Properties

Label 165.2.a
Level $165$
Weight $2$
Character orbit 165.a
Rep. character $\chi_{165}(1,\cdot)$
Character field $\Q$
Dimension $7$
Newform subspaces $3$
Sturm bound $48$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 165 = 3 \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 165.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(48\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(165))\).

Total New Old
Modular forms 28 7 21
Cusp forms 21 7 14
Eisenstein series 7 0 7

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

\(3\)\(5\)\(11\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(2\)
\(-\)\(+\)\(+\)\(-\)\(2\)
\(-\)\(-\)\(-\)\(-\)\(3\)
Plus space\(+\)\(2\)
Minus space\(-\)\(5\)

Trace form

\( 7q - 3q^{2} + 3q^{3} + 9q^{4} - q^{5} + q^{6} - 15q^{8} + 7q^{9} + O(q^{10}) \) \( 7q - 3q^{2} + 3q^{3} + 9q^{4} - q^{5} + q^{6} - 15q^{8} + 7q^{9} + q^{10} - q^{11} + 5q^{12} + 2q^{13} - 16q^{14} + 3q^{15} + 9q^{16} - 10q^{17} - 3q^{18} + 4q^{19} + q^{20} + 8q^{21} + q^{22} - 8q^{23} - 3q^{24} + 7q^{25} + 14q^{26} + 3q^{27} + 8q^{28} - 14q^{29} - 3q^{30} - 23q^{32} + 3q^{33} - 30q^{34} + 9q^{36} + 10q^{37} + 4q^{38} + 2q^{39} - 3q^{40} - 10q^{41} - 8q^{42} - 4q^{43} + q^{44} - q^{45} + 8q^{46} - 16q^{47} - 3q^{48} + 15q^{49} - 3q^{50} + 6q^{51} - 58q^{52} - 22q^{53} + q^{54} + 7q^{55} + 20q^{57} + 6q^{58} + 4q^{59} + 5q^{60} - 14q^{61} + 40q^{62} + q^{64} - 6q^{65} - 3q^{66} + 12q^{67} + 50q^{68} + 8q^{69} - 8q^{70} + 24q^{71} - 15q^{72} - 10q^{73} - 2q^{74} + 3q^{75} + 28q^{76} - 18q^{78} - 8q^{79} + 17q^{80} + 7q^{81} + 2q^{82} + 4q^{83} - 16q^{84} + 6q^{85} + 36q^{86} - 6q^{87} - 3q^{88} - 26q^{89} + q^{90} - 16q^{91} + 8q^{92} + 16q^{94} + 12q^{95} - 35q^{96} + 14q^{97} + 61q^{98} - q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(165))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 3 5 11
165.2.a.a \(2\) \(1.318\) \(\Q(\sqrt{2}) \) None \(-2\) \(-2\) \(-2\) \(-4\) \(+\) \(+\) \(+\) \(q+(-1+\beta )q^{2}-q^{3}+(1-2\beta )q^{4}-q^{5}+\cdots\)
165.2.a.b \(2\) \(1.318\) \(\Q(\sqrt{3}) \) None \(0\) \(2\) \(-2\) \(4\) \(-\) \(+\) \(+\) \(q+\beta q^{2}+q^{3}+q^{4}-q^{5}+\beta q^{6}+2q^{7}+\cdots\)
165.2.a.c \(3\) \(1.318\) 3.3.148.1 None \(-1\) \(3\) \(3\) \(0\) \(-\) \(-\) \(-\) \(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(165))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(165)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(55))\)\(^{\oplus 2}\)