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Properties

Label 888.2.bo
Level $888$
Weight $2$
Character orbit 888.bo
Rep. character $\chi_{888}(49,\cdot)$
Character field $\Q(\zeta_{9})$
Dimension $120$
Newform subspaces $5$
Sturm bound $304$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 888 = 2^{3} \cdot 3 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 888.bo (of order \(9\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 37 \)
Character field: \(\Q(\zeta_{9})\)
Newform subspaces: \( 5 \)
Sturm bound: \(304\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(888, [\chi])\).

Total New Old
Modular forms 960 120 840
Cusp forms 864 120 744
Eisenstein series 96 0 96

Trace form

\( 120 q + 6 q^{5} + 6 q^{7} + O(q^{10}) \) \( 120 q + 6 q^{5} + 6 q^{7} - 12 q^{13} + 6 q^{17} - 12 q^{19} + 6 q^{21} + 30 q^{25} + 6 q^{27} - 24 q^{31} - 24 q^{35} - 6 q^{37} + 30 q^{39} - 6 q^{41} + 30 q^{49} - 12 q^{55} - 12 q^{57} + 12 q^{61} + 78 q^{65} + 30 q^{67} - 12 q^{69} + 60 q^{71} + 84 q^{73} - 84 q^{75} + 48 q^{77} + 78 q^{79} - 6 q^{85} + 24 q^{89} + 54 q^{91} + 42 q^{93} - 24 q^{95} + 12 q^{97} - 12 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(888, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
888.2.bo.a 888.bo 37.f $6$ $7.091$ \(\Q(\zeta_{18})\) None \(0\) \(0\) \(3\) \(-6\) $\mathrm{SU}(2)[C_{9}]$ \(q+\zeta_{18}^{2}q^{3}+(1+\zeta_{18}-\zeta_{18}^{3})q^{5}+\cdots\)
888.2.bo.b 888.bo 37.f $24$ $7.091$ None \(0\) \(0\) \(-3\) \(-3\) $\mathrm{SU}(2)[C_{9}]$
888.2.bo.c 888.bo 37.f $24$ $7.091$ None \(0\) \(0\) \(3\) \(15\) $\mathrm{SU}(2)[C_{9}]$
888.2.bo.d 888.bo 37.f $30$ $7.091$ None \(0\) \(0\) \(9\) \(6\) $\mathrm{SU}(2)[C_{9}]$
888.2.bo.e 888.bo 37.f $36$ $7.091$ None \(0\) \(0\) \(-6\) \(-6\) $\mathrm{SU}(2)[C_{9}]$

Decomposition of \(S_{2}^{\mathrm{old}}(888, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(888, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(37, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(74, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(111, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(148, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(222, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(296, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(444, [\chi])\)\(^{\oplus 2}\)