Properties

Label 186.2.p
Level $186$
Weight $2$
Character orbit 186.p
Rep. character $\chi_{186}(11,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $80$
Newform subspaces $1$
Sturm bound $64$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 186 = 2 \cdot 3 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 186.p (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 93 \)
Character field: \(\Q(\zeta_{30})\)
Newform subspaces: \( 1 \)
Sturm bound: \(64\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(186, [\chi])\).

Total New Old
Modular forms 288 80 208
Cusp forms 224 80 144
Eisenstein series 64 0 64

Trace form

\( 80q + 20q^{4} + 8q^{7} + 4q^{9} + O(q^{10}) \) \( 80q + 20q^{4} + 8q^{7} + 4q^{9} - 4q^{10} - 10q^{15} - 20q^{16} - 8q^{18} - 4q^{19} + 30q^{21} - 2q^{22} + 12q^{25} - 38q^{28} - 86q^{31} - 28q^{34} - 4q^{36} - 144q^{37} - 16q^{39} - 6q^{40} - 6q^{42} + 40q^{43} - 24q^{45} - 20q^{46} + 10q^{48} - 14q^{49} - 92q^{51} - 92q^{55} - 96q^{57} + 20q^{58} - 10q^{60} + 88q^{63} + 20q^{64} + 12q^{66} + 40q^{67} - 60q^{69} + 24q^{70} + 8q^{72} + 56q^{73} - 30q^{75} - 36q^{76} + 32q^{78} + 32q^{79} + 128q^{81} + 36q^{82} + 10q^{84} + 100q^{85} + 34q^{87} + 42q^{88} + 34q^{90} + 60q^{91} + 172q^{93} + 24q^{94} - 4q^{97} + 150q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(186, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
186.2.p.a \(80\) \(1.485\) None \(0\) \(0\) \(0\) \(8\)

Decomposition of \(S_{2}^{\mathrm{old}}(186, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(186, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(93, [\chi])\)\(^{\oplus 2}\)