Properties

Label 133.2.a
Level $133$
Weight $2$
Character orbit 133.a
Rep. character $\chi_{133}(1,\cdot)$
Character field $\Q$
Dimension $9$
Newform subspaces $4$
Sturm bound $26$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 133 = 7 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 133.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(26\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(133))\).

Total New Old
Modular forms 14 9 5
Cusp forms 11 9 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.

\(7\)\(19\)FrickeDim.
\(+\)\(+\)\(+\)\(2\)
\(+\)\(-\)\(-\)\(3\)
\(-\)\(+\)\(-\)\(2\)
\(-\)\(-\)\(+\)\(2\)
Plus space\(+\)\(4\)
Minus space\(-\)\(5\)

Trace form

\( 9q - q^{2} + 11q^{4} - 6q^{5} - q^{7} - 9q^{8} + 9q^{9} + O(q^{10}) \) \( 9q - q^{2} + 11q^{4} - 6q^{5} - q^{7} - 9q^{8} + 9q^{9} - 10q^{10} - 8q^{11} - 16q^{12} - 6q^{13} + q^{14} + 3q^{16} - 2q^{17} + 7q^{18} + q^{19} + 6q^{20} + 8q^{22} + 20q^{24} - q^{25} + 2q^{26} - 12q^{27} - 7q^{28} + 2q^{29} + 12q^{30} - 8q^{31} - 9q^{32} + 36q^{33} + 18q^{34} - 2q^{35} - 5q^{36} - 22q^{37} + 3q^{38} - 20q^{39} + 6q^{40} + 10q^{41} - 12q^{42} - 20q^{43} - 8q^{44} - 18q^{45} + 24q^{46} + 12q^{47} - 36q^{48} + 9q^{49} - 7q^{50} + 36q^{51} - 14q^{52} - 10q^{53} + 16q^{54} + 12q^{55} - 3q^{56} + 10q^{58} - 36q^{60} - 6q^{61} + 4q^{62} + 3q^{63} - q^{64} + 24q^{65} - 24q^{66} + 8q^{67} - 42q^{68} + 28q^{69} + 18q^{70} + 20q^{71} - 57q^{72} - 6q^{73} + 46q^{74} - 4q^{75} + 7q^{76} - 4q^{77} - 12q^{78} - 16q^{79} + 26q^{80} + 41q^{81} + 18q^{82} + 20q^{83} + 12q^{84} + 12q^{86} + 52q^{87} + 48q^{88} - 14q^{89} - 102q^{90} - 6q^{91} + 12q^{92} - 40q^{93} - 12q^{94} - 10q^{95} + 16q^{96} - 10q^{97} - q^{98} - 52q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(133))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 7 19
133.2.a.a \(2\) \(1.062\) \(\Q(\sqrt{5}) \) None \(-3\) \(-3\) \(0\) \(-2\) \(+\) \(+\) \(q+(-1-\beta )q^{2}+(-1-\beta )q^{3}+3\beta q^{4}+\cdots\)
133.2.a.b \(2\) \(1.062\) \(\Q(\sqrt{13}) \) None \(-1\) \(-3\) \(-6\) \(2\) \(-\) \(-\) \(q-\beta q^{2}+(-2+\beta )q^{3}+(1+\beta )q^{4}-3q^{5}+\cdots\)
133.2.a.c \(2\) \(1.062\) \(\Q(\sqrt{5}) \) None \(1\) \(3\) \(2\) \(2\) \(-\) \(+\) \(q+\beta q^{2}+(2-\beta )q^{3}+(-1+\beta )q^{4}+q^{5}+\cdots\)
133.2.a.d \(3\) \(1.062\) 3.3.229.1 None \(2\) \(3\) \(-2\) \(-3\) \(+\) \(-\) \(q+(1+\beta _{2})q^{2}+(1-\beta _{1})q^{3}+(2+\beta _{1}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(133))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(133)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 2}\)