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Properties

Label 744.2.bf
Level $744$
Weight $2$
Character orbit 744.bf
Rep. character $\chi_{744}(595,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $128$
Newform subspaces $1$
Sturm bound $256$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 744 = 2^{3} \cdot 3 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 744.bf (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 248 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(256\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(744, [\chi])\).

Total New Old
Modular forms 264 128 136
Cusp forms 248 128 120
Eisenstein series 16 0 16

Trace form

\( 128 q + 4 q^{4} + 6 q^{6} + 12 q^{8} + 64 q^{9} + 4 q^{10} - 22 q^{14} + 12 q^{16} - 8 q^{19} + 6 q^{20} - 30 q^{22} + 64 q^{25} + 30 q^{26} + 6 q^{28} + 40 q^{32} - 60 q^{34} + 48 q^{35} + 2 q^{36} + 18 q^{38}+ \cdots - 24 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{2}^{\mathrm{new}}(744, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
744.2.bf.a 744.bf 248.q $128$ $5.941$ None 744.2.bf.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{2}^{\mathrm{old}}(744, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(744, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(248, [\chi])\)\(^{\oplus 2}\)