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

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

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

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3
162.2.a.a \(1\) \(1.294\) \(\Q\) None \(-1\) \(0\) \(-3\) \(-4\) \(+\) \(+\) \(q-q^{2}+q^{4}-3q^{5}-4q^{7}-q^{8}+3q^{10}+\cdots\)
162.2.a.b \(1\) \(1.294\) \(\Q\) None \(-1\) \(0\) \(0\) \(2\) \(+\) \(-\) \(q-q^{2}+q^{4}+2q^{7}-q^{8}+3q^{11}+2q^{13}+\cdots\)
162.2.a.c \(1\) \(1.294\) \(\Q\) None \(1\) \(0\) \(0\) \(2\) \(-\) \(+\) \(q+q^{2}+q^{4}+2q^{7}+q^{8}-3q^{11}+2q^{13}+\cdots\)
162.2.a.d \(1\) \(1.294\) \(\Q\) None \(1\) \(0\) \(3\) \(-4\) \(-\) \(+\) \(q+q^{2}+q^{4}+3q^{5}-4q^{7}+q^{8}+3q^{10}+\cdots\)

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

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