Properties

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

Related objects

Downloads

Learn more about

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

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

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

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 3 11
33.2.a.a \(1\) \(0.264\) \(\Q\) None \(1\) \(-1\) \(-2\) \(4\) \(+\) \(-\) \(q+q^{2}-q^{3}-q^{4}-2q^{5}-q^{6}+4q^{7}+\cdots\)

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

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

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( 1 - T + 2 T^{2} \)
$3$ \( 1 + T \)
$5$ \( 1 + 2 T + 5 T^{2} \)
$7$ \( 1 - 4 T + 7 T^{2} \)
$11$ \( 1 - T \)
$13$ \( 1 + 2 T + 13 T^{2} \)
$17$ \( 1 + 2 T + 17 T^{2} \)
$19$ \( 1 + 19 T^{2} \)
$23$ \( 1 - 8 T + 23 T^{2} \)
$29$ \( 1 + 6 T + 29 T^{2} \)
$31$ \( 1 + 8 T + 31 T^{2} \)
$37$ \( 1 - 6 T + 37 T^{2} \)
$41$ \( 1 + 2 T + 41 T^{2} \)
$43$ \( 1 + 43 T^{2} \)
$47$ \( 1 - 8 T + 47 T^{2} \)
$53$ \( 1 - 6 T + 53 T^{2} \)
$59$ \( 1 + 4 T + 59 T^{2} \)
$61$ \( 1 - 6 T + 61 T^{2} \)
$67$ \( 1 + 4 T + 67 T^{2} \)
$71$ \( 1 + 71 T^{2} \)
$73$ \( 1 + 14 T + 73 T^{2} \)
$79$ \( 1 + 4 T + 79 T^{2} \)
$83$ \( 1 - 12 T + 83 T^{2} \)
$89$ \( 1 + 6 T + 89 T^{2} \)
$97$ \( 1 - 2 T + 97 T^{2} \)
show more
show less