Properties

Label 33.2.e
Level 33
Weight 2
Character orbit e
Rep. character \(\chi_{33}(4,\cdot)\)
Character field \(\Q(\zeta_{5})\)
Dimension 8
Newforms 2
Sturm bound 8
Trace bound 2

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Defining parameters

Level: \( N \) = \( 33 = 3 \cdot 11 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 33.e (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 11 \)
Character field: \(\Q(\zeta_{5})\)
Newforms: \( 2 \)
Sturm bound: \(8\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(33, [\chi])\).

Total New Old
Modular forms 24 8 16
Cusp forms 8 8 0
Eisenstein series 16 0 16

Trace form

\( 8q - 4q^{2} - 6q^{4} - 4q^{5} - 2q^{6} - 2q^{7} + 8q^{8} - 2q^{9} + O(q^{10}) \) \( 8q - 4q^{2} - 6q^{4} - 4q^{5} - 2q^{6} - 2q^{7} + 8q^{8} - 2q^{9} + 4q^{10} - 2q^{11} - 8q^{12} - 2q^{13} + 2q^{14} + 2q^{15} + 10q^{16} + 14q^{17} + 6q^{18} - 20q^{19} + 6q^{20} + 16q^{21} - 4q^{22} - 12q^{23} + 12q^{24} + 10q^{26} - 12q^{28} - 4q^{29} - 4q^{31} - 48q^{32} - 10q^{33} + 8q^{34} - 6q^{36} + 6q^{37} - 10q^{38} - 16q^{39} + 4q^{40} + 20q^{41} - 10q^{42} + 16q^{43} + 34q^{44} - 4q^{45} + 10q^{46} + 14q^{47} + 8q^{48} + 4q^{49} + 18q^{50} + 10q^{52} + 10q^{53} + 8q^{54} + 16q^{55} + 12q^{56} - 24q^{58} - 26q^{59} - 18q^{61} - 28q^{62} - 2q^{63} + 6q^{64} - 28q^{65} - 12q^{66} - 4q^{67} - 28q^{68} - 6q^{69} - 6q^{70} - 12q^{71} - 2q^{72} + 20q^{73} - 30q^{74} + 8q^{75} + 40q^{76} - 2q^{77} + 16q^{78} - 6q^{79} + 22q^{80} - 2q^{81} - 14q^{82} + 34q^{83} - 2q^{85} + 8q^{86} + 24q^{87} - 62q^{88} - 4q^{89} + 4q^{90} + 6q^{91} + 10q^{92} + 20q^{93} + 18q^{94} + 30q^{95} - 8q^{96} - 30q^{97} + 40q^{98} + 8q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(33, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
33.2.e.a \(4\) \(0.264\) \(\Q(\zeta_{10})\) None \(-3\) \(-1\) \(-1\) \(-3\) \(q+(-1-\zeta_{10}^{2})q^{2}-\zeta_{10}^{3}q^{3}+(\zeta_{10}+\cdots)q^{4}+\cdots\)
33.2.e.b \(4\) \(0.264\) \(\Q(\zeta_{10})\) None \(-1\) \(1\) \(-3\) \(1\) \(q+(-1+2\zeta_{10}-\zeta_{10}^{2})q^{2}+\zeta_{10}^{3}q^{3}+\cdots\)