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Properties

Label 33.2.f
Level $33$
Weight $2$
Character orbit 33.f
Rep. character $\chi_{33}(2,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $8$
Newform subspaces $1$
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: \(\Q(\zeta_{10})\)
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 24 24 0
Cusp forms 8 8 0
Eisenstein series 16 16 0

Trace form

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

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
33.2.f.a 33.f 33.f $8$ $0.264$ \(\Q(\zeta_{20})\) None \(0\) \(-6\) \(0\) \(-10\) $\mathrm{SU}(2)[C_{10}]$ \(q+(-\zeta_{20}^{5}-\zeta_{20}^{7})q^{2}+(-1+\zeta_{20}+\cdots)q^{3}+\cdots\)