Properties

Label 1152.1.b
Level $1152$
Weight $1$
Character orbit 1152.b
Rep. character $\chi_{1152}(703,\cdot)$
Character field $\Q$
Dimension $3$
Newform subspaces $2$
Sturm bound $192$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 1152 = 2^{7} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1152.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 8 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(192\)
Trace bound: \(1\)

Dimensions

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

Total New Old
Modular forms 42 3 39
Cusp forms 10 3 7
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 3 0 0 0

Trace form

\( 3 q + O(q^{10}) \) \( 3 q + 2 q^{17} - 5 q^{25} - 2 q^{41} + 3 q^{49} + 2 q^{73} + 2 q^{89} + 2 q^{97} + O(q^{100}) \)

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

Label Char Prim Dim $A$ Field Image CM RM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1152.1.b.a 1152.b 8.d $1$ $0.575$ \(\Q\) $D_{2}$ \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{2}) \) 128.1.d.a \(0\) \(0\) \(0\) \(0\) \(q+2q^{17}+q^{25}-2q^{41}+q^{49}-2q^{73}+\cdots\)
1152.1.b.b 1152.b 8.d $2$ $0.575$ \(\Q(\sqrt{-1}) \) $D_{2}$ \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-6}) \) \(\Q(\sqrt{6}) \) 1152.1.b.b \(0\) \(0\) \(0\) \(0\) \(q-iq^{5}-3q^{25}-iq^{29}+q^{49}+iq^{53}+\cdots\)

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

\( S_{1}^{\mathrm{old}}(1152, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(128, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(384, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(576, [\chi])\)\(^{\oplus 2}\)