Properties

Label 847.2.n
Level $847$
Weight $2$
Character orbit 847.n
Rep. character $\chi_{847}(9,\cdot)$
Character field $\Q(\zeta_{15})$
Dimension $512$
Newform subspaces $14$
Sturm bound $176$
Trace bound $6$

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Defining parameters

Level: \( N \) \(=\) \( 847 = 7 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 847.n (of order \(15\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 77 \)
Character field: \(\Q(\zeta_{15})\)
Newform subspaces: \( 14 \)
Sturm bound: \(176\)
Trace bound: \(6\)
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

\( 512q + 5q^{2} + 3q^{3} + 61q^{4} + q^{5} + 12q^{6} + 7q^{7} + 28q^{8} + 45q^{9} + O(q^{10}) \) \( 512q + 5q^{2} + 3q^{3} + 61q^{4} + q^{5} + 12q^{6} + 7q^{7} + 28q^{8} + 45q^{9} - 4q^{10} - 24q^{12} + 4q^{13} - 8q^{14} + 24q^{15} + 35q^{16} + 11q^{17} - 18q^{18} + 7q^{19} + 48q^{20} + 18q^{21} - 42q^{23} + 7q^{24} + 9q^{25} + 43q^{26} + 6q^{27} - 4q^{28} - 24q^{29} - 21q^{30} + 9q^{31} + 12q^{32} - 296q^{34} + 19q^{35} - 42q^{36} - 15q^{37} - 13q^{38} - 33q^{39} - 5q^{40} - 62q^{41} + 32q^{42} + 44q^{43} - 24q^{45} - 16q^{46} - 21q^{47} - 226q^{48} + 15q^{49} - 6q^{50} + q^{51} + 3q^{52} - 23q^{53} - 44q^{54} - 144q^{56} - 20q^{57} + 46q^{58} - 7q^{59} + 95q^{60} - 18q^{61} + 80q^{62} - 22q^{63} - 108q^{64} + 10q^{65} + 76q^{67} + 21q^{68} + 134q^{69} - 37q^{70} + 12q^{71} + 48q^{72} - 26q^{73} + 55q^{74} - 57q^{75} + 144q^{76} + 60q^{78} - 30q^{79} - 105q^{80} + 55q^{81} - 13q^{82} + 28q^{83} + 27q^{84} + 98q^{85} + 4q^{86} - 66q^{87} + 2q^{89} + 18q^{90} + 52q^{91} + 74q^{92} + 24q^{93} - 45q^{94} - 22q^{95} + 55q^{96} + 4q^{97} - 120q^{98} + O(q^{100}) \)

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.n.a \(8\) \(6.763\) \(\Q(\zeta_{15})\) None \(-3\) \(1\) \(5\) \(5\) \(q+(-1-\zeta_{15}^{5}+\zeta_{15}^{7})q^{2}+(-1+\zeta_{15}+\cdots)q^{3}+\cdots\)
847.2.n.b \(8\) \(6.763\) \(\Q(\zeta_{15})\) None \(2\) \(1\) \(-5\) \(5\) \(q+(1-\zeta_{15}+\zeta_{15}^{5}-\zeta_{15}^{7})q^{2}+(-1+\cdots)q^{3}+\cdots\)
847.2.n.c \(8\) \(6.763\) \(\Q(\zeta_{15})\) None \(3\) \(1\) \(5\) \(-5\) \(q+(1+\zeta_{15}^{5}-\zeta_{15}^{7})q^{2}+(-1+\zeta_{15}+\cdots)q^{3}+\cdots\)
847.2.n.d \(24\) \(6.763\) None \(0\) \(-1\) \(-2\) \(2\)
847.2.n.e \(24\) \(6.763\) None \(0\) \(-1\) \(-2\) \(-2\)
847.2.n.f \(24\) \(6.763\) None \(0\) \(3\) \(6\) \(0\)
847.2.n.g \(24\) \(6.763\) None \(0\) \(3\) \(6\) \(0\)
847.2.n.h \(40\) \(6.763\) None \(-2\) \(1\) \(-6\) \(-13\)
847.2.n.i \(40\) \(6.763\) None \(2\) \(1\) \(-6\) \(13\)
847.2.n.j \(40\) \(6.763\) None \(3\) \(-4\) \(4\) \(2\)
847.2.n.k \(48\) \(6.763\) None \(0\) \(-2\) \(-4\) \(0\)
847.2.n.l \(56\) \(6.763\) None \(0\) \(3\) \(4\) \(2\)
847.2.n.m \(56\) \(6.763\) None \(0\) \(3\) \(4\) \(-2\)
847.2.n.n \(112\) \(6.763\) None \(0\) \(-6\) \(-8\) \(0\)

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

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