Properties

Label 32.2.a
Level 32
Weight 2
Character orbit a
Rep. character \(\chi_{32}(1,\cdot)\)
Character field \(\Q\)
Dimension 1
Newform subspaces 1
Sturm bound 8
Trace bound 0

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) \(=\) \( 32 = 2^{5} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 32.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(8\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(32))\).

Total New Old
Modular forms 8 1 7
Cusp forms 1 1 0
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.

\(2\)Dim.
\(-\)\(1\)

Trace form

\( q - 2q^{5} - 3q^{9} + O(q^{10}) \) \( q - 2q^{5} - 3q^{9} + 6q^{13} + 2q^{17} - q^{25} - 10q^{29} - 2q^{37} + 10q^{41} + 6q^{45} - 7q^{49} + 14q^{53} - 10q^{61} - 12q^{65} - 6q^{73} + 9q^{81} - 4q^{85} + 10q^{89} + 18q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(32))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2
32.2.a.a \(1\) \(0.256\) \(\Q\) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(-2\) \(0\) \(-\) \(q-2q^{5}-3q^{9}+6q^{13}+2q^{17}-q^{25}+\cdots\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ 1
$3$ \( 1 + 3 T^{2} \)
$5$ \( 1 + 2 T + 5 T^{2} \)
$7$ \( 1 + 7 T^{2} \)
$11$ \( 1 + 11 T^{2} \)
$13$ \( 1 - 6 T + 13 T^{2} \)
$17$ \( 1 - 2 T + 17 T^{2} \)
$19$ \( 1 + 19 T^{2} \)
$23$ \( 1 + 23 T^{2} \)
$29$ \( 1 + 10 T + 29 T^{2} \)
$31$ \( 1 + 31 T^{2} \)
$37$ \( 1 + 2 T + 37 T^{2} \)
$41$ \( 1 - 10 T + 41 T^{2} \)
$43$ \( 1 + 43 T^{2} \)
$47$ \( 1 + 47 T^{2} \)
$53$ \( 1 - 14 T + 53 T^{2} \)
$59$ \( 1 + 59 T^{2} \)
$61$ \( 1 + 10 T + 61 T^{2} \)
$67$ \( 1 + 67 T^{2} \)
$71$ \( 1 + 71 T^{2} \)
$73$ \( 1 + 6 T + 73 T^{2} \)
$79$ \( 1 + 79 T^{2} \)
$83$ \( 1 + 83 T^{2} \)
$89$ \( 1 - 10 T + 89 T^{2} \)
$97$ \( 1 - 18 T + 97 T^{2} \)
show more
show less