Properties

Label 128.3.f
Level $128$
Weight $3$
Character orbit 128.f
Rep. character $\chi_{128}(31,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $12$
Newform subspaces $2$
Sturm bound $48$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 128 = 2^{7} \)
Weight: \( k \) \(=\) \( 3 \)
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: \(48\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(128, [\chi])\).

Total New Old
Modular forms 80 20 60
Cusp forms 48 12 36
Eisenstein series 32 8 24

Trace form

\( 12q + 4q^{5} + O(q^{10}) \) \( 12q + 4q^{5} + 4q^{13} - 8q^{17} + 40q^{21} + 36q^{29} - 8q^{33} - 92q^{37} - 132q^{45} - 92q^{49} - 156q^{53} - 60q^{61} + 24q^{65} + 232q^{69} + 424q^{77} + 172q^{81} + 424q^{85} + 64q^{93} - 8q^{97} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(128, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
128.3.f.a \(6\) \(3.488\) 6.0.399424.1 None \(0\) \(-2\) \(2\) \(4\) \(q+\beta _{4}q^{3}+(1-\beta _{1}+\beta _{2}+\beta _{4})q^{5}+(-\beta _{2}+\cdots)q^{7}+\cdots\)
128.3.f.b \(6\) \(3.488\) 6.0.399424.1 None \(0\) \(2\) \(2\) \(-4\) \(q-\beta _{5}q^{3}+(1+\beta _{1}+\beta _{3}+\beta _{5})q^{5}+(\beta _{2}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(128, [\chi])\) into lower level spaces

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