Properties

Label 672.1.ba
Level $672$
Weight $1$
Character orbit 672.ba
Rep. character $\chi_{672}(305,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $4$
Newform subspaces $2$
Sturm bound $128$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 672 = 2^{5} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 672.ba (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 168 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(128\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(672, [\chi])\).

Total New Old
Modular forms 48 12 36
Cusp forms 16 4 12
Eisenstein series 32 8 24

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

\( 4 q + 2 q^{7} - 2 q^{9} + O(q^{10}) \) \( 4 q + 2 q^{7} - 2 q^{9} + 4 q^{15} - 2 q^{31} + 2 q^{33} - 2 q^{49} - 4 q^{55} - 4 q^{63} - 4 q^{73} - 2 q^{79} - 2 q^{81} - 2 q^{87} - 4 q^{97} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(672, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
672.1.ba.a 672.ba 168.s $2$ $0.335$ \(\Q(\sqrt{-3}) \) $D_{3}$ \(\Q(\sqrt{-6}) \) None \(0\) \(-1\) \(-1\) \(1\) \(q-\zeta_{6}q^{3}+\zeta_{6}^{2}q^{5}+\zeta_{6}q^{7}+\zeta_{6}^{2}q^{9}+\cdots\)
672.1.ba.b 672.ba 168.s $2$ $0.335$ \(\Q(\sqrt{-3}) \) $D_{3}$ \(\Q(\sqrt{-6}) \) None \(0\) \(1\) \(1\) \(1\) \(q+\zeta_{6}q^{3}-\zeta_{6}^{2}q^{5}+\zeta_{6}q^{7}+\zeta_{6}^{2}q^{9}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(672, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(672, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(168, [\chi])\)\(^{\oplus 3}\)