Properties

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

Related objects

Downloads

Learn more about

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

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

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ (\( 1 + T \))(\( 1 + T \))(\( 1 - T \))(\( 1 - T \))
$3$ 1
$5$ (\( 1 + 3 T + 5 T^{2} \))(\( 1 + 5 T^{2} \))(\( 1 + 5 T^{2} \))(\( 1 - 3 T + 5 T^{2} \))
$7$ (\( 1 + 4 T + 7 T^{2} \))(\( 1 - 2 T + 7 T^{2} \))(\( 1 - 2 T + 7 T^{2} \))(\( 1 + 4 T + 7 T^{2} \))
$11$ (\( 1 + 11 T^{2} \))(\( 1 - 3 T + 11 T^{2} \))(\( 1 + 3 T + 11 T^{2} \))(\( 1 + 11 T^{2} \))
$13$ (\( 1 + T + 13 T^{2} \))(\( 1 - 2 T + 13 T^{2} \))(\( 1 - 2 T + 13 T^{2} \))(\( 1 + T + 13 T^{2} \))
$17$ (\( 1 + 3 T + 17 T^{2} \))(\( 1 - 3 T + 17 T^{2} \))(\( 1 + 3 T + 17 T^{2} \))(\( 1 - 3 T + 17 T^{2} \))
$19$ (\( 1 + 4 T + 19 T^{2} \))(\( 1 + T + 19 T^{2} \))(\( 1 + T + 19 T^{2} \))(\( 1 + 4 T + 19 T^{2} \))
$23$ (\( 1 + 23 T^{2} \))(\( 1 - 6 T + 23 T^{2} \))(\( 1 + 6 T + 23 T^{2} \))(\( 1 + 23 T^{2} \))
$29$ (\( 1 - 9 T + 29 T^{2} \))(\( 1 + 6 T + 29 T^{2} \))(\( 1 - 6 T + 29 T^{2} \))(\( 1 + 9 T + 29 T^{2} \))
$31$ (\( 1 + 4 T + 31 T^{2} \))(\( 1 + 4 T + 31 T^{2} \))(\( 1 + 4 T + 31 T^{2} \))(\( 1 + 4 T + 31 T^{2} \))
$37$ (\( 1 + T + 37 T^{2} \))(\( 1 + 4 T + 37 T^{2} \))(\( 1 + 4 T + 37 T^{2} \))(\( 1 + T + 37 T^{2} \))
$41$ (\( 1 - 6 T + 41 T^{2} \))(\( 1 + 9 T + 41 T^{2} \))(\( 1 - 9 T + 41 T^{2} \))(\( 1 + 6 T + 41 T^{2} \))
$43$ (\( 1 - 8 T + 43 T^{2} \))(\( 1 + T + 43 T^{2} \))(\( 1 + T + 43 T^{2} \))(\( 1 - 8 T + 43 T^{2} \))
$47$ (\( 1 + 12 T + 47 T^{2} \))(\( 1 - 6 T + 47 T^{2} \))(\( 1 + 6 T + 47 T^{2} \))(\( 1 - 12 T + 47 T^{2} \))
$53$ (\( 1 + 6 T + 53 T^{2} \))(\( 1 + 12 T + 53 T^{2} \))(\( 1 - 12 T + 53 T^{2} \))(\( 1 - 6 T + 53 T^{2} \))
$59$ (\( 1 + 59 T^{2} \))(\( 1 + 3 T + 59 T^{2} \))(\( 1 - 3 T + 59 T^{2} \))(\( 1 + 59 T^{2} \))
$61$ (\( 1 + T + 61 T^{2} \))(\( 1 - 8 T + 61 T^{2} \))(\( 1 - 8 T + 61 T^{2} \))(\( 1 + T + 61 T^{2} \))
$67$ (\( 1 + 4 T + 67 T^{2} \))(\( 1 - 5 T + 67 T^{2} \))(\( 1 - 5 T + 67 T^{2} \))(\( 1 + 4 T + 67 T^{2} \))
$71$ (\( 1 + 12 T + 71 T^{2} \))(\( 1 - 12 T + 71 T^{2} \))(\( 1 + 12 T + 71 T^{2} \))(\( 1 - 12 T + 71 T^{2} \))
$73$ (\( 1 - 11 T + 73 T^{2} \))(\( 1 - 11 T + 73 T^{2} \))(\( 1 - 11 T + 73 T^{2} \))(\( 1 - 11 T + 73 T^{2} \))
$79$ (\( 1 + 16 T + 79 T^{2} \))(\( 1 + 4 T + 79 T^{2} \))(\( 1 + 4 T + 79 T^{2} \))(\( 1 + 16 T + 79 T^{2} \))
$83$ (\( 1 + 12 T + 83 T^{2} \))(\( 1 + 12 T + 83 T^{2} \))(\( 1 - 12 T + 83 T^{2} \))(\( 1 - 12 T + 83 T^{2} \))
$89$ (\( 1 + 3 T + 89 T^{2} \))(\( 1 + 6 T + 89 T^{2} \))(\( 1 - 6 T + 89 T^{2} \))(\( 1 - 3 T + 89 T^{2} \))
$97$ (\( 1 - 2 T + 97 T^{2} \))(\( 1 - 5 T + 97 T^{2} \))(\( 1 - 5 T + 97 T^{2} \))(\( 1 - 2 T + 97 T^{2} \))
show more
show less