Properties

Label 731.2.d
Level 731
Weight 2
Character orbit d
Rep. character \(\chi_{731}(560,\cdot)\)
Character field \(\Q\)
Dimension 64
Newforms 4
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.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 17 \)
Character field: \(\Q\)
Newforms: \( 4 \)
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 68 64 4
Cusp forms 64 64 0
Eisenstein series 4 0 4

Trace form

\( 64q - 2q^{2} + 58q^{4} - 6q^{8} - 76q^{9} + O(q^{10}) \) \( 64q - 2q^{2} + 58q^{4} - 6q^{8} - 76q^{9} - 10q^{13} + 12q^{15} + 62q^{16} + 7q^{17} - 2q^{18} + 20q^{19} + 8q^{21} - 60q^{25} - 16q^{26} + 16q^{30} + 6q^{32} + 20q^{33} - 36q^{34} + 4q^{35} - 78q^{36} + 4q^{38} + 12q^{42} - 4q^{43} - 12q^{47} - 52q^{49} - 10q^{50} + 26q^{51} - 52q^{52} - 6q^{53} - 24q^{59} + 12q^{60} + 30q^{64} - 20q^{66} - 22q^{67} + 52q^{68} - 12q^{69} + 100q^{70} - 46q^{72} + 16q^{76} + 4q^{77} + 104q^{81} - 18q^{83} + 28q^{84} + 12q^{85} + 10q^{86} + 40q^{87} - 36q^{89} + 24q^{93} - 96q^{94} + 30q^{98} + O(q^{100}) \)

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.d.a \(2\) \(5.837\) \(\Q(\sqrt{-2}) \) None \(2\) \(0\) \(0\) \(0\) \(q+q^{2}-q^{4}+\beta q^{5}-3q^{8}+3q^{9}+\beta q^{10}+\cdots\)
731.2.d.b \(8\) \(5.837\) \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{3}-2q^{4}-\beta _{3}q^{5}+(\beta _{1}-\beta _{7})q^{7}+\cdots\)
731.2.d.c \(20\) \(5.837\) \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None \(2\) \(0\) \(0\) \(0\) \(q+\beta _{6}q^{2}+\beta _{13}q^{3}+(2+\beta _{1})q^{4}+\beta _{10}q^{5}+\cdots\)
731.2.d.d \(34\) \(5.837\) None \(-6\) \(0\) \(0\) \(0\)