Properties

Label 87.2.g
Level $87$
Weight $2$
Character orbit 87.g
Rep. character $\chi_{87}(7,\cdot)$
Character field $\Q(\zeta_{7})$
Dimension $36$
Newform subspaces $2$
Sturm bound $20$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 87 = 3 \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 87.g (of order \(7\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 29 \)
Character field: \(\Q(\zeta_{7})\)
Newform subspaces: \( 2 \)
Sturm bound: \(20\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(87, [\chi])\).

Total New Old
Modular forms 72 36 36
Cusp forms 48 36 12
Eisenstein series 24 0 24

Trace form

\( 36q - 6q^{2} - 12q^{4} - 8q^{5} - 2q^{6} - 8q^{7} - 18q^{8} - 6q^{9} + O(q^{10}) \) \( 36q - 6q^{2} - 12q^{4} - 8q^{5} - 2q^{6} - 8q^{7} - 18q^{8} - 6q^{9} - 8q^{10} + 20q^{11} - 2q^{13} - 12q^{14} + 6q^{15} + 4q^{16} - 28q^{17} - 6q^{18} - 8q^{19} + 50q^{20} + 12q^{22} - 14q^{23} - 12q^{24} + 20q^{25} + 2q^{26} + 32q^{28} - 2q^{29} + 8q^{30} - 4q^{31} + 64q^{32} - 24q^{33} - 16q^{34} + 40q^{35} - 12q^{36} + 4q^{37} - 52q^{38} - 8q^{39} - 26q^{40} - 44q^{41} - 22q^{42} - 34q^{43} - 62q^{44} + 20q^{45} - 56q^{46} + 24q^{47} + 24q^{48} - 30q^{49} + 16q^{50} + 22q^{51} + 76q^{52} + 4q^{53} - 2q^{54} - 14q^{55} + 52q^{56} + 16q^{57} + 24q^{58} - 12q^{59} + 74q^{60} - 4q^{61} + 148q^{62} + 6q^{63} - 98q^{64} + 28q^{65} + 84q^{66} - 8q^{67} + 30q^{68} + 12q^{69} + 16q^{70} + 18q^{71} - 4q^{72} + 42q^{73} - 82q^{74} - 16q^{75} - 26q^{76} - 10q^{77} - 62q^{78} - 6q^{79} - 160q^{80} - 6q^{81} + 30q^{82} - 8q^{83} - 40q^{84} - 2q^{85} - 24q^{86} + 32q^{87} - 4q^{88} - 78q^{89} - 8q^{90} - 62q^{91} - 110q^{92} - 20q^{93} - 16q^{94} - 88q^{95} + 24q^{96} - 38q^{97} + 20q^{98} - 8q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(87, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
87.2.g.a \(18\) \(0.695\) \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(-4\) \(-3\) \(-1\) \(-4\) \(q+(-\beta _{3}+\beta _{9})q^{2}-\beta _{10}q^{3}+(2\beta _{1}+\beta _{5}+\cdots)q^{4}+\cdots\)
87.2.g.b \(18\) \(0.695\) \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(-2\) \(3\) \(-7\) \(-4\) \(q-\beta _{3}q^{2}+\beta _{14}q^{3}+(-\beta _{10}-\beta _{16}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(87, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(87, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(29, [\chi])\)\(^{\oplus 2}\)