Properties

Label 33.2.d
Level 33
Weight 2
Character orbit d
Rep. character \(\chi_{33}(32,\cdot)\)
Character field \(\Q\)
Dimension 2
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.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 33 \)
Character field: \(\Q\)
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 6 6 0
Cusp forms 2 2 0
Eisenstein series 4 4 0

Trace form

\(2q \) \(\mathstrut +\mathstrut q^{3} \) \(\mathstrut -\mathstrut 4q^{4} \) \(\mathstrut -\mathstrut 5q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(2q \) \(\mathstrut +\mathstrut q^{3} \) \(\mathstrut -\mathstrut 4q^{4} \) \(\mathstrut -\mathstrut 5q^{9} \) \(\mathstrut -\mathstrut 2q^{12} \) \(\mathstrut +\mathstrut 11q^{15} \) \(\mathstrut +\mathstrut 8q^{16} \) \(\mathstrut -\mathstrut 12q^{25} \) \(\mathstrut -\mathstrut 8q^{27} \) \(\mathstrut +\mathstrut 10q^{31} \) \(\mathstrut -\mathstrut 11q^{33} \) \(\mathstrut +\mathstrut 10q^{36} \) \(\mathstrut -\mathstrut 14q^{37} \) \(\mathstrut +\mathstrut 11q^{45} \) \(\mathstrut +\mathstrut 4q^{48} \) \(\mathstrut +\mathstrut 14q^{49} \) \(\mathstrut +\mathstrut 22q^{55} \) \(\mathstrut -\mathstrut 22q^{60} \) \(\mathstrut -\mathstrut 16q^{64} \) \(\mathstrut -\mathstrut 26q^{67} \) \(\mathstrut +\mathstrut 11q^{69} \) \(\mathstrut -\mathstrut 6q^{75} \) \(\mathstrut +\mathstrut 7q^{81} \) \(\mathstrut +\mathstrut 5q^{93} \) \(\mathstrut +\mathstrut 34q^{97} \) \(\mathstrut -\mathstrut 11q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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.d.a \(2\) \(0.264\) \(\Q(\sqrt{-11}) \) \(\Q(\sqrt{-11}) \) \(0\) \(1\) \(0\) \(0\) \(q+\beta q^{3}-2q^{4}+(1-2\beta )q^{5}+(-3+\beta )q^{9}+\cdots\)