Properties

Label 731.2.a
Level 731
Weight 2
Character orbit a
Rep. character \(\chi_{731}(1,\cdot)\)
Character field \(\Q\)
Dimension 57
Newforms 6
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.a (trivial)
Character field: \(\Q\)
Newforms: \( 6 \)
Sturm bound: \(132\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(731))\).

Total New Old
Modular forms 68 57 11
Cusp forms 65 57 8
Eisenstein series 3 0 3

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(17\)\(43\)FrickeDim.
\(+\)\(+\)\(+\)\(9\)
\(+\)\(-\)\(-\)\(21\)
\(-\)\(+\)\(-\)\(19\)
\(-\)\(-\)\(+\)\(8\)
Plus space\(+\)\(17\)
Minus space\(-\)\(40\)

Trace form

\( 57q + 3q^{2} + 63q^{4} + 2q^{5} - 4q^{6} - 9q^{8} + 65q^{9} + O(q^{10}) \) \( 57q + 3q^{2} + 63q^{4} + 2q^{5} - 4q^{6} - 9q^{8} + 65q^{9} - 6q^{10} - 4q^{11} + 14q^{13} - 4q^{14} - 20q^{15} + 87q^{16} - 3q^{17} + 3q^{18} + 12q^{19} - 6q^{20} + 24q^{21} + 8q^{22} - 8q^{23} - 8q^{24} + 51q^{25} - 38q^{26} - 24q^{27} + 20q^{28} + 18q^{29} + 24q^{30} - 5q^{32} + 3q^{34} + 4q^{35} + 47q^{36} + 14q^{37} + 8q^{38} + 4q^{39} + 10q^{40} - 10q^{41} - 36q^{42} + q^{43} - 36q^{44} - 10q^{45} + 64q^{46} - 20q^{47} - 36q^{48} + 61q^{49} + 13q^{50} + 4q^{51} + 62q^{52} + 2q^{53} - 36q^{54} + 8q^{55} - 20q^{56} - 20q^{57} - 46q^{58} + 12q^{59} - 36q^{60} + 46q^{61} + 12q^{62} + 56q^{63} + 63q^{64} - 36q^{66} + 12q^{67} - 5q^{68} - 8q^{69} - 28q^{70} + 40q^{71} - 41q^{72} + 14q^{73} + 50q^{74} + 12q^{75} + 12q^{76} - 20q^{77} - 72q^{78} + 4q^{79} - 38q^{80} + 57q^{81} - 2q^{82} - 28q^{83} + 28q^{84} + 6q^{85} + 3q^{86} + 32q^{87} + 68q^{88} + 42q^{89} - 26q^{90} + 40q^{91} - 16q^{92} - 4q^{93} - 16q^{94} - 36q^{95} + 40q^{96} + 2q^{97} - 49q^{98} - 44q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(731))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 17 43
731.2.a.a \(1\) \(5.837\) \(\Q\) None \(1\) \(1\) \(-1\) \(0\) \(+\) \(+\) \(q+q^{2}+q^{3}-q^{4}-q^{5}+q^{6}-3q^{8}+\cdots\)
731.2.a.b \(2\) \(5.837\) \(\Q(\sqrt{17}) \) None \(-2\) \(1\) \(-1\) \(0\) \(+\) \(+\) \(q-q^{2}+(1-\beta )q^{3}-q^{4}+(-1+\beta )q^{5}+\cdots\)
731.2.a.c \(6\) \(5.837\) 6.6.2460365.1 None \(-1\) \(-3\) \(3\) \(-7\) \(+\) \(+\) \(q+(-\beta _{3}-\beta _{4})q^{2}+(-1+\beta _{4})q^{3}+(\beta _{4}+\cdots)q^{4}+\cdots\)
731.2.a.d \(8\) \(5.837\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(1\) \(-3\) \(-7\) \(-5\) \(-\) \(-\) \(q+\beta _{1}q^{2}+(\beta _{3}+\beta _{4})q^{3}+(\beta _{2}-\beta _{3})q^{4}+\cdots\)
731.2.a.e \(19\) \(5.837\) \(\mathbb{Q}[x]/(x^{19} - \cdots)\) None \(2\) \(5\) \(11\) \(7\) \(-\) \(+\) \(q+\beta _{1}q^{2}+\beta _{16}q^{3}+(1+\beta _{2})q^{4}+(1+\cdots)q^{5}+\cdots\)
731.2.a.f \(21\) \(5.837\) None \(2\) \(-1\) \(-3\) \(5\) \(+\) \(-\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(731))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(731)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(43))\)\(^{\oplus 2}\)