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Properties

Label 861.2.bp
Level $861$
Weight $2$
Character orbit 861.bp
Rep. character $\chi_{861}(44,\cdot)$
Character field $\Q(\zeta_{24})$
Dimension $864$
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.bp (of order \(24\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 861 \)
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 928 928 0
Cusp forms 864 864 0
Eisenstein series 64 64 0

Trace form

\( 864 q - 4 q^{3} - 16 q^{6} - 16 q^{7} - 12 q^{9} + O(q^{10}) \) \( 864 q - 4 q^{3} - 16 q^{6} - 16 q^{7} - 12 q^{9} - 16 q^{10} - 28 q^{12} - 32 q^{13} - 40 q^{15} + 368 q^{16} - 8 q^{18} - 8 q^{19} - 16 q^{21} - 112 q^{22} + 36 q^{24} - 16 q^{27} - 48 q^{28} + 28 q^{30} - 48 q^{33} - 32 q^{34} - 112 q^{36} - 16 q^{37} - 4 q^{39} - 48 q^{42} - 64 q^{43} - 184 q^{48} + 32 q^{49} + 16 q^{51} - 32 q^{52} + 36 q^{54} - 64 q^{55} - 16 q^{57} - 8 q^{58} + 28 q^{60} - 40 q^{61} - 68 q^{63} - 24 q^{67} + 8 q^{69} - 96 q^{70} - 8 q^{73} - 480 q^{76} - 144 q^{78} - 24 q^{79} + 40 q^{82} - 112 q^{84} + 32 q^{85} + 16 q^{87} + 24 q^{88} + 32 q^{90} - 160 q^{91} - 68 q^{93} - 8 q^{94} - 116 q^{96} - 64 q^{97} + 112 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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.bp.a 861.bp 861.ap $864$ $6.875$ None \(0\) \(-4\) \(0\) \(-16\) $\mathrm{SU}(2)[C_{24}]$