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Properties

Label 888.2.bh
Level $888$
Weight $2$
Character orbit 888.bh
Rep. character $\chi_{888}(565,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $152$
Newform subspaces $1$
Sturm bound $304$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 888 = 2^{3} \cdot 3 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 888.bh (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 296 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(304\)
Trace bound: \(0\)

Dimensions

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

Total New Old
Modular forms 312 152 160
Cusp forms 296 152 144
Eisenstein series 16 0 16

Trace form

\( 152 q - 2 q^{2} + 2 q^{4} + 8 q^{7} - 8 q^{8} + 76 q^{9} - 4 q^{14} + 2 q^{16} - 4 q^{17} + 2 q^{18} - 6 q^{22} - 16 q^{23} + 80 q^{25} + 6 q^{28} + 8 q^{30} + 8 q^{32} + 2 q^{34} + 4 q^{36} + 76 q^{38}+ \cdots + 52 q^{98}+O(q^{100}) \) Copy content Toggle raw display

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

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
888.2.bh.a 888.bh 296.s $152$ $7.091$ None 888.2.bh.a \(-2\) \(0\) \(0\) \(8\) $\mathrm{SU}(2)[C_{6}]$

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

\( S_{2}^{\mathrm{old}}(888, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(296, [\chi])\)\(^{\oplus 2}\)