Properties

Label 128.2.e
Level $128$
Weight $2$
Character orbit 128.e
Rep. character $\chi_{128}(33,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $4$
Newform subspaces $2$
Sturm bound $32$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 128 = 2^{7} \)
Weight: \( k \) \(=\) \( 2 \)
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: \(32\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(128, [\chi])\).

Total New Old
Modular forms 48 12 36
Cusp forms 16 4 12
Eisenstein series 32 8 24

Trace form

\( 4 q + 4 q^{5} + O(q^{10}) \) \( 4 q + 4 q^{5} + 4 q^{13} - 8 q^{17} - 8 q^{21} - 12 q^{29} - 8 q^{33} - 12 q^{37} - 4 q^{45} + 12 q^{49} + 20 q^{53} + 36 q^{61} + 8 q^{65} + 24 q^{69} - 8 q^{77} + 20 q^{81} - 8 q^{85} - 32 q^{93} - 8 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(128, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
128.2.e.a 128.e 16.e $2$ $1.022$ \(\Q(\sqrt{-1}) \) None 16.2.e.a \(0\) \(-2\) \(2\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-1+i)q^{3}+(1+i)q^{5}+2iq^{7}+\cdots\)
128.2.e.b 128.e 16.e $2$ $1.022$ \(\Q(\sqrt{-1}) \) None 16.2.e.a \(0\) \(2\) \(2\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+(1-i)q^{3}+(1+i)q^{5}-2iq^{7}+iq^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(128, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(128, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 2}\)