Properties

Label 87.2.a
Level $87$
Weight $2$
Character orbit 87.a
Rep. character $\chi_{87}(1,\cdot)$
Character field $\Q$
Dimension $5$
Newform subspaces $2$
Sturm bound $20$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 87 = 3 \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 87.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(20\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(87))\).

Total New Old
Modular forms 12 5 7
Cusp forms 9 5 4
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.

\(3\)\(29\)FrickeDim.
\(+\)\(-\)\(-\)\(3\)
\(-\)\(+\)\(-\)\(2\)
Plus space\(+\)\(0\)
Minus space\(-\)\(5\)

Trace form

\( 5q + 3q^{2} - q^{3} + 5q^{4} + 2q^{5} - q^{6} + 3q^{8} + 5q^{9} + O(q^{10}) \) \( 5q + 3q^{2} - q^{3} + 5q^{4} + 2q^{5} - q^{6} + 3q^{8} + 5q^{9} - 10q^{10} - 4q^{11} - 7q^{12} + 2q^{13} - 12q^{14} + 2q^{15} - 7q^{16} + 10q^{17} + 3q^{18} - 12q^{19} - 22q^{20} - 8q^{21} - 6q^{22} + 4q^{23} - 3q^{24} + 19q^{25} - 2q^{26} - q^{27} + 10q^{28} + q^{29} + 2q^{30} - q^{32} + 12q^{33} + 4q^{34} - 4q^{35} + 5q^{36} + 14q^{37} + 20q^{38} - 6q^{39} - 22q^{40} + 2q^{41} - 2q^{42} + 4q^{43} - 8q^{44} + 2q^{45} + 12q^{46} - 16q^{47} + q^{48} + q^{49} + 45q^{50} + 2q^{51} + 8q^{52} + 26q^{53} - q^{54} - 16q^{55} + 24q^{56} - 8q^{57} + q^{58} - 20q^{59} + 10q^{60} - 2q^{61} - 20q^{62} - q^{64} + 20q^{66} - 4q^{67} + 26q^{68} - 8q^{69} - 20q^{70} - 20q^{71} + 3q^{72} + 10q^{73} - 18q^{74} - 15q^{75} + 12q^{76} - 16q^{77} + 20q^{78} - 32q^{79} - 26q^{80} + 5q^{81} - 30q^{82} - 20q^{83} - 16q^{84} - 36q^{85} + 32q^{86} - 5q^{87} - 8q^{88} + 2q^{89} - 10q^{90} - 8q^{91} + 12q^{92} - 12q^{93} - 2q^{94} - 32q^{95} - 17q^{96} + 10q^{97} - 9q^{98} - 4q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(87))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 3 29
87.2.a.a \(2\) \(0.695\) \(\Q(\sqrt{5}) \) None \(1\) \(2\) \(2\) \(-4\) \(-\) \(+\) \(q+\beta q^{2}+q^{3}+(-1+\beta )q^{4}+(2-2\beta )q^{5}+\cdots\)
87.2.a.b \(3\) \(0.695\) 3.3.229.1 None \(2\) \(-3\) \(0\) \(4\) \(+\) \(-\) \(q+(1+\beta _{2})q^{2}-q^{3}+(2+\beta _{1})q^{4}-2\beta _{1}q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(87))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(87)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(29))\)\(^{\oplus 2}\)