Properties

Label 64.2.a
Level 64
Weight 2
Character orbit a
Rep. character \(\chi_{64}(1,\cdot)\)
Character field \(\Q\)
Dimension 1
Newform subspaces 1
Sturm bound 16
Trace bound 0

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Defining parameters

Level: \( N \) \(=\) \( 64 = 2^{6} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 64.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(16\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(64))\).

Total New Old
Modular forms 14 3 11
Cusp forms 3 1 2
Eisenstein series 11 2 9

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 \(S_{2}^{\mathrm{new}}(\Gamma_0(64))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2
64.2.a.a \(1\) \(0.511\) \(\Q\) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(2\) \(0\) \(-\) \(q+2q^{5}-3q^{9}-6q^{13}+2q^{17}-q^{25}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(64))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(64)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 2}\)

Hecke characteristic polynomials

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