Properties

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

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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

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

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

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2
128.2.a.a 128.a 1.a $1$ $1.022$ \(\Q\) None \(0\) \(-2\) \(-2\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q-2q^{3}-2q^{5}-4q^{7}+q^{9}+2q^{11}+\cdots\)
128.2.a.b 128.a 1.a $1$ $1.022$ \(\Q\) None \(0\) \(-2\) \(2\) \(4\) $-$ $\mathrm{SU}(2)$ \(q-2q^{3}+2q^{5}+4q^{7}+q^{9}+2q^{11}+\cdots\)
128.2.a.c 128.a 1.a $1$ $1.022$ \(\Q\) None \(0\) \(2\) \(-2\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+2q^{3}-2q^{5}+4q^{7}+q^{9}-2q^{11}+\cdots\)
128.2.a.d 128.a 1.a $1$ $1.022$ \(\Q\) None \(0\) \(2\) \(2\) \(-4\) $-$ $\mathrm{SU}(2)$ \(q+2q^{3}+2q^{5}-4q^{7}+q^{9}-2q^{11}+\cdots\)

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

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