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Properties

Label 187.2.g
Level $187$
Weight $2$
Character orbit 187.g
Rep. character $\chi_{187}(69,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $64$
Newform subspaces $6$
Sturm bound $36$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 187 = 11 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 187.g (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 11 \)
Character field: \(\Q(\zeta_{5})\)
Newform subspaces: \( 6 \)
Sturm bound: \(36\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\), \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(187, [\chi])\).

Total New Old
Modular forms 80 64 16
Cusp forms 64 64 0
Eisenstein series 16 0 16

Trace form

\( 64 q - 4 q^{2} - 2 q^{3} - 20 q^{4} - 2 q^{5} - 4 q^{6} - 12 q^{7} + 8 q^{8} - 18 q^{9} + O(q^{10}) \) \( 64 q - 4 q^{2} - 2 q^{3} - 20 q^{4} - 2 q^{5} - 4 q^{6} - 12 q^{7} + 8 q^{8} - 18 q^{9} - 8 q^{10} - 8 q^{11} + 16 q^{12} - 4 q^{13} + 18 q^{14} - 2 q^{15} - 4 q^{17} + 22 q^{18} - 12 q^{19} + 22 q^{20} - 8 q^{21} - 34 q^{22} + 16 q^{23} - 44 q^{24} - 40 q^{25} - 2 q^{26} - 26 q^{27} + 58 q^{28} - 10 q^{29} + 28 q^{30} + 2 q^{31} - 28 q^{32} + 4 q^{33} + 10 q^{35} - 16 q^{36} + 6 q^{37} + 12 q^{38} - 18 q^{39} - 44 q^{40} + 8 q^{41} + 38 q^{42} - 24 q^{43} - 4 q^{44} + 36 q^{45} + 6 q^{46} - 24 q^{47} + 74 q^{48} - 6 q^{49} - 56 q^{50} - 8 q^{51} + 48 q^{52} + 12 q^{53} + 68 q^{54} - 66 q^{55} - 36 q^{56} + 8 q^{57} - 10 q^{58} - 14 q^{59} + 32 q^{60} + 12 q^{61} - 80 q^{62} - 44 q^{63} + 28 q^{65} - 44 q^{66} - 24 q^{67} - 12 q^{68} + 18 q^{69} + 28 q^{70} + 18 q^{71} - 18 q^{72} + 58 q^{73} + 16 q^{74} + 16 q^{75} - 124 q^{76} - 14 q^{77} + 40 q^{78} + 8 q^{79} - 12 q^{80} - 4 q^{81} + 76 q^{82} + 44 q^{83} - 88 q^{84} - 8 q^{85} + 44 q^{86} - 28 q^{87} + 110 q^{88} + 8 q^{89} + 120 q^{90} - 38 q^{91} + 58 q^{92} - 44 q^{93} - 36 q^{94} + 56 q^{95} + 180 q^{96} - 54 q^{97} - 160 q^{98} + 66 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(187, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
187.2.g.a 187.g 11.c $4$ $1.493$ \(\Q(\zeta_{10})\) None \(-2\) \(-5\) \(-5\) \(-8\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-\zeta_{10}+\zeta_{10}^{2})q^{2}+(-2\zeta_{10}+\zeta_{10}^{2}+\cdots)q^{3}+\cdots\)
187.2.g.b 187.g 11.c $4$ $1.493$ \(\Q(\zeta_{10})\) None \(2\) \(-4\) \(-1\) \(-8\) $\mathrm{SU}(2)[C_{5}]$ \(q+(\zeta_{10}-\zeta_{10}^{2})q^{2}+(-\zeta_{10}+2\zeta_{10}^{2}+\cdots)q^{3}+\cdots\)
187.2.g.c 187.g 11.c $4$ $1.493$ \(\Q(\zeta_{10})\) None \(5\) \(-1\) \(2\) \(-2\) $\mathrm{SU}(2)[C_{5}]$ \(q+(1+\zeta_{10}-\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+(-\zeta_{10}+\cdots)q^{3}+\cdots\)
187.2.g.d 187.g 11.c $8$ $1.493$ 8.0.324000000.3 None \(-4\) \(6\) \(4\) \(2\) $\mathrm{SU}(2)[C_{5}]$ \(q+(\beta _{2}+\beta _{4})q^{2}+(-\beta _{1}-\beta _{2}-\beta _{3}-\beta _{4}+\cdots)q^{3}+\cdots\)
187.2.g.e 187.g 11.c $8$ $1.493$ 8.0.13140625.1 None \(-1\) \(3\) \(-3\) \(3\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-\beta _{1}+\beta _{5})q^{2}+(-\beta _{2}+\beta _{3}-\beta _{4}+\cdots)q^{3}+\cdots\)
187.2.g.f 187.g 11.c $36$ $1.493$ None \(-4\) \(-1\) \(1\) \(1\) $\mathrm{SU}(2)[C_{5}]$