Properties

Label 33.6.d
Level $33$
Weight $6$
Character orbit 33.d
Rep. character $\chi_{33}(32,\cdot)$
Character field $\Q$
Dimension $18$
Newform subspaces $2$
Sturm bound $24$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 33 = 3 \cdot 11 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 33.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 33 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(24\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(33, [\chi])\).

Total New Old
Modular forms 22 22 0
Cusp forms 18 18 0
Eisenstein series 4 4 0

Trace form

\( 18 q - 23 q^{3} + 252 q^{4} + 253 q^{9} + O(q^{10}) \) \( 18 q - 23 q^{3} + 252 q^{4} + 253 q^{9} - 1544 q^{12} - 1993 q^{15} + 3732 q^{16} + 7932 q^{22} - 13608 q^{25} + 3952 q^{27} + 3570 q^{31} - 6437 q^{33} - 34032 q^{34} - 1184 q^{36} + 6822 q^{37} + 45912 q^{42} + 67541 q^{45} - 46268 q^{48} + 32478 q^{49} + 40110 q^{55} + 31848 q^{58} - 210340 q^{60} - 59676 q^{64} - 164796 q^{66} - 218298 q^{67} + 130301 q^{69} + 231144 q^{70} + 130458 q^{75} + 296088 q^{78} - 143807 q^{81} + 4824 q^{82} + 586836 q^{88} - 209184 q^{91} - 280021 q^{93} - 206514 q^{97} - 285155 q^{99} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(33, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
33.6.d.a 33.d 33.d $2$ $5.293$ \(\Q(\sqrt{-11}) \) \(\Q(\sqrt{-11}) \) 33.6.d.a \(0\) \(31\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+(2^{4}-\beta )q^{3}-2^{5}q^{4}+(29-58\beta )q^{5}+\cdots\)
33.6.d.b 33.d 33.d $16$ $5.293$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None 33.6.d.b \(0\) \(-54\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{3}q^{2}+(-3-\beta _{2})q^{3}+(20+\beta _{9}+\cdots)q^{4}+\cdots\)