Properties

Label 128.2.a
Level 128
Weight 2
Character orbit a
Rep. character \(\chi_{128}(1,\cdot)\)
Character field \(\Q\)
Dimension 4
Newform subspaces 4
Sturm bound 32
Trace bound 5

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 128 = 2^{7} \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 128.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(32\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(3\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(128))\).

Total New Old
Modular forms 24 4 20
Cusp forms 9 4 5
Eisenstein series 15 0 15

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.
\(+\)\(1\)
\(-\)\(3\)

Trace form

\( 4q + 4q^{9} + O(q^{10}) \) \( 4q + 4q^{9} - 8q^{17} - 4q^{25} - 16q^{33} - 24q^{41} + 36q^{49} + 16q^{57} + 16q^{65} + 56q^{73} - 44q^{81} - 8q^{89} - 8q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(128))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2
128.2.a.a \(1\) \(1.022\) \(\Q\) None \(0\) \(-2\) \(-2\) \(-4\) \(+\) \(q-2q^{3}-2q^{5}-4q^{7}+q^{9}+2q^{11}+\cdots\)
128.2.a.b \(1\) \(1.022\) \(\Q\) None \(0\) \(-2\) \(2\) \(4\) \(-\) \(q-2q^{3}+2q^{5}+4q^{7}+q^{9}+2q^{11}+\cdots\)
128.2.a.c \(1\) \(1.022\) \(\Q\) None \(0\) \(2\) \(-2\) \(4\) \(-\) \(q+2q^{3}-2q^{5}+4q^{7}+q^{9}-2q^{11}+\cdots\)
128.2.a.d \(1\) \(1.022\) \(\Q\) None \(0\) \(2\) \(2\) \(-4\) \(-\) \(q+2q^{3}+2q^{5}-4q^{7}+q^{9}-2q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(128))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(128)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(64))\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ 1
$3$ (\( 1 + 2 T + 3 T^{2} \))(\( 1 + 2 T + 3 T^{2} \))(\( 1 - 2 T + 3 T^{2} \))(\( 1 - 2 T + 3 T^{2} \))
$5$ (\( 1 + 2 T + 5 T^{2} \))(\( 1 - 2 T + 5 T^{2} \))(\( 1 + 2 T + 5 T^{2} \))(\( 1 - 2 T + 5 T^{2} \))
$7$ (\( 1 + 4 T + 7 T^{2} \))(\( 1 - 4 T + 7 T^{2} \))(\( 1 - 4 T + 7 T^{2} \))(\( 1 + 4 T + 7 T^{2} \))
$11$ (\( 1 - 2 T + 11 T^{2} \))(\( 1 - 2 T + 11 T^{2} \))(\( 1 + 2 T + 11 T^{2} \))(\( 1 + 2 T + 11 T^{2} \))
$13$ (\( 1 + 2 T + 13 T^{2} \))(\( 1 - 2 T + 13 T^{2} \))(\( 1 + 2 T + 13 T^{2} \))(\( 1 - 2 T + 13 T^{2} \))
$17$ (\( 1 + 2 T + 17 T^{2} \))(\( 1 + 2 T + 17 T^{2} \))(\( 1 + 2 T + 17 T^{2} \))(\( 1 + 2 T + 17 T^{2} \))
$19$ (\( 1 + 2 T + 19 T^{2} \))(\( 1 + 2 T + 19 T^{2} \))(\( 1 - 2 T + 19 T^{2} \))(\( 1 - 2 T + 19 T^{2} \))
$23$ (\( 1 - 4 T + 23 T^{2} \))(\( 1 + 4 T + 23 T^{2} \))(\( 1 + 4 T + 23 T^{2} \))(\( 1 - 4 T + 23 T^{2} \))
$29$ (\( 1 - 6 T + 29 T^{2} \))(\( 1 + 6 T + 29 T^{2} \))(\( 1 - 6 T + 29 T^{2} \))(\( 1 + 6 T + 29 T^{2} \))
$31$ (\( 1 + 31 T^{2} \))(\( 1 + 31 T^{2} \))(\( 1 + 31 T^{2} \))(\( 1 + 31 T^{2} \))
$37$ (\( 1 + 10 T + 37 T^{2} \))(\( 1 - 10 T + 37 T^{2} \))(\( 1 + 10 T + 37 T^{2} \))(\( 1 - 10 T + 37 T^{2} \))
$41$ (\( 1 + 6 T + 41 T^{2} \))(\( 1 + 6 T + 41 T^{2} \))(\( 1 + 6 T + 41 T^{2} \))(\( 1 + 6 T + 41 T^{2} \))
$43$ (\( 1 + 6 T + 43 T^{2} \))(\( 1 + 6 T + 43 T^{2} \))(\( 1 - 6 T + 43 T^{2} \))(\( 1 - 6 T + 43 T^{2} \))
$47$ (\( 1 + 8 T + 47 T^{2} \))(\( 1 - 8 T + 47 T^{2} \))(\( 1 - 8 T + 47 T^{2} \))(\( 1 + 8 T + 47 T^{2} \))
$53$ (\( 1 - 6 T + 53 T^{2} \))(\( 1 + 6 T + 53 T^{2} \))(\( 1 - 6 T + 53 T^{2} \))(\( 1 + 6 T + 53 T^{2} \))
$59$ (\( 1 + 14 T + 59 T^{2} \))(\( 1 + 14 T + 59 T^{2} \))(\( 1 - 14 T + 59 T^{2} \))(\( 1 - 14 T + 59 T^{2} \))
$61$ (\( 1 + 2 T + 61 T^{2} \))(\( 1 - 2 T + 61 T^{2} \))(\( 1 + 2 T + 61 T^{2} \))(\( 1 - 2 T + 61 T^{2} \))
$67$ (\( 1 + 10 T + 67 T^{2} \))(\( 1 + 10 T + 67 T^{2} \))(\( 1 - 10 T + 67 T^{2} \))(\( 1 - 10 T + 67 T^{2} \))
$71$ (\( 1 - 12 T + 71 T^{2} \))(\( 1 + 12 T + 71 T^{2} \))(\( 1 + 12 T + 71 T^{2} \))(\( 1 - 12 T + 71 T^{2} \))
$73$ (\( 1 - 14 T + 73 T^{2} \))(\( 1 - 14 T + 73 T^{2} \))(\( 1 - 14 T + 73 T^{2} \))(\( 1 - 14 T + 73 T^{2} \))
$79$ (\( 1 + 8 T + 79 T^{2} \))(\( 1 - 8 T + 79 T^{2} \))(\( 1 - 8 T + 79 T^{2} \))(\( 1 + 8 T + 79 T^{2} \))
$83$ (\( 1 - 6 T + 83 T^{2} \))(\( 1 - 6 T + 83 T^{2} \))(\( 1 + 6 T + 83 T^{2} \))(\( 1 + 6 T + 83 T^{2} \))
$89$ (\( 1 + 2 T + 89 T^{2} \))(\( 1 + 2 T + 89 T^{2} \))(\( 1 + 2 T + 89 T^{2} \))(\( 1 + 2 T + 89 T^{2} \))
$97$ (\( 1 + 2 T + 97 T^{2} \))(\( 1 + 2 T + 97 T^{2} \))(\( 1 + 2 T + 97 T^{2} \))(\( 1 + 2 T + 97 T^{2} \))
show more
show less