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Properties

Label 128.4.e
Level $128$
Weight $4$
Character orbit 128.e
Rep. character $\chi_{128}(33,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $20$
Newform subspaces $2$
Sturm bound $64$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 128 = 2^{7} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 128.e (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 16 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 2 \)
Sturm bound: \(64\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(128, [\chi])\).

Total New Old
Modular forms 112 28 84
Cusp forms 80 20 60
Eisenstein series 32 8 24

Trace form

\( 20 q + 4 q^{5} + 4 q^{13} - 8 q^{17} - 104 q^{21} + 404 q^{29} - 8 q^{33} + 20 q^{37} - 388 q^{45} + 188 q^{49} + 756 q^{53} - 1820 q^{61} - 984 q^{65} - 1160 q^{69} + 536 q^{77} + 964 q^{81} + 24 q^{85}+ \cdots - 8 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{4}^{\mathrm{new}}(128, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
128.4.e.a 128.e 16.e $10$ $7.552$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None 16.4.e.a \(0\) \(-2\) \(2\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{5}q^{3}-\beta _{3}q^{5}+(3\beta _{1}-\beta _{4})q^{7}+(5\beta _{1}+\cdots)q^{9}+\cdots\)
128.4.e.b 128.e 16.e $10$ $7.552$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None 16.4.e.a \(0\) \(2\) \(2\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{5}q^{3}-\beta _{3}q^{5}+(-3\beta _{1}+\beta _{4})q^{7}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(128, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(128, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 2}\)