Properties

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

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(33))\).

Total New Old
Modular forms 6 1 5
Cusp forms 3 1 2
Eisenstein series 3 0 3

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(3\)\(11\)FrickeDim
\(+\)\(-\)\(-\)\(1\)
Plus space\(+\)\(0\)
Minus space\(-\)\(1\)

Trace form

\( q + q^{2} - q^{3} - q^{4} - 2 q^{5} - q^{6} + 4 q^{7} - 3 q^{8} + q^{9} + O(q^{10}) \) \( q + q^{2} - q^{3} - q^{4} - 2 q^{5} - q^{6} + 4 q^{7} - 3 q^{8} + q^{9} - 2 q^{10} + q^{11} + q^{12} - 2 q^{13} + 4 q^{14} + 2 q^{15} - q^{16} - 2 q^{17} + q^{18} + 2 q^{20} - 4 q^{21} + q^{22} + 8 q^{23} + 3 q^{24} - q^{25} - 2 q^{26} - q^{27} - 4 q^{28} - 6 q^{29} + 2 q^{30} - 8 q^{31} + 5 q^{32} - q^{33} - 2 q^{34} - 8 q^{35} - q^{36} + 6 q^{37} + 2 q^{39} + 6 q^{40} - 2 q^{41} - 4 q^{42} - q^{44} - 2 q^{45} + 8 q^{46} + 8 q^{47} + q^{48} + 9 q^{49} - q^{50} + 2 q^{51} + 2 q^{52} + 6 q^{53} - q^{54} - 2 q^{55} - 12 q^{56} - 6 q^{58} - 4 q^{59} - 2 q^{60} + 6 q^{61} - 8 q^{62} + 4 q^{63} + 7 q^{64} + 4 q^{65} - q^{66} - 4 q^{67} + 2 q^{68} - 8 q^{69} - 8 q^{70} - 3 q^{72} - 14 q^{73} + 6 q^{74} + q^{75} + 4 q^{77} + 2 q^{78} - 4 q^{79} + 2 q^{80} + q^{81} - 2 q^{82} + 12 q^{83} + 4 q^{84} + 4 q^{85} + 6 q^{87} - 3 q^{88} - 6 q^{89} - 2 q^{90} - 8 q^{91} - 8 q^{92} + 8 q^{93} + 8 q^{94} - 5 q^{96} + 2 q^{97} + 9 q^{98} + q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(33))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 3 11
33.2.a.a 33.a 1.a $1$ $0.264$ \(\Q\) None 33.2.a.a \(1\) \(-1\) \(-2\) \(4\) $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}-q^{4}-2q^{5}-q^{6}+4q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(33))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(33)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 2}\)