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Properties

Label 889.2.x
Level $889$
Weight $2$
Character orbit 889.x
Rep. character $\chi_{889}(22,\cdot)$
Character field $\Q(\zeta_{9})$
Dimension $384$
Newform subspaces $2$
Sturm bound $170$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 889 = 7 \cdot 127 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 889.x (of order \(9\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 127 \)
Character field: \(\Q(\zeta_{9})\)
Newform subspaces: \( 2 \)
Sturm bound: \(170\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(889, [\chi])\).

Total New Old
Modular forms 528 384 144
Cusp forms 504 384 120
Eisenstein series 24 0 24

Trace form

\( 384 q + 384 q^{4} - 18 q^{6} - 6 q^{8} + O(q^{10}) \) \( 384 q + 384 q^{4} - 18 q^{6} - 6 q^{8} - 12 q^{11} - 18 q^{12} - 3 q^{14} + 336 q^{16} - 12 q^{17} - 27 q^{18} + 45 q^{22} + 6 q^{23} + 60 q^{24} - 216 q^{25} - 12 q^{26} + 30 q^{28} + 6 q^{30} + 24 q^{31} + 48 q^{32} + 12 q^{33} + 12 q^{35} - 18 q^{36} - 12 q^{37} - 30 q^{38} - 72 q^{39} - 84 q^{40} - 24 q^{41} - 30 q^{42} - 78 q^{43} - 120 q^{44} + 12 q^{45} + 27 q^{46} + 30 q^{47} - 84 q^{48} - 48 q^{51} - 48 q^{52} + 12 q^{53} - 72 q^{54} - 12 q^{55} - 6 q^{56} - 24 q^{57} - 141 q^{58} - 60 q^{59} - 90 q^{60} + 24 q^{61} - 144 q^{62} + 60 q^{63} + 246 q^{64} - 54 q^{65} - 96 q^{66} - 72 q^{67} - 90 q^{68} - 48 q^{69} + 12 q^{71} - 150 q^{72} - 81 q^{74} + 48 q^{76} - 48 q^{77} + 126 q^{78} + 84 q^{79} - 108 q^{81} - 162 q^{82} - 24 q^{83} - 42 q^{84} + 6 q^{85} + 108 q^{86} - 30 q^{87} - 15 q^{88} + 42 q^{89} + 66 q^{90} - 147 q^{92} + 120 q^{93} - 48 q^{94} + 324 q^{95} - 42 q^{96} + 48 q^{97} - 3 q^{98} + 24 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(889, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
889.2.x.a 889.x 127.f $186$ $7.099$ None \(-12\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{9}]$
889.2.x.b 889.x 127.f $198$ $7.099$ None \(12\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{9}]$

Decomposition of \(S_{2}^{\mathrm{old}}(889, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(889, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(127, [\chi])\)\(^{\oplus 2}\)