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Properties

Label 33.2.e
Level $33$
Weight $2$
Character orbit 33.e
Rep. character $\chi_{33}(4,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $8$
Newform subspaces $2$
Sturm bound $8$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 33 = 3 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 33.e (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 11 \)
Character field: \(\Q(\zeta_{5})\)
Newform subspaces: \( 2 \)
Sturm bound: \(8\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

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

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

Trace form

\( 8 q - 4 q^{2} - 6 q^{4} - 4 q^{5} - 2 q^{6} - 2 q^{7} + 8 q^{8} - 2 q^{9} + O(q^{10}) \) \( 8 q - 4 q^{2} - 6 q^{4} - 4 q^{5} - 2 q^{6} - 2 q^{7} + 8 q^{8} - 2 q^{9} + 4 q^{10} - 2 q^{11} - 8 q^{12} - 2 q^{13} + 2 q^{14} + 2 q^{15} + 10 q^{16} + 14 q^{17} + 6 q^{18} - 20 q^{19} + 6 q^{20} + 16 q^{21} - 4 q^{22} - 12 q^{23} + 12 q^{24} + 10 q^{26} - 12 q^{28} - 4 q^{29} - 4 q^{31} - 48 q^{32} - 10 q^{33} + 8 q^{34} - 6 q^{36} + 6 q^{37} - 10 q^{38} - 16 q^{39} + 4 q^{40} + 20 q^{41} - 10 q^{42} + 16 q^{43} + 34 q^{44} - 4 q^{45} + 10 q^{46} + 14 q^{47} + 8 q^{48} + 4 q^{49} + 18 q^{50} + 10 q^{52} + 10 q^{53} + 8 q^{54} + 16 q^{55} + 12 q^{56} - 24 q^{58} - 26 q^{59} - 18 q^{61} - 28 q^{62} - 2 q^{63} + 6 q^{64} - 28 q^{65} - 12 q^{66} - 4 q^{67} - 28 q^{68} - 6 q^{69} - 6 q^{70} - 12 q^{71} - 2 q^{72} + 20 q^{73} - 30 q^{74} + 8 q^{75} + 40 q^{76} - 2 q^{77} + 16 q^{78} - 6 q^{79} + 22 q^{80} - 2 q^{81} - 14 q^{82} + 34 q^{83} - 2 q^{85} + 8 q^{86} + 24 q^{87} - 62 q^{88} - 4 q^{89} + 4 q^{90} + 6 q^{91} + 10 q^{92} + 20 q^{93} + 18 q^{94} + 30 q^{95} - 8 q^{96} - 30 q^{97} + 40 q^{98} + 8 q^{99} + O(q^{100}) \)

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.e.a 33.e 11.c $4$ $0.264$ \(\Q(\zeta_{10})\) None \(-3\) \(-1\) \(-1\) \(-3\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-1-\zeta_{10}^{2})q^{2}-\zeta_{10}^{3}q^{3}+(\zeta_{10}+\cdots)q^{4}+\cdots\)
33.2.e.b 33.e 11.c $4$ $0.264$ \(\Q(\zeta_{10})\) None \(-1\) \(1\) \(-3\) \(1\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-1+2\zeta_{10}-\zeta_{10}^{2})q^{2}+\zeta_{10}^{3}q^{3}+\cdots\)