Properties

Label 186.2.f
Level $186$
Weight $2$
Character orbit 186.f
Rep. character $\chi_{186}(97,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $16$
Newform subspaces $3$
Sturm bound $64$
Trace bound $3$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 186 = 2 \cdot 3 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 186.f (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 31 \)
Character field: \(\Q(\zeta_{5})\)
Newform subspaces: \( 3 \)
Sturm bound: \(64\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(5\)

Dimensions

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

Total New Old
Modular forms 144 16 128
Cusp forms 112 16 96
Eisenstein series 32 0 32

Trace form

\( 16 q + 2 q^{3} - 4 q^{4} - 8 q^{6} - 2 q^{7} - 4 q^{9} + O(q^{10}) \) \( 16 q + 2 q^{3} - 4 q^{4} - 8 q^{6} - 2 q^{7} - 4 q^{9} + 4 q^{10} - 12 q^{11} + 2 q^{12} - 4 q^{13} - 12 q^{14} + 4 q^{15} - 4 q^{16} - 4 q^{17} + 12 q^{19} - 14 q^{21} + 14 q^{22} + 12 q^{23} + 2 q^{24} + 12 q^{25} - 32 q^{26} + 2 q^{27} - 2 q^{28} - 8 q^{30} - 8 q^{31} - 8 q^{33} - 4 q^{34} + 32 q^{35} + 16 q^{36} + 36 q^{37} - 22 q^{39} - 6 q^{40} - 4 q^{41} - 2 q^{42} + 34 q^{43} + 8 q^{44} + 20 q^{46} + 16 q^{47} + 2 q^{48} - 26 q^{49} - 8 q^{50} - 4 q^{51} - 4 q^{52} - 20 q^{53} + 2 q^{54} - 4 q^{55} + 8 q^{56} + 4 q^{57} + 12 q^{58} - 32 q^{59} + 4 q^{60} - 52 q^{61} + 32 q^{62} + 8 q^{63} - 4 q^{64} - 4 q^{65} - 4 q^{66} + 28 q^{67} + 16 q^{68} + 16 q^{70} - 8 q^{71} - 24 q^{73} + 4 q^{74} - 10 q^{75} - 18 q^{76} - 48 q^{77} - 12 q^{78} + 2 q^{79} - 4 q^{81} + 20 q^{82} + 56 q^{83} + 16 q^{84} - 44 q^{85} - 24 q^{86} + 36 q^{87} - 36 q^{88} - 16 q^{89} + 4 q^{90} - 46 q^{91} + 32 q^{92} + 10 q^{93} + 24 q^{94} + 4 q^{95} + 2 q^{96} - 18 q^{97} + 32 q^{98} + 8 q^{99} + O(q^{100}) \)

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.f.a 186.f 31.d $4$ $1.485$ \(\Q(\zeta_{10})\) None \(1\) \(-1\) \(2\) \(7\) $\mathrm{SU}(2)[C_{5}]$ \(q+\zeta_{10}q^{2}+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{3}+\cdots\)
186.2.f.b 186.f 31.d $4$ $1.485$ \(\Q(\zeta_{10})\) None \(1\) \(1\) \(-4\) \(-2\) $\mathrm{SU}(2)[C_{5}]$ \(q+\zeta_{10}q^{2}+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{3}+\cdots\)
186.2.f.c 186.f 31.d $8$ $1.485$ 8.0.9240015625.1 None \(-2\) \(2\) \(2\) \(-7\) $\mathrm{SU}(2)[C_{5}]$ \(q-\beta _{3}q^{2}+\beta _{5}q^{3}+\beta _{4}q^{4}+(1+\beta _{2}+\cdots)q^{5}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(186, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(31, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(62, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(93, [\chi])\)\(^{\oplus 2}\)