Properties

Label 128.4.a
Level $128$
Weight $4$
Character orbit 128.a
Rep. character $\chi_{128}(1,\cdot)$
Character field $\Q$
Dimension $12$
Newform subspaces $8$
Sturm bound $64$
Trace bound $5$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 128 = 2^{7} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 128.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 8 \)
Sturm bound: \(64\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(3\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(128))\).

Total New Old
Modular forms 56 12 44
Cusp forms 40 12 28
Eisenstein series 16 0 16

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
\(+\)\(7\)
\(-\)\(5\)

Trace form

\( 12 q + 108 q^{9} + O(q^{10}) \) \( 12 q + 108 q^{9} + 104 q^{17} + 212 q^{25} + 464 q^{33} - 392 q^{41} - 852 q^{49} - 1360 q^{57} - 2512 q^{65} - 24 q^{73} + 1596 q^{81} + 1960 q^{89} + 4328 q^{97} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(128))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2
128.4.a.a 128.a 1.a $1$ $7.552$ \(\Q\) None 128.4.a.a \(0\) \(-2\) \(-6\) \(20\) $-$ $\mathrm{SU}(2)$ \(q-2q^{3}-6q^{5}+20q^{7}-23q^{9}-14q^{11}+\cdots\)
128.4.a.b 128.a 1.a $1$ $7.552$ \(\Q\) None 128.4.a.a \(0\) \(-2\) \(6\) \(-20\) $-$ $\mathrm{SU}(2)$ \(q-2q^{3}+6q^{5}-20q^{7}-23q^{9}-14q^{11}+\cdots\)
128.4.a.c 128.a 1.a $1$ $7.552$ \(\Q\) None 128.4.a.a \(0\) \(2\) \(-6\) \(-20\) $-$ $\mathrm{SU}(2)$ \(q+2q^{3}-6q^{5}-20q^{7}-23q^{9}+14q^{11}+\cdots\)
128.4.a.d 128.a 1.a $1$ $7.552$ \(\Q\) None 128.4.a.a \(0\) \(2\) \(6\) \(20\) $+$ $\mathrm{SU}(2)$ \(q+2q^{3}+6q^{5}+20q^{7}-23q^{9}+14q^{11}+\cdots\)
128.4.a.e 128.a 1.a $2$ $7.552$ \(\Q(\sqrt{3}) \) None 128.4.a.e \(0\) \(-4\) \(-4\) \(-8\) $-$ $\mathrm{SU}(2)$ \(q+(-2+\beta )q^{3}+(-2-2\beta )q^{5}+(-4+\cdots)q^{7}+\cdots\)
128.4.a.f 128.a 1.a $2$ $7.552$ \(\Q(\sqrt{3}) \) None 128.4.a.e \(0\) \(-4\) \(4\) \(8\) $+$ $\mathrm{SU}(2)$ \(q+(-2+\beta )q^{3}+(2+2\beta )q^{5}+(4+2\beta )q^{7}+\cdots\)
128.4.a.g 128.a 1.a $2$ $7.552$ \(\Q(\sqrt{3}) \) None 128.4.a.e \(0\) \(4\) \(-4\) \(8\) $+$ $\mathrm{SU}(2)$ \(q+(2+\beta )q^{3}+(-2+2\beta )q^{5}+(4-2\beta )q^{7}+\cdots\)
128.4.a.h 128.a 1.a $2$ $7.552$ \(\Q(\sqrt{3}) \) None 128.4.a.e \(0\) \(4\) \(4\) \(-8\) $+$ $\mathrm{SU}(2)$ \(q+(2+\beta )q^{3}+(2-2\beta )q^{5}+(-4+2\beta )q^{7}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(128))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(128)) \simeq \) \(S_{4}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(16))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(64))\)\(^{\oplus 2}\)