Properties

Label 861.2.s
Level $861$
Weight $2$
Character orbit 861.s
Rep. character $\chi_{861}(206,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $212$
Newform subspaces $2$
Sturm bound $224$
Trace bound $12$

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Defining parameters

Level: \( N \) \(=\) \( 861 = 3 \cdot 7 \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 861.s (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 21 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(224\)
Trace bound: \(12\)
Distinguishing \(T_p\): \(2\)

Dimensions

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

Total New Old
Modular forms 232 212 20
Cusp forms 216 212 4
Eisenstein series 16 0 16

Trace form

\( 212 q + 104 q^{4} - 10 q^{7} - 4 q^{9} + O(q^{10}) \) \( 212 q + 104 q^{4} - 10 q^{7} - 4 q^{9} - 12 q^{10} - 30 q^{12} - 8 q^{15} - 84 q^{16} - 10 q^{18} + 6 q^{19} - 8 q^{21} - 24 q^{22} - 114 q^{25} - 28 q^{28} - 4 q^{30} - 42 q^{31} + 24 q^{33} - 32 q^{36} - 2 q^{37} + 8 q^{39} - 36 q^{40} + 34 q^{42} - 12 q^{43} + 24 q^{45} - 16 q^{46} - 6 q^{49} + 12 q^{51} + 12 q^{52} + 66 q^{54} - 44 q^{57} + 20 q^{58} - 8 q^{60} + 36 q^{61} - 38 q^{63} - 168 q^{64} - 24 q^{66} + 42 q^{67} + 76 q^{70} + 28 q^{72} + 42 q^{73} - 48 q^{75} + 120 q^{78} - 22 q^{79} - 4 q^{81} - 68 q^{84} - 8 q^{85} - 30 q^{87} - 28 q^{88} + 38 q^{91} + 48 q^{94} - 102 q^{96} + 36 q^{99} + O(q^{100}) \)

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.s.a 861.s 21.g $106$ $6.875$ None \(0\) \(0\) \(0\) \(-5\) $\mathrm{SU}(2)[C_{6}]$
861.2.s.b 861.s 21.g $106$ $6.875$ None \(0\) \(0\) \(0\) \(-5\) $\mathrm{SU}(2)[C_{6}]$

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

\( S_{2}^{\mathrm{old}}(861, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 2}\)