Properties

Label 861.2.bj
Level $861$
Weight $2$
Character orbit 861.bj
Rep. character $\chi_{861}(214,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $224$
Newform subspaces $1$
Sturm bound $224$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 861 = 3 \cdot 7 \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 861.bj (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 287 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 1 \)
Sturm bound: \(224\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(861, [\chi])\).

Total New Old
Modular forms 464 224 240
Cusp forms 432 224 208
Eisenstein series 32 0 32

Trace form

\( 224 q + 112 q^{4} + O(q^{10}) \) \( 224 q + 112 q^{4} + 16 q^{10} - 8 q^{11} - 20 q^{14} - 112 q^{16} + 8 q^{19} - 8 q^{22} + 12 q^{24} + 112 q^{25} - 12 q^{26} + 44 q^{28} - 8 q^{30} - 64 q^{31} - 32 q^{34} - 64 q^{35} + 8 q^{37} - 28 q^{38} - 48 q^{40} + 72 q^{41} + 72 q^{42} + 24 q^{44} - 40 q^{47} - 28 q^{52} + 48 q^{53} + 8 q^{55} + 52 q^{56} - 32 q^{57} - 4 q^{58} - 16 q^{59} - 20 q^{60} - 176 q^{64} + 12 q^{65} - 32 q^{66} - 8 q^{67} + 120 q^{68} - 8 q^{70} + 8 q^{71} - 24 q^{72} + 16 q^{75} + 176 q^{76} - 48 q^{78} + 28 q^{79} + 112 q^{81} + 8 q^{82} + 64 q^{83} + 112 q^{85} - 16 q^{86} + 20 q^{88} + 32 q^{89} + 144 q^{92} + 24 q^{93} - 56 q^{94} - 48 q^{95} - 4 q^{96} - 88 q^{97} + 136 q^{98} - 16 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(861, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
861.2.bj.a 861.bj 287.r $224$ $6.875$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{12}]$

Decomposition of \(S_{2}^{\mathrm{old}}(861, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(861, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(287, [\chi])\)\(^{\oplus 2}\)