Properties

Label 33.2.d
Level $33$
Weight $2$
Character orbit 33.d
Rep. character $\chi_{33}(32,\cdot)$
Character field $\Q$
Dimension $2$
Newform subspaces $1$
Sturm bound $8$
Trace bound $0$

Related objects

Downloads

Learn more

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: \(\Q\)
Newform subspaces: \( 1 \)
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

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

Decomposition of \(S_{2}^{\mathrm{new}}(33, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
33.2.d.a 33.d 33.d $2$ $0.264$ \(\Q(\sqrt{-11}) \) \(\Q(\sqrt{-11}) \) 33.2.d.a \(0\) \(1\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta q^{3}-2q^{4}+(1-2\beta )q^{5}+(-3+\beta )q^{9}+\cdots\)