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Properties

Label 888.2.bu
Level $888$
Weight $2$
Character orbit 888.bu
Rep. character $\chi_{888}(547,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $304$
Newform subspaces $4$
Sturm bound $304$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 888 = 2^{3} \cdot 3 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 888.bu (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 296 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 4 \)
Sturm bound: \(304\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(5\)

Dimensions

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

Total New Old
Modular forms 624 304 320
Cusp forms 592 304 288
Eisenstein series 32 0 32

Trace form

\( 304 q - 4 q^{2} - 12 q^{4} + 8 q^{8} + 152 q^{9} + O(q^{10}) \) \( 304 q - 4 q^{2} - 12 q^{4} + 8 q^{8} + 152 q^{9} - 4 q^{14} + 4 q^{16} - 8 q^{17} - 8 q^{18} + 8 q^{22} + 24 q^{25} - 24 q^{32} - 16 q^{34} + 72 q^{38} + 20 q^{42} + 32 q^{43} + 20 q^{44} + 76 q^{46} + 168 q^{49} - 16 q^{57} + 84 q^{58} + 28 q^{60} + 60 q^{62} - 120 q^{65} + 24 q^{66} - 36 q^{68} + 60 q^{70} + 4 q^{72} + 32 q^{74} - 76 q^{76} - 60 q^{78} - 92 q^{80} - 152 q^{81} + 68 q^{82} + 32 q^{84} + 120 q^{86} - 124 q^{88} + 40 q^{89} + 12 q^{92} - 48 q^{94} - 40 q^{96} - 8 q^{97} - 64 q^{98} + O(q^{100}) \)

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.bu.a 888.bu 296.y $4$ $7.091$ \(\Q(\zeta_{12})\) None \(-4\) \(0\) \(2\) \(6\) $\mathrm{SU}(2)[C_{12}]$ \(q+(-1-\zeta_{12}^{3})q^{2}+\zeta_{12}q^{3}+2\zeta_{12}^{3}q^{4}+\cdots\)
888.2.bu.b 888.bu 296.y $4$ $7.091$ \(\Q(\zeta_{12})\) None \(-2\) \(0\) \(-2\) \(-6\) $\mathrm{SU}(2)[C_{12}]$ \(q+(-1-\zeta_{12}+\zeta_{12}^{2})q^{2}+\zeta_{12}q^{3}+\cdots\)
888.2.bu.c 888.bu 296.y $144$ $7.091$ None \(4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{12}]$
888.2.bu.d 888.bu 296.y $152$ $7.091$ None \(-2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{12}]$

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

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