Properties

Label 128.5.f
Level $128$
Weight $5$
Character orbit 128.f
Rep. character $\chi_{128}(31,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $28$
Newform subspaces $2$
Sturm bound $80$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 128 = 2^{7} \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 128.f (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 16 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 2 \)
Sturm bound: \(80\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(128, [\chi])\).

Total New Old
Modular forms 144 36 108
Cusp forms 112 28 84
Eisenstein series 32 8 24

Trace form

\( 28q + 4q^{5} + O(q^{10}) \) \( 28q + 4q^{5} + 4q^{13} - 8q^{17} + 328q^{21} - 1724q^{29} - 8q^{33} + 3652q^{37} - 2820q^{45} + 1364q^{49} + 964q^{53} + 7556q^{61} - 4040q^{65} - 19256q^{69} + 19016q^{77} + 2908q^{81} - 19896q^{85} - 17792q^{93} - 8q^{97} + O(q^{100}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(128, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
128.5.f.a \(14\) \(13.231\) \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(0\) \(-2\) \(2\) \(4\) \(q+\beta _{5}q^{3}+\beta _{8}q^{5}+\beta _{9}q^{7}+(-19\beta _{1}+\cdots)q^{9}+\cdots\)
128.5.f.b \(14\) \(13.231\) \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(0\) \(2\) \(2\) \(-4\) \(q+\beta _{2}q^{3}-\beta _{3}q^{5}-\beta _{9}q^{7}+(19\beta _{1}-\beta _{2}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{5}^{\mathrm{old}}(128, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(128, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 2}\)