Properties

Label 847.2.r
Level 847
Weight 2
Character orbit 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

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

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.r.a \(48\) \(6.763\) None \(-5\) \(6\) \(15\) \(10\)
847.2.r.b \(48\) \(6.763\) None \(0\) \(6\) \(0\) \(0\)
847.2.r.c \(48\) \(6.763\) None \(5\) \(-9\) \(-15\) \(5\)
847.2.r.d \(48\) \(6.763\) None \(5\) \(6\) \(15\) \(-10\)
847.2.r.e \(96\) \(6.763\) None \(0\) \(0\) \(0\) \(0\)
847.2.r.f \(224\) \(6.763\) None \(0\) \(0\) \(0\) \(0\)

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

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

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database