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Properties

Label 861.2.i
Level $861$
Weight $2$
Character orbit 861.i
Rep. character $\chi_{861}(247,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $108$
Newform subspaces $7$
Sturm bound $224$
Trace bound $2$

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Defining parameters

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

Dimensions

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

Total New Old
Modular forms 232 108 124
Cusp forms 216 108 108
Eisenstein series 16 0 16

Trace form

\( 108 q + 4 q^{2} + 2 q^{3} - 52 q^{4} - 4 q^{5} - 8 q^{6} + 10 q^{7} - 24 q^{8} - 54 q^{9} + O(q^{10}) \) \( 108 q + 4 q^{2} + 2 q^{3} - 52 q^{4} - 4 q^{5} - 8 q^{6} + 10 q^{7} - 24 q^{8} - 54 q^{9} - 4 q^{10} + 4 q^{11} + 4 q^{12} - 4 q^{13} - 24 q^{14} + 8 q^{15} - 64 q^{16} + 4 q^{18} + 10 q^{19} + 64 q^{20} - 8 q^{21} + 8 q^{22} - 8 q^{23} + 12 q^{24} - 74 q^{25} + 32 q^{26} - 4 q^{27} - 60 q^{28} - 16 q^{29} - 16 q^{30} + 2 q^{31} + 28 q^{32} - 12 q^{33} + 32 q^{34} - 12 q^{35} + 104 q^{36} + 18 q^{37} - 24 q^{38} + 2 q^{39} + 20 q^{40} + 4 q^{42} + 12 q^{43} + 16 q^{44} - 4 q^{45} + 32 q^{46} - 4 q^{47} + 16 q^{48} + 42 q^{49} + 48 q^{50} - 24 q^{52} - 8 q^{53} + 4 q^{54} - 56 q^{55} + 60 q^{56} + 12 q^{57} + 12 q^{58} - 48 q^{59} + 12 q^{60} - 20 q^{61} - 176 q^{62} - 2 q^{63} + 48 q^{64} + 16 q^{65} + 30 q^{67} + 8 q^{68} - 32 q^{69} - 16 q^{71} + 12 q^{72} - 10 q^{73} + 48 q^{74} + 14 q^{75} - 40 q^{76} + 76 q^{77} - 16 q^{78} + 10 q^{79} - 108 q^{80} - 54 q^{81} + 8 q^{82} - 16 q^{83} - 52 q^{84} + 112 q^{85} + 80 q^{86} - 16 q^{87} + 68 q^{88} - 16 q^{89} + 8 q^{90} - 2 q^{91} - 8 q^{92} - 6 q^{93} + 8 q^{94} - 20 q^{95} + 28 q^{96} - 64 q^{97} - 64 q^{98} - 8 q^{99} + O(q^{100}) \)

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.i.a 861.i 7.c $2$ $6.875$ \(\Q(\sqrt{-3}) \) None \(-2\) \(-1\) \(0\) \(5\) $\mathrm{SU}(2)[C_{3}]$ \(q-2\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-2+2\zeta_{6})q^{4}+\cdots\)
861.2.i.b 861.i 7.c $6$ $6.875$ 6.0.16638075.1 None \(-1\) \(3\) \(3\) \(-12\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{1}q^{2}+(1+\beta _{4})q^{3}+(-2-\beta _{3}-2\beta _{4}+\cdots)q^{4}+\cdots\)
861.2.i.c 861.i 7.c $6$ $6.875$ 6.0.7873200.1 None \(0\) \(3\) \(0\) \(3\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{2}q^{3}+2\beta _{2}q^{4}+(-\beta _{4}+\beta _{5})q^{5}+\cdots\)
861.2.i.d 861.i 7.c $16$ $6.875$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(-1\) \(8\) \(7\) \(9\) $\mathrm{SU}(2)[C_{3}]$ \(q+(\beta _{1}-\beta _{3}-\beta _{5}+\beta _{10})q^{2}+\beta _{10}q^{3}+\cdots\)
861.2.i.e 861.i 7.c $24$ $6.875$ None \(2\) \(-12\) \(-12\) \(0\) $\mathrm{SU}(2)[C_{3}]$
861.2.i.f 861.i 7.c $26$ $6.875$ None \(4\) \(-13\) \(8\) \(5\) $\mathrm{SU}(2)[C_{3}]$
861.2.i.g 861.i 7.c $28$ $6.875$ None \(2\) \(14\) \(-10\) \(0\) $\mathrm{SU}(2)[C_{3}]$

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

\( S_{2}^{\mathrm{old}}(861, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(287, [\chi])\)\(^{\oplus 2}\)