Properties

Label 162.2.a
Level 162
Weight 2
Character orbit a
Rep. character \(\chi_{162}(1,\cdot)\)
Character field \(\Q\)
Dimension 4
Newforms 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: \(\Q\)
Newforms: \( 4 \)
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

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

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(162))\) into irreducible Hecke orbits

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

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