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 $2$

Related objects

Downloads

Learn more

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

\( 7 q - 3 q^{2} + 3 q^{3} + 9 q^{4} - q^{5} + q^{6} - 15 q^{8} + 7 q^{9} + q^{10} - q^{11} + 5 q^{12} + 2 q^{13} - 16 q^{14} + 3 q^{15} + 9 q^{16} - 10 q^{17} - 3 q^{18} + 4 q^{19} + q^{20} + 8 q^{21}+ \cdots - q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(165))\) 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 5 11
165.2.a.a 165.a 1.a $2$ $1.318$ \(\Q(\sqrt{2}) \) None 165.2.a.a \(-2\) \(-2\) \(-2\) \(-4\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{2}-q^{3}+(1-2\beta )q^{4}-q^{5}+\cdots\)
165.2.a.b 165.a 1.a $2$ $1.318$ \(\Q(\sqrt{3}) \) None 165.2.a.b \(0\) \(2\) \(-2\) \(4\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+q^{3}+q^{4}-q^{5}+\beta q^{6}+2q^{7}+\cdots\)
165.2.a.c 165.a 1.a $3$ $1.318$ 3.3.148.1 None 165.2.a.c \(-1\) \(3\) \(3\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+q^{5}+\cdots\)

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

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