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Properties

Label 847.2.m
Level $847$
Weight $2$
Character orbit 847.m
Rep. character $\chi_{847}(78,\cdot)$
Character field $\Q(\zeta_{11})$
Dimension $660$
Newform subspaces $2$
Sturm bound $176$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 847 = 7 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 847.m (of order \(11\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 121 \)
Character field: \(\Q(\zeta_{11})\)
Newform subspaces: \( 2 \)
Sturm bound: \(176\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

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

Total New Old
Modular forms 900 660 240
Cusp forms 860 660 200
Eisenstein series 40 0 40

Trace form

\( 660 q - 4 q^{2} - 4 q^{3} - 68 q^{4} - 4 q^{6} - 2 q^{7} - 12 q^{8} + 644 q^{9} + O(q^{10}) \) \( 660 q - 4 q^{2} - 4 q^{3} - 68 q^{4} - 4 q^{6} - 2 q^{7} - 12 q^{8} + 644 q^{9} - 16 q^{10} - 8 q^{11} + 38 q^{12} + 54 q^{13} - 2 q^{14} + 10 q^{15} - 96 q^{16} - 16 q^{17} - 20 q^{18} - 20 q^{19} - 20 q^{20} - 8 q^{21} + 10 q^{22} + 14 q^{23} + 132 q^{24} - 82 q^{25} - 52 q^{26} - 28 q^{27} - 14 q^{28} - 36 q^{29} - 88 q^{30} + 16 q^{31} - 68 q^{32} - 46 q^{33} - 48 q^{34} - 8 q^{35} - 152 q^{36} - 24 q^{37} + 56 q^{38} - 64 q^{39} - 96 q^{40} - 32 q^{41} - 72 q^{43} - 63 q^{44} - 24 q^{45} - 88 q^{46} - 44 q^{47} - 92 q^{48} - 66 q^{49} + 172 q^{50} + 166 q^{51} + 60 q^{52} - 24 q^{53} - 96 q^{54} + 110 q^{55} + 59 q^{56} + 70 q^{57} + 55 q^{58} - 56 q^{59} - 108 q^{60} - 40 q^{61} - 6 q^{62} - 10 q^{63} - 30 q^{64} + 2 q^{65} - 122 q^{66} - 26 q^{67} - 124 q^{68} - 52 q^{69} + 36 q^{70} + 44 q^{71} - 172 q^{72} - 28 q^{73} - 88 q^{74} - 116 q^{75} + 148 q^{76} - 8 q^{77} + 64 q^{78} + 4 q^{79} + 170 q^{80} + 548 q^{81} - 12 q^{82} - 112 q^{83} - 28 q^{84} + 26 q^{85} - 112 q^{86} - 60 q^{87} + 58 q^{88} - 48 q^{89} - 96 q^{90} + 54 q^{91} - 124 q^{92} - 100 q^{93} + 52 q^{94} - 36 q^{95} - 292 q^{96} - 72 q^{97} + 7 q^{98} - 134 q^{99} + O(q^{100}) \)

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.m.a 847.m 121.e $320$ $6.763$ None \(-1\) \(-20\) \(4\) \(32\) $\mathrm{SU}(2)[C_{11}]$
847.2.m.b 847.m 121.e $340$ $6.763$ None \(-3\) \(16\) \(-4\) \(-34\) $\mathrm{SU}(2)[C_{11}]$

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

\( S_{2}^{\mathrm{old}}(847, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(121, [\chi])\)\(^{\oplus 2}\)