Properties

Label 128.3.c
Level $128$
Weight $3$
Character orbit 128.c
Rep. character $\chi_{128}(127,\cdot)$
Character field $\Q$
Dimension $8$
Newform subspaces $2$
Sturm bound $48$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 128 = 2^{7} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 128.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 4 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(48\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\)

Dimensions

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

Total New Old
Modular forms 40 8 32
Cusp forms 24 8 16
Eisenstein series 16 0 16

Trace form

\( 8q - 24q^{9} + O(q^{10}) \) \( 8q - 24q^{9} - 16q^{17} + 88q^{25} - 32q^{33} + 16q^{41} + 8q^{49} - 352q^{57} + 160q^{65} + 176q^{73} + 232q^{81} + 432q^{89} - 656q^{97} + O(q^{100}) \)

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.c.a \(4\) \(3.488\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(-8\) \(0\) \(q+\zeta_{8}q^{3}+(-2-\zeta_{8}^{2})q^{5}+(-\zeta_{8}-\zeta_{8}^{3})q^{7}+\cdots\)
128.3.c.b \(4\) \(3.488\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(8\) \(0\) \(q+\zeta_{8}q^{3}+(2+\zeta_{8}^{2})q^{5}+(\zeta_{8}+\zeta_{8}^{3})q^{7}+\cdots\)

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

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