Properties

Label 672.2.bi
Level $672$
Weight $2$
Character orbit 672.bi
Rep. character $\chi_{672}(17,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $56$
Newform subspaces $3$
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.bi (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 168 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 3 \)
Sturm bound: \(256\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(5\)

Dimensions

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

Total New Old
Modular forms 288 72 216
Cusp forms 224 56 168
Eisenstein series 64 16 48

Trace form

\( 56 q + 8 q^{7} - 2 q^{9} + O(q^{10}) \) \( 56 q + 8 q^{7} - 2 q^{9} + 20 q^{15} + 8 q^{25} + 12 q^{31} - 6 q^{33} + 8 q^{39} - 16 q^{49} + 4 q^{57} + 30 q^{63} - 36 q^{73} + 36 q^{79} + 6 q^{81} + 24 q^{87} + O(q^{100}) \)

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

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
672.2.bi.a 672.bi 168.aa $4$ $5.366$ \(\Q(\sqrt{2}, \sqrt{-3})\) \(\Q(\sqrt{-6}) \) 168.2.ba.a \(0\) \(-6\) \(-6\) \(2\) $\mathrm{U}(1)[D_{6}]$ \(q+(-1+\beta _{2})q^{3}+(-2+\beta _{1}-\beta _{2}-\beta _{3})q^{5}+\cdots\)
672.2.bi.b 672.bi 168.aa $4$ $5.366$ \(\Q(\sqrt{2}, \sqrt{-3})\) \(\Q(\sqrt{-6}) \) 168.2.ba.a \(0\) \(6\) \(6\) \(2\) $\mathrm{U}(1)[D_{6}]$ \(q+(1-\beta _{2})q^{3}+(2+\beta _{1}+\beta _{2}-\beta _{3})q^{5}+\cdots\)
672.2.bi.c 672.bi 168.aa $48$ $5.366$ None 168.2.ba.c \(0\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{6}]$

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

\( S_{2}^{\mathrm{old}}(672, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(168, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(336, [\chi])\)\(^{\oplus 2}\)