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Properties

Label 186.2.h
Level $186$
Weight $2$
Character orbit 186.h
Rep. character $\chi_{186}(119,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $20$
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.h (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 93 \)
Character field: \(\Q(\zeta_{6})\)
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 72 20 52
Cusp forms 56 20 36
Eisenstein series 16 0 16

Trace form

\( 20 q - 20 q^{4} + 2 q^{7} - 4 q^{9} + O(q^{10}) \) \( 20 q - 20 q^{4} + 2 q^{7} - 4 q^{9} + 4 q^{10} + 20 q^{16} + 8 q^{18} + 4 q^{19} - 30 q^{21} - 18 q^{22} + 18 q^{25} - 2 q^{28} - 14 q^{31} - 12 q^{34} + 4 q^{36} - 36 q^{37} + 16 q^{39} - 4 q^{40} + 6 q^{42} + 34 q^{45} + 4 q^{49} - 8 q^{51} + 72 q^{55} + 6 q^{57} - 28 q^{63} - 20 q^{64} + 8 q^{66} - 40 q^{67} - 20 q^{69} - 24 q^{70} - 8 q^{72} - 36 q^{73} - 60 q^{75} - 4 q^{76} + 68 q^{78} - 12 q^{79} + 12 q^{81} + 4 q^{82} + 30 q^{84} - 34 q^{87} + 18 q^{88} - 4 q^{90} + 38 q^{93} + 16 q^{94} + 124 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
186.2.h.a 186.h 93.g $20$ $1.485$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(0\) \(0\) \(0\) \(2\) $\mathrm{SU}(2)[C_{6}]$ \(q-\beta _{6}q^{2}+(-\beta _{9}-\beta _{14})q^{3}-q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)

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

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