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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

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

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 3 29
87.2.a.a 87.a 1.a $2$ $0.695$ \(\Q(\sqrt{5}) \) None \(1\) \(2\) \(2\) \(-4\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+q^{3}+(-1+\beta )q^{4}+(2-2\beta )q^{5}+\cdots\)
87.2.a.b 87.a 1.a $3$ $0.695$ 3.3.229.1 None \(2\) \(-3\) \(0\) \(4\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta _{2})q^{2}-q^{3}+(2+\beta _{1})q^{4}-2\beta _{1}q^{5}+\cdots\)

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

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