Properties

Label 128.1.d
Level $128$
Weight $1$
Character orbit 128.d
Rep. character $\chi_{128}(63,\cdot)$
Character field $\Q$
Dimension $1$
Newform subspaces $1$
Sturm bound $16$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 128 = 2^{7} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 128.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 8 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(16\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(128, [\chi])\).

Total New Old
Modular forms 9 1 8
Cusp forms 1 1 0
Eisenstein series 8 0 8

The following table gives the dimensions of subspaces with specified projective image type.

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 1 0 0 0

Trace form

\( q - q^{9} + O(q^{10}) \) \( q - q^{9} - 2q^{17} + q^{25} + 2q^{41} + q^{49} - 2q^{73} + q^{81} - 2q^{89} - 2q^{97} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(128, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
128.1.d.a \(1\) \(0.064\) \(\Q\) \(D_{2}\) \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{2}) \) \(0\) \(0\) \(0\) \(0\) \(q-q^{9}-2q^{17}+q^{25}+2q^{41}+q^{49}+\cdots\)