Properties

Label 187.2.t
Level $187$
Weight $2$
Character orbit 187.t
Rep. character $\chi_{187}(6,\cdot)$
Character field $\Q(\zeta_{80})$
Dimension $512$
Newform subspaces $1$
Sturm bound $36$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 187 = 11 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 187.t (of order \(80\) and degree \(32\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 187 \)
Character field: \(\Q(\zeta_{80})\)
Newform subspaces: \( 1 \)
Sturm bound: \(36\)
Trace bound: \(0\)

Dimensions

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

Total New Old
Modular forms 640 640 0
Cusp forms 512 512 0
Eisenstein series 128 128 0

Trace form

\( 512 q - 40 q^{2} - 24 q^{3} - 24 q^{4} - 24 q^{5} - 40 q^{6} - 40 q^{7} - 40 q^{8} - 24 q^{9} + O(q^{10}) \) \( 512 q - 40 q^{2} - 24 q^{3} - 24 q^{4} - 24 q^{5} - 40 q^{6} - 40 q^{7} - 40 q^{8} - 24 q^{9} - 40 q^{11} - 16 q^{12} - 56 q^{14} - 24 q^{15} - 40 q^{17} - 80 q^{18} - 40 q^{19} - 24 q^{20} - 48 q^{22} - 48 q^{23} + 80 q^{24} - 40 q^{25} - 56 q^{26} + 48 q^{27} - 40 q^{28} - 40 q^{29} - 40 q^{30} + 40 q^{31} - 64 q^{34} - 80 q^{35} - 56 q^{36} - 56 q^{37} + 80 q^{38} - 40 q^{39} - 40 q^{40} + 80 q^{41} + 72 q^{42} + 32 q^{44} - 64 q^{45} - 40 q^{46} - 24 q^{47} - 72 q^{48} - 88 q^{49} - 40 q^{51} + 240 q^{52} - 24 q^{53} + 128 q^{55} - 64 q^{56} - 40 q^{57} + 88 q^{58} - 88 q^{59} - 152 q^{60} - 40 q^{61} - 40 q^{62} + 80 q^{63} - 88 q^{64} + 408 q^{66} - 40 q^{68} + 192 q^{69} - 168 q^{70} - 24 q^{71} - 40 q^{72} - 40 q^{73} - 40 q^{74} - 88 q^{75} + 192 q^{77} - 64 q^{78} - 40 q^{79} + 248 q^{80} - 40 q^{81} - 24 q^{82} - 40 q^{85} - 112 q^{86} + 128 q^{88} - 64 q^{89} - 40 q^{90} + 56 q^{91} + 136 q^{92} - 88 q^{93} + 440 q^{94} - 40 q^{95} - 40 q^{96} - 88 q^{97} + 72 q^{99} + O(q^{100}) \)

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.t.a 187.t 187.t $512$ $1.493$ None \(-40\) \(-24\) \(-24\) \(-40\) $\mathrm{SU}(2)[C_{80}]$