - 586956 q^{66} - 86074 q^{67} - 144976 q^{68} - 38285 q^{69} + 416860 q^{70} + 343116 q^{71} + 388834 q^{72} + 234640 q^{73} - 18810 q^{74} + 270702 q^{75} + 8368 q^{76} - 281850 q^{77} + 141964 q^{78} - 401280 q^{79} - 30258 q^{80} - 365017 q^{81} - 274510 q^{82} + 63866 q^{83} + 74340 q^{84} + 680436 q^{85} + 182608 q^{86} + 370656 q^{87} + 1238902 q^{88} + 427492 q^{89} + 414292 q^{90} + 1133540 q^{91} + 926650 q^{92} + 113295 q^{93} - 638944 q^{94} - 477378 q^{95} - 1649900 q^{96} - 1950194 q^{97} - 2674864 q^{98} - 1074091 q^{99} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(33))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
33.6.a \(\chi_{33}(1, \cdot)\) 33.6.a.a 1 1
33.6.a.b 1
33.6.a.c 2
33.6.a.d 2
33.6.a.e 2
33.6.d \(\chi_{33}(32, \cdot)\) 33.6.d.a 2 1
33.6.d.b 16
33.6.e \(\chi_{33}(4, \cdot)\) 33.6.e.a 20 4
33.6.e.b 20
33.6.f \(\chi_{33}(2, \cdot)\) 33.6.f.a 72 4

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(33))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(33)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 2}\)