Properties

Label 756.2.bp
Level $756$
Weight $2$
Character orbit 756.bp
Rep. character $\chi_{756}(193,\cdot)$
Character field $\Q(\zeta_{9})$
Dimension $144$
Newform subspaces $1$
Sturm bound $288$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 756.bp (of order \(9\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 189 \)
Character field: \(\Q(\zeta_{9})\)
Newform subspaces: \( 1 \)
Sturm bound: \(288\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(756, [\chi])\).

Total New Old
Modular forms 900 144 756
Cusp forms 828 144 684
Eisenstein series 72 0 72

Trace form

\( 144 q - 12 q^{9} + O(q^{10}) \) \( 144 q - 12 q^{9} - 12 q^{11} - 12 q^{15} - 24 q^{17} - 3 q^{21} + 15 q^{23} + 6 q^{29} + 18 q^{33} + 18 q^{35} + 18 q^{39} - 12 q^{41} + 6 q^{45} + 18 q^{47} + 36 q^{49} + 18 q^{51} + 15 q^{53} + 3 q^{57} + 30 q^{59} + 18 q^{61} + 3 q^{63} + 9 q^{65} + 30 q^{69} - 12 q^{71} - 36 q^{73} + 102 q^{75} + 69 q^{77} + 18 q^{79} + 12 q^{81} - 36 q^{85} + 78 q^{87} - 72 q^{89} - 18 q^{91} - 60 q^{93} + 42 q^{95} - 72 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(756, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
756.2.bp.a 756.bp 189.u $144$ $6.037$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{9}]$

Decomposition of \(S_{2}^{\mathrm{old}}(756, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(756, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(189, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(378, [\chi])\)\(^{\oplus 2}\)