Properties

Label 847.2.m
Level 847
Weight 2
Character orbit 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

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

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
847.2.m.a \(320\) \(6.763\) None \(-1\) \(-20\) \(4\) \(32\)
847.2.m.b \(340\) \(6.763\) None \(-3\) \(16\) \(-4\) \(-34\)

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

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

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database