Properties

Label 187.2.e
Level $187$
Weight $2$
Character orbit 187.e
Rep. character $\chi_{187}(89,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $32$
Newform subspaces $2$
Sturm bound $36$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 187 = 11 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 187.e (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 17 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 2 \)
Sturm bound: \(36\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

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

Total New Old
Modular forms 40 32 8
Cusp forms 32 32 0
Eisenstein series 8 0 8

Trace form

\( 32 q - 36 q^{4} - 8 q^{5} + 8 q^{6} + O(q^{10}) \) \( 32 q - 36 q^{4} - 8 q^{5} + 8 q^{6} + 4 q^{10} - 20 q^{12} - 12 q^{14} + 28 q^{16} - 12 q^{17} - 20 q^{18} + 12 q^{20} + 24 q^{21} - 4 q^{23} + 12 q^{24} + 12 q^{27} - 52 q^{28} + 12 q^{29} + 24 q^{30} - 24 q^{31} + 8 q^{33} + 16 q^{34} - 32 q^{35} - 20 q^{37} - 40 q^{38} - 8 q^{39} - 20 q^{40} + 16 q^{41} + 8 q^{44} + 48 q^{45} + 36 q^{46} - 4 q^{47} + 60 q^{48} + 36 q^{50} + 56 q^{51} - 16 q^{55} + 64 q^{56} - 32 q^{57} - 64 q^{58} - 8 q^{61} + 52 q^{62} + 20 q^{63} + 20 q^{64} - 48 q^{65} - 12 q^{67} - 32 q^{68} - 64 q^{69} + 28 q^{71} + 20 q^{72} + 20 q^{73} + 68 q^{74} + 4 q^{78} + 16 q^{79} - 48 q^{80} - 80 q^{81} - 12 q^{82} - 168 q^{84} + 24 q^{85} + 8 q^{86} + 12 q^{89} - 104 q^{90} + 8 q^{91} + 68 q^{92} - 36 q^{95} - 140 q^{96} - 16 q^{97} + 116 q^{98} + O(q^{100}) \)

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.e.a 187.e 17.c $4$ $1.493$ \(\Q(\zeta_{8})\) None \(0\) \(-4\) \(8\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+2\zeta_{8}^{2}q^{2}+(-1+2\zeta_{8}-\zeta_{8}^{2})q^{3}+\cdots\)
187.2.e.b 187.e 17.c $28$ $1.493$ None \(0\) \(4\) \(-16\) \(0\) $\mathrm{SU}(2)[C_{4}]$