Properties

Label 731.2.m
Level 731
Weight 2
Character orbit m
Rep. character \(\chi_{731}(87,\cdot)\)
Character field \(\Q(\zeta_{8})\)
Dimension 248
Newforms 3
Sturm bound 132
Trace bound 1

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Defining parameters

Level: \( N \) = \( 731 = 17 \cdot 43 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 731.m (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 17 \)
Character field: \(\Q(\zeta_{8})\)
Newforms: \( 3 \)
Sturm bound: \(132\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(731, [\chi])\).

Total New Old
Modular forms 272 248 24
Cusp forms 256 248 8
Eisenstein series 16 0 16

Trace form

\( 248q - 16q^{6} + O(q^{10}) \) \( 248q - 16q^{6} - 16q^{10} + 16q^{14} + 8q^{15} - 224q^{16} - 8q^{17} + 32q^{18} - 24q^{19} + 16q^{20} - 32q^{22} - 20q^{23} - 24q^{24} - 8q^{25} - 16q^{26} + 48q^{28} - 32q^{33} + 64q^{34} - 64q^{35} + 64q^{36} - 40q^{37} + 16q^{39} + 96q^{40} + 16q^{41} + 8q^{42} + 48q^{44} - 64q^{45} - 80q^{46} + 80q^{48} + 16q^{49} - 64q^{51} - 48q^{52} + 4q^{53} - 72q^{54} + 120q^{56} - 32q^{57} - 64q^{58} + 16q^{59} - 48q^{60} - 16q^{61} - 88q^{62} + 40q^{63} + 40q^{65} - 120q^{66} + 16q^{67} + 96q^{69} - 8q^{70} + 40q^{73} + 16q^{74} + 72q^{75} - 32q^{76} + 56q^{77} - 48q^{78} - 16q^{79} - 88q^{80} + 104q^{82} - 104q^{83} - 16q^{84} + 24q^{85} - 40q^{86} + 72q^{88} + 16q^{90} + 80q^{91} - 32q^{92} - 152q^{93} - 16q^{94} + 72q^{95} + 120q^{96} - 16q^{97} - 48q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(731, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
731.2.m.a \(4\) \(5.837\) \(\Q(\zeta_{8})\) None \(-4\) \(-4\) \(-8\) \(-4\) \(q+(-1+\zeta_{8}^{2}+\zeta_{8}^{3})q^{2}+(-1-\zeta_{8}+\cdots)q^{3}+\cdots\)
731.2.m.b \(116\) \(5.837\) None \(0\) \(0\) \(0\) \(0\)
731.2.m.c \(128\) \(5.837\) None \(4\) \(4\) \(8\) \(4\)

Decomposition of \(S_{2}^{\mathrm{old}}(731, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(731, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(17, [\chi])\)\(^{\oplus 2}\)