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Properties

Label 847.2.r
Level $847$
Weight $2$
Character orbit 847.r
Rep. character $\chi_{847}(40,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $512$
Newform subspaces $6$
Sturm bound $176$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 847 = 7 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 847.r (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 77 \)
Character field: \(\Q(\zeta_{30})\)
Newform subspaces: \( 6 \)
Sturm bound: \(176\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(847, [\chi])\).

Total New Old
Modular forms 800 640 160
Cusp forms 608 512 96
Eisenstein series 192 128 64

Trace form

\( 512 q + 5 q^{2} + 9 q^{3} - 51 q^{4} + 15 q^{5} + 5 q^{7} - 39 q^{9} + O(q^{10}) \) \( 512 q + 5 q^{2} + 9 q^{3} - 51 q^{4} + 15 q^{5} + 5 q^{7} - 39 q^{9} - 108 q^{12} + 16 q^{14} + 71 q^{16} - 15 q^{17} - 20 q^{18} + 15 q^{19} - 50 q^{23} - 75 q^{24} - 31 q^{25} + 33 q^{26} + 40 q^{28} + 40 q^{29} - 25 q^{30} - 9 q^{31} - 5 q^{35} + 18 q^{36} - 3 q^{37} - 63 q^{38} + 45 q^{39} - 75 q^{40} - 16 q^{42} - 36 q^{45} + 20 q^{46} - 9 q^{47} - 65 q^{49} - 30 q^{50} - 55 q^{51} + 15 q^{52} + 5 q^{53} - 96 q^{56} - 60 q^{57} - 62 q^{58} + 27 q^{59} + 67 q^{60} + 30 q^{61} + 40 q^{63} - 20 q^{64} - 108 q^{67} + 75 q^{68} + 47 q^{70} - 36 q^{71} + 60 q^{72} + 60 q^{73} - 45 q^{74} + 33 q^{75} - 364 q^{78} + 70 q^{79} + 99 q^{80} + 11 q^{81} + 153 q^{82} + 125 q^{84} - 10 q^{85} + 50 q^{86} - 102 q^{89} - 60 q^{91} + 30 q^{92} + 64 q^{93} - 105 q^{94} - 30 q^{95} - 75 q^{96} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(847, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
847.2.r.a 847.r 77.n $48$ $6.763$ None \(-5\) \(6\) \(15\) \(10\) $\mathrm{SU}(2)[C_{30}]$
847.2.r.b 847.r 77.n $48$ $6.763$ None \(0\) \(6\) \(0\) \(0\) $\mathrm{SU}(2)[C_{30}]$
847.2.r.c 847.r 77.n $48$ $6.763$ None \(5\) \(-9\) \(-15\) \(5\) $\mathrm{SU}(2)[C_{30}]$
847.2.r.d 847.r 77.n $48$ $6.763$ None \(5\) \(6\) \(15\) \(-10\) $\mathrm{SU}(2)[C_{30}]$
847.2.r.e 847.r 77.n $96$ $6.763$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{30}]$
847.2.r.f 847.r 77.n $224$ $6.763$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{30}]$

Decomposition of \(S_{2}^{\mathrm{old}}(847, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(847, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(77, [\chi])\)\(^{\oplus 2}\)