Properties

Label 185.2.p
Level $185$
Weight $2$
Character orbit 185.p
Rep. character $\chi_{185}(82,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $68$
Newform subspaces $1$
Sturm bound $38$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 185 = 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 185.p (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 185 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 1 \)
Sturm bound: \(38\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(185, [\chi])\).

Total New Old
Modular forms 84 84 0
Cusp forms 68 68 0
Eisenstein series 16 16 0

Trace form

\( 68 q - 4 q^{2} - 8 q^{3} - 30 q^{4} - 10 q^{5} - 8 q^{6} - 2 q^{7} + 12 q^{8} + O(q^{10}) \) \( 68 q - 4 q^{2} - 8 q^{3} - 30 q^{4} - 10 q^{5} - 8 q^{6} - 2 q^{7} + 12 q^{8} - 6 q^{10} + 14 q^{12} - 6 q^{13} - 8 q^{15} - 26 q^{16} + 12 q^{17} + 18 q^{18} + 4 q^{19} + 48 q^{20} - 12 q^{21} + 6 q^{22} - 12 q^{23} + 10 q^{25} - 24 q^{26} - 68 q^{27} - 26 q^{28} + 14 q^{29} + 10 q^{30} - 24 q^{31} - 16 q^{32} - 2 q^{33} - 10 q^{35} - 16 q^{37} - 36 q^{38} + 52 q^{39} + 42 q^{40} - 18 q^{41} + 132 q^{42} + 8 q^{43} - 36 q^{44} - 32 q^{45} - 52 q^{46} - 24 q^{47} - 60 q^{48} - 36 q^{49} - 8 q^{50} - 8 q^{51} - 26 q^{52} + 82 q^{53} + 40 q^{54} + 18 q^{55} + 16 q^{56} - 6 q^{57} + 86 q^{58} - 8 q^{59} + 36 q^{60} + 4 q^{61} + 10 q^{62} - 48 q^{63} - 20 q^{64} + 8 q^{65} + 80 q^{66} - 40 q^{67} + 8 q^{69} - 82 q^{70} + 4 q^{71} - 90 q^{72} - 60 q^{73} - 44 q^{74} + 64 q^{75} + 72 q^{76} + 66 q^{77} - 24 q^{78} + 56 q^{79} + 34 q^{80} - 6 q^{81} + 24 q^{83} - 20 q^{85} - 4 q^{86} - 84 q^{87} - 22 q^{89} - 50 q^{90} + 44 q^{91} + 44 q^{92} - 34 q^{93} - 20 q^{94} - 28 q^{95} - 8 q^{96} + 42 q^{98} + 32 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(185, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
185.2.p.a 185.p 185.p $68$ $1.477$ None \(-4\) \(-8\) \(-10\) \(-2\) $\mathrm{SU}(2)[C_{12}]$