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Properties

Label 87.4.a
Level $87$
Weight $4$
Character orbit 87.a
Rep. character $\chi_{87}(1,\cdot)$
Character field $\Q$
Dimension $14$
Newform subspaces $4$
Sturm bound $40$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 87 = 3 \cdot 29 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 87.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(40\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(87))\).

Total New Old
Modular forms 32 14 18
Cusp forms 28 14 14
Eisenstein series 4 0 4

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
\(+\)\(+\)\(+\)\(5\)
\(+\)\(-\)\(-\)\(2\)
\(-\)\(+\)\(-\)\(2\)
\(-\)\(-\)\(+\)\(5\)
Plus space\(+\)\(10\)
Minus space\(-\)\(4\)

Trace form

\( 14 q + 68 q^{4} + 16 q^{5} - 12 q^{6} - 40 q^{7} + 84 q^{8} + 126 q^{9} + O(q^{10}) \) \( 14 q + 68 q^{4} + 16 q^{5} - 12 q^{6} - 40 q^{7} + 84 q^{8} + 126 q^{9} + 64 q^{10} + 40 q^{11} + 44 q^{13} + 60 q^{14} + 60 q^{15} + 228 q^{16} - 160 q^{17} - 16 q^{19} + 208 q^{20} + 314 q^{22} + 8 q^{23} - 234 q^{24} + 198 q^{25} - 652 q^{26} - 1114 q^{28} - 456 q^{30} - 196 q^{31} + 952 q^{32} - 558 q^{34} - 872 q^{35} + 612 q^{36} - 376 q^{37} - 464 q^{38} - 24 q^{39} + 44 q^{40} + 928 q^{41} + 426 q^{42} + 1024 q^{43} - 916 q^{44} + 144 q^{45} - 852 q^{46} + 376 q^{47} - 96 q^{48} + 1722 q^{49} - 2304 q^{50} - 408 q^{51} - 1598 q^{52} + 88 q^{53} - 108 q^{54} + 432 q^{55} - 1392 q^{56} - 612 q^{57} + 116 q^{58} + 1292 q^{59} - 600 q^{60} + 56 q^{61} - 616 q^{62} - 360 q^{63} - 542 q^{64} + 1872 q^{65} - 744 q^{66} - 1148 q^{67} + 1420 q^{68} + 984 q^{69} + 2300 q^{70} + 1544 q^{71} + 756 q^{72} + 116 q^{73} + 1488 q^{74} - 480 q^{75} - 3688 q^{76} + 4720 q^{77} - 210 q^{78} + 916 q^{79} + 2612 q^{80} + 1134 q^{81} + 460 q^{82} - 100 q^{83} + 2184 q^{84} + 3952 q^{85} - 1580 q^{86} + 522 q^{87} + 2864 q^{88} - 8 q^{89} + 576 q^{90} - 3012 q^{91} - 1044 q^{92} - 60 q^{93} + 5942 q^{94} - 5008 q^{95} - 2364 q^{96} - 236 q^{97} + 5364 q^{98} + 360 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(87))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 3 29
87.4.a.a 87.a 1.a $2$ $5.133$ \(\Q(\sqrt{17}) \) None 87.4.a.a \(-5\) \(6\) \(-11\) \(-24\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(-2-\beta )q^{2}+3q^{3}+5\beta q^{4}+(-4+\cdots)q^{5}+\cdots\)
87.4.a.b 87.a 1.a $2$ $5.133$ \(\Q(\sqrt{41}) \) None 87.4.a.b \(-1\) \(-6\) \(-1\) \(-24\) $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta q^{2}-3q^{3}+(2+\beta )q^{4}+(-2+3\beta )q^{5}+\cdots\)
87.4.a.c 87.a 1.a $5$ $5.133$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None 87.4.a.c \(3\) \(-15\) \(-1\) \(4\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}-3q^{3}+(6-2\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
87.4.a.d 87.a 1.a $5$ $5.133$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None 87.4.a.d \(3\) \(15\) \(29\) \(4\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+3q^{3}+(6+\beta _{2}+\beta _{3}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(87))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(87)) \simeq \) \(S_{4}^{\mathrm{new}}(\Gamma_0(29))\)\(^{\oplus 2}\)