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Properties

Label 672.2.bl
Level $672$
Weight $2$
Character orbit 672.bl
Rep. character $\chi_{672}(31,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $32$
Newform subspaces $2$
Sturm bound $256$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 672 = 2^{5} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 672.bl (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 28 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(256\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(672, [\chi])\).

Total New Old
Modular forms 288 32 256
Cusp forms 224 32 192
Eisenstein series 64 0 64

Trace form

\( 32 q - 16 q^{9} + O(q^{10}) \) \( 32 q - 16 q^{9} + 16 q^{21} + 8 q^{25} - 24 q^{33} + 8 q^{37} + 48 q^{49} + 16 q^{53} - 16 q^{57} + 48 q^{61} + 16 q^{65} + 24 q^{73} - 64 q^{77} - 16 q^{81} + 64 q^{85} + 8 q^{93} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(672, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
672.2.bl.a 672.bl 28.f $16$ $5.366$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(-8\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-1-\beta _{1})q^{3}-\beta _{6}q^{5}+(-\beta _{9}+\beta _{13}+\cdots)q^{7}+\cdots\)
672.2.bl.b 672.bl 28.f $16$ $5.366$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(8\) \(0\) \(4\) $\mathrm{SU}(2)[C_{6}]$ \(q-\beta _{1}q^{3}-\beta _{3}q^{5}+(1+\beta _{1}-\beta _{4}+\beta _{12}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(672, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(672, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(168, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(224, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(336, [\chi])\)\(^{\oplus 2}\)