Properties

Label 162.2.a
Level $162$
Weight $2$
Character orbit 162.a
Rep. character $\chi_{162}(1,\cdot)$
Character field $\Q$
Dimension $4$
Newform subspaces $4$
Sturm bound $54$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 162 = 2 \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 162.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(54\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(162))\).

Total New Old
Modular forms 39 4 35
Cusp forms 16 4 12
Eisenstein series 23 0 23

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

\(2\)\(3\)FrickeDim
\(+\)\(+\)$+$\(1\)
\(+\)\(-\)$-$\(1\)
\(-\)\(+\)$-$\(2\)
Plus space\(+\)\(1\)
Minus space\(-\)\(3\)

Trace form

\( 4 q + 4 q^{4} - 4 q^{7} + O(q^{10}) \) \( 4 q + 4 q^{4} - 4 q^{7} + 6 q^{10} + 2 q^{13} + 4 q^{16} - 10 q^{19} - 6 q^{22} - 2 q^{25} - 4 q^{28} - 16 q^{31} - 10 q^{37} + 6 q^{40} + 14 q^{43} - 12 q^{46} + 12 q^{49} + 2 q^{52} - 6 q^{58} + 14 q^{61} + 4 q^{64} + 2 q^{67} - 24 q^{70} + 44 q^{73} - 10 q^{76} - 40 q^{79} + 6 q^{82} + 18 q^{85} - 6 q^{88} + 16 q^{91} + 12 q^{94} + 14 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(162))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 3
162.2.a.a 162.a 1.a $1$ $1.294$ \(\Q\) None \(-1\) \(0\) \(-3\) \(-4\) $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-3q^{5}-4q^{7}-q^{8}+3q^{10}+\cdots\)
162.2.a.b 162.a 1.a $1$ $1.294$ \(\Q\) None \(-1\) \(0\) \(0\) \(2\) $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+2q^{7}-q^{8}+3q^{11}+2q^{13}+\cdots\)
162.2.a.c 162.a 1.a $1$ $1.294$ \(\Q\) None \(1\) \(0\) \(0\) \(2\) $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+2q^{7}+q^{8}-3q^{11}+2q^{13}+\cdots\)
162.2.a.d 162.a 1.a $1$ $1.294$ \(\Q\) None \(1\) \(0\) \(3\) \(-4\) $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+3q^{5}-4q^{7}+q^{8}+3q^{10}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(162))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(162)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(27))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(54))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(81))\)\(^{\oplus 2}\)