Properties

Label 384.1.h
Level $384$
Weight $1$
Character orbit 384.h
Rep. character $\chi_{384}(65,\cdot)$
Character field $\Q$
Dimension $2$
Newform subspaces $2$
Sturm bound $64$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 384 = 2^{7} \cdot 3 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 384.h (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 24 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(64\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(384, [\chi])\).

Total New Old
Modular forms 22 2 20
Cusp forms 6 2 4
Eisenstein series 16 0 16

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 2 0 0 0

Trace form

\( 2q + 2q^{9} + O(q^{10}) \) \( 2q + 2q^{9} - 2q^{25} - 4q^{33} - 2q^{49} - 4q^{73} + 2q^{81} + 4q^{97} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(384, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
384.1.h.a \(1\) \(0.192\) \(\Q\) \(D_{2}\) \(\Q(\sqrt{-2}) \), \(\Q(\sqrt{-6}) \) \(\Q(\sqrt{3}) \) \(0\) \(-1\) \(0\) \(0\) \(q-q^{3}+q^{9}+2q^{11}-q^{25}-q^{27}+\cdots\)
384.1.h.b \(1\) \(0.192\) \(\Q\) \(D_{2}\) \(\Q(\sqrt{-2}) \), \(\Q(\sqrt{-6}) \) \(\Q(\sqrt{3}) \) \(0\) \(1\) \(0\) \(0\) \(q+q^{3}+q^{9}-2q^{11}-q^{25}+q^{27}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(384, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(384, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 2}\)