Properties

Label 128.3.d
Level $128$
Weight $3$
Character orbit 128.d
Rep. character $\chi_{128}(63,\cdot)$
Character field $\Q$
Dimension $8$
Newform subspaces $3$
Sturm bound $48$
Trace bound $9$

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Defining parameters

Level: \( N \) \(=\) \( 128 = 2^{7} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 128.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 8 \)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(48\)
Trace bound: \(9\)
Distinguishing \(T_p\): \(3\)

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

\( 8q + 24q^{9} + O(q^{10}) \) \( 8q + 24q^{9} + 16q^{17} + 8q^{25} - 32q^{33} - 176q^{41} - 120q^{49} - 32q^{57} - 64q^{65} + 464q^{73} + 360q^{81} - 48q^{89} + 528q^{97} + O(q^{100}) \)

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.d.a \(2\) \(3.488\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(0\) \(0\) \(q+iq^{5}-9q^{9}+3iq^{13}+30q^{17}+\cdots\)
128.3.d.b \(2\) \(3.488\) \(\Q(\sqrt{2}) \) \(\Q(\sqrt{-2}) \) \(0\) \(0\) \(0\) \(0\) \(q+\beta q^{3}+23q^{9}-3\beta q^{11}-2q^{17}+\cdots\)
128.3.d.c \(4\) \(3.488\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}^{2}q^{3}+\zeta_{8}q^{5}+\zeta_{8}^{3}q^{7}-q^{9}+\cdots\)

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

\( S_{3}^{\mathrm{old}}(128, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(8, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 2}\)