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Properties

Label 33.8
Level 33
Weight 8
Dimension 198
Nonzero newspaces 4
Newform subspaces 10
Sturm bound 640
Trace bound 1

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Defining parameters

Level: \( N \) = \( 33 = 3 \cdot 11 \)
Weight: \( k \) = \( 8 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 10 \)
Sturm bound: \(640\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(33))\).

Total New Old
Modular forms 300 218 82
Cusp forms 260 198 62
Eisenstein series 40 20 20

Trace form

\( 198 q - 12 q^{2} + 49 q^{3} + 174 q^{4} - 780 q^{5} - 1401 q^{6} + 2088 q^{7} + 11600 q^{8} - 4333 q^{9} + O(q^{10}) \) \( 198 q - 12 q^{2} + 49 q^{3} + 174 q^{4} - 780 q^{5} - 1401 q^{6} + 2088 q^{7} + 11600 q^{8} - 4333 q^{9} - 24680 q^{10} - 5642 q^{11} + 11662 q^{12} + 34116 q^{13} + 90318 q^{14} - 40885 q^{15} - 127042 q^{16} - 17262 q^{17} + 102717 q^{18} + 27700 q^{19} - 213190 q^{20} - 188676 q^{21} - 465502 q^{22} + 5636 q^{23} + 508265 q^{24} + 510880 q^{25} + 971126 q^{26} - 274394 q^{27} - 509136 q^{28} - 737440 q^{29} - 476810 q^{30} + 489786 q^{31} + 2408948 q^{32} + 225519 q^{33} - 2797332 q^{34} - 1035320 q^{35} - 324549 q^{36} + 1540818 q^{37} + 3033590 q^{38} + 799988 q^{39} + 1678460 q^{40} - 648144 q^{41} - 397516 q^{42} - 6819564 q^{43} - 10195666 q^{44} - 4685725 q^{45} + 1527496 q^{46} + 3891598 q^{47} + 10568634 q^{48} + 14695114 q^{49} + 10234070 q^{50} + 1344354 q^{51} - 7366832 q^{52} - 7651574 q^{53} - 1338444 q^{54} - 16337890 q^{55} - 15189720 q^{56} - 4146720 q^{57} + 14733540 q^{58} + 1827870 q^{59} - 2017730 q^{60} + 16955836 q^{61} + 10583616 q^{62} + 1989312 q^{63} - 16592266 q^{64} - 7665900 q^{65} + 10284204 q^{66} - 9398882 q^{67} + 8723824 q^{68} + 6664093 q^{69} + 47502620 q^{70} + 14498316 q^{71} - 28296830 q^{72} - 43505804 q^{73} - 44074602 q^{74} - 32730330 q^{75} - 48493200 q^{76} + 2351058 q^{77} + 43122988 q^{78} + 62981600 q^{79} + 55355310 q^{80} + 348683 q^{81} + 55345226 q^{82} + 24739186 q^{83} + 57102612 q^{84} - 32239040 q^{85} - 25505344 q^{86} - 37538640 q^{87} - 144529290 q^{88} - 25376860 q^{89} - 64502420 q^{90} - 56226644 q^{91} - 50393302 q^{92} - 34022697 q^{93} + 18723488 q^{94} + 99060750 q^{95} + 93808684 q^{96} + 131543758 q^{97} + 148165624 q^{98} + 89574197 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(33))\)

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 available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
33.8.a \(\chi_{33}(1, \cdot)\) 33.8.a.a 1 1
33.8.a.b 2
33.8.a.c 2
33.8.a.d 3
33.8.a.e 4
33.8.d \(\chi_{33}(32, \cdot)\) 33.8.d.a 2 1
33.8.d.b 24
33.8.e \(\chi_{33}(4, \cdot)\) 33.8.e.a 28 4
33.8.e.b 28
33.8.f \(\chi_{33}(2, \cdot)\) 33.8.f.a 104 4

Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_1(33))\) into lower level spaces

\( S_{8}^{\mathrm{old}}(\Gamma_1(33)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 2}\)