Properties

Label 1152.1.h
Level $1152$
Weight $1$
Character orbit 1152.h
Rep. character $\chi_{1152}(449,\cdot)$
Character field $\Q$
Dimension $4$
Newform subspaces $1$
Sturm bound $192$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 1152 = 2^{7} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1152.h (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 24 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(192\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1152, [\chi])\).

Total New Old
Modular forms 48 4 44
Cusp forms 16 4 12
Eisenstein series 32 0 32

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 4 0 0 0

Trace form

\( 4 q + O(q^{10}) \) \( 4 q + 4 q^{25} - 4 q^{49} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1152, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1152.1.h.a $4$ $0.575$ \(\Q(\zeta_{8})\) $D_{4}$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(-\zeta_{8}+\zeta_{8}^{3})q^{5}+\zeta_{8}^{2}q^{13}+(\zeta_{8}+\cdots)q^{17}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(1152, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(1152, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(384, [\chi])\)\(^{\oplus 2}\)