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

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

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

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