Properties

Label 33.2.f
Level 33
Weight 2
Character orbit f
Rep. character \(\chi_{33}(2,\cdot)\)
Character field \(\Q(\zeta_{10})\)
Dimension 8
Newforms 1
Sturm bound 8
Trace bound 0

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Defining parameters

Level: \( N \) = \( 33 = 3 \cdot 11 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 33.f (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 33 \)
Character field: \(\Q(\zeta_{10})\)
Newforms: \( 1 \)
Sturm bound: \(8\)
Trace bound: \(0\)

Dimensions

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

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

Trace form

\(8q \) \(\mathstrut -\mathstrut 6q^{3} \) \(\mathstrut -\mathstrut 6q^{4} \) \(\mathstrut -\mathstrut 10q^{7} \) \(\mathstrut +\mathstrut 10q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(8q \) \(\mathstrut -\mathstrut 6q^{3} \) \(\mathstrut -\mathstrut 6q^{4} \) \(\mathstrut -\mathstrut 10q^{7} \) \(\mathstrut +\mathstrut 10q^{9} \) \(\mathstrut +\mathstrut 12q^{12} \) \(\mathstrut -\mathstrut 10q^{13} \) \(\mathstrut -\mathstrut 6q^{15} \) \(\mathstrut +\mathstrut 2q^{16} \) \(\mathstrut +\mathstrut 20q^{19} \) \(\mathstrut +\mathstrut 20q^{22} \) \(\mathstrut -\mathstrut 10q^{24} \) \(\mathstrut +\mathstrut 12q^{25} \) \(\mathstrut -\mathstrut 12q^{27} \) \(\mathstrut -\mathstrut 20q^{30} \) \(\mathstrut -\mathstrut 20q^{31} \) \(\mathstrut -\mathstrut 4q^{33} \) \(\mathstrut -\mathstrut 40q^{34} \) \(\mathstrut -\mathstrut 10q^{36} \) \(\mathstrut -\mathstrut 6q^{37} \) \(\mathstrut +\mathstrut 20q^{39} \) \(\mathstrut +\mathstrut 20q^{42} \) \(\mathstrut +\mathstrut 24q^{45} \) \(\mathstrut +\mathstrut 30q^{46} \) \(\mathstrut +\mathstrut 26q^{48} \) \(\mathstrut +\mathstrut 16q^{49} \) \(\mathstrut +\mathstrut 30q^{51} \) \(\mathstrut +\mathstrut 10q^{52} \) \(\mathstrut -\mathstrut 32q^{55} \) \(\mathstrut -\mathstrut 30q^{57} \) \(\mathstrut +\mathstrut 20q^{58} \) \(\mathstrut +\mathstrut 2q^{60} \) \(\mathstrut -\mathstrut 10q^{61} \) \(\mathstrut -\mathstrut 30q^{63} \) \(\mathstrut -\mathstrut 34q^{64} \) \(\mathstrut -\mathstrut 30q^{66} \) \(\mathstrut -\mathstrut 4q^{67} \) \(\mathstrut -\mathstrut 16q^{69} \) \(\mathstrut +\mathstrut 10q^{70} \) \(\mathstrut -\mathstrut 20q^{72} \) \(\mathstrut +\mathstrut 6q^{75} \) \(\mathstrut -\mathstrut 20q^{78} \) \(\mathstrut +\mathstrut 50q^{79} \) \(\mathstrut -\mathstrut 2q^{81} \) \(\mathstrut -\mathstrut 10q^{82} \) \(\mathstrut +\mathstrut 10q^{85} \) \(\mathstrut +\mathstrut 50q^{88} \) \(\mathstrut +\mathstrut 40q^{90} \) \(\mathstrut -\mathstrut 10q^{91} \) \(\mathstrut +\mathstrut 10q^{93} \) \(\mathstrut -\mathstrut 30q^{94} \) \(\mathstrut +\mathstrut 10q^{96} \) \(\mathstrut +\mathstrut 6q^{97} \) \(\mathstrut +\mathstrut 16q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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.f.a \(8\) \(0.264\) \(\Q(\zeta_{20})\) None \(0\) \(-6\) \(0\) \(-10\) \(q+(-\zeta_{20}^{5}-\zeta_{20}^{7})q^{2}+(-1+\zeta_{20}+\cdots)q^{3}+\cdots\)