Properties

Label 861.2.bs
Level $861$
Weight $2$
Character orbit 861.bs
Rep. character $\chi_{861}(178,\cdot)$
Character field $\Q(\zeta_{24})$
Dimension $448$
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.bs (of order \(24\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 287 \)
Character field: \(\Q(\zeta_{24})\)
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 928 448 480
Cusp forms 864 448 416
Eisenstein series 64 0 64

Trace form

\( 448 q + O(q^{10}) \) \( 448 q - 8 q^{14} + 224 q^{16} - 48 q^{19} + 80 q^{22} + 72 q^{24} + 48 q^{26} - 64 q^{29} + 16 q^{30} + 40 q^{32} - 80 q^{35} - 48 q^{37} + 72 q^{38} - 64 q^{42} + 64 q^{43} - 48 q^{44} + 24 q^{46} - 48 q^{47} + 80 q^{49} - 128 q^{50} - 72 q^{52} + 16 q^{53} - 112 q^{56} - 8 q^{58} + 64 q^{65} - 32 q^{67} + 144 q^{68} + 40 q^{70} - 32 q^{71} + 72 q^{73} - 56 q^{74} - 96 q^{75} + 192 q^{77} - 96 q^{78} + 8 q^{79} - 72 q^{80} - 144 q^{82} - 32 q^{85} + 88 q^{88} - 96 q^{89} + 48 q^{91} - 216 q^{94} - 64 q^{95} - 120 q^{96} + 240 q^{98} + 32 q^{99} + O(q^{100}) \)

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.bs.a 861.bs 287.w $448$ $6.875$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{24}]$

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

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