Properties

Label 287.2.a
Level 287
Weight 2
Character orbit a
Rep. character \(\chi_{287}(1,\cdot)\)
Character field \(\Q\)
Dimension 21
Newforms 6
Sturm bound 56
Trace bound 3

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Defining parameters

Level: \( N \) = \( 287 = 7 \cdot 41 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 287.a (trivial)
Character field: \(\Q\)
Newforms: \( 6 \)
Sturm bound: \(56\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(2\), \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(287))\).

Total New Old
Modular forms 30 21 9
Cusp forms 27 21 6
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.

\(7\)\(41\)FrickeDim.
\(+\)\(+\)\(+\)\(2\)
\(+\)\(-\)\(-\)\(9\)
\(-\)\(+\)\(-\)\(8\)
\(-\)\(-\)\(+\)\(2\)
Plus space\(+\)\(4\)
Minus space\(-\)\(17\)

Trace form

\( 21q + q^{2} + 17q^{4} + 2q^{5} + 4q^{6} - q^{7} + 9q^{8} + 25q^{9} + O(q^{10}) \) \( 21q + q^{2} + 17q^{4} + 2q^{5} + 4q^{6} - q^{7} + 9q^{8} + 25q^{9} + 10q^{10} - 4q^{11} + 12q^{12} + 14q^{13} - 3q^{14} - 16q^{15} + 13q^{16} + 14q^{17} - 7q^{18} - 22q^{20} - 4q^{23} - 24q^{24} + 39q^{25} - 18q^{26} + 12q^{27} - 7q^{28} + 2q^{29} - 28q^{30} - 24q^{31} + 29q^{32} + 16q^{33} - 2q^{34} - 2q^{35} + 5q^{36} + 10q^{37} - 28q^{38} + 12q^{39} - 6q^{40} + q^{41} + 12q^{42} + 36q^{43} - 36q^{44} - 22q^{45} - 40q^{46} - 28q^{48} + 21q^{49} - 29q^{50} + 12q^{51} + 66q^{52} - 18q^{53} - 44q^{54} + 16q^{55} - 15q^{56} - 4q^{57} - 18q^{58} + 24q^{59} - 116q^{60} + 2q^{61} - 16q^{62} - 5q^{63} + q^{64} - 32q^{65} - 80q^{66} - 4q^{67} - 22q^{68} - 52q^{69} - 10q^{70} - 44q^{71} - 41q^{72} + 54q^{73} + 8q^{74} - 8q^{75} - 4q^{77} - 30q^{78} - 20q^{79} - 70q^{80} + 37q^{81} + 3q^{82} - 4q^{83} - 2q^{84} + 20q^{85} + 32q^{86} + 20q^{87} + 36q^{88} - 38q^{89} + 30q^{90} + 2q^{91} + 42q^{92} + 32q^{93} + 4q^{94} - 48q^{96} + 30q^{97} + q^{98} - 24q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(287))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 7 41
287.2.a.a \(2\) \(2.292\) \(\Q(\sqrt{5}) \) None \(-1\) \(-3\) \(-1\) \(2\) \(-\) \(-\) \(q-\beta q^{2}+(-1-\beta )q^{3}+(-1+\beta )q^{4}+\cdots\)
287.2.a.b \(2\) \(2.292\) \(\Q(\sqrt{5}) \) None \(-1\) \(-1\) \(1\) \(-2\) \(+\) \(+\) \(q-\beta q^{2}+(-1+\beta )q^{3}+(-1+\beta )q^{4}+\cdots\)
287.2.a.c \(3\) \(2.292\) 3.3.257.1 None \(1\) \(-1\) \(6\) \(3\) \(-\) \(+\) \(q+\beta _{1}q^{2}+(-\beta _{1}+\beta _{2})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
287.2.a.d \(3\) \(2.292\) \(\Q(\zeta_{14})^+\) None \(4\) \(5\) \(2\) \(-3\) \(+\) \(-\) \(q+(1+\beta _{1})q^{2}+(2-\beta _{1})q^{3}+(1+2\beta _{1}+\cdots)q^{4}+\cdots\)
287.2.a.e \(5\) \(2.292\) 5.5.633117.1 None \(-1\) \(4\) \(-5\) \(5\) \(-\) \(+\) \(q-\beta _{1}q^{2}+(1-\beta _{1})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
287.2.a.f \(6\) \(2.292\) 6.6.185257757.1 None \(-1\) \(-4\) \(-1\) \(-6\) \(+\) \(-\) \(q-\beta _{1}q^{2}+(-1+\beta _{2})q^{3}+(1+\beta _{2}+\beta _{3}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(287))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(287)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(41))\)\(^{\oplus 2}\)