Properties

Label 185.2.n
Level $185$
Weight $2$
Character orbit 185.n
Rep. character $\chi_{185}(84,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $36$
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.n (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 185 \)
Character field: \(\Q(\zeta_{6})\)
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 44 44 0
Cusp forms 36 36 0
Eisenstein series 8 8 0

Trace form

\( 36q + 16q^{4} - 2q^{5} - 16q^{6} + 14q^{9} + O(q^{10}) \) \( 36q + 16q^{4} - 2q^{5} - 16q^{6} + 14q^{9} - 12q^{10} + 12q^{11} - 8q^{14} - 10q^{15} - 16q^{16} - 8q^{19} + 22q^{20} - 26q^{21} - 42q^{24} + 12q^{26} - 16q^{29} + 18q^{34} - 16q^{35} + 32q^{36} - 2q^{39} - 42q^{40} + 2q^{41} - 10q^{44} - 56q^{45} + 52q^{46} + 10q^{49} + 34q^{50} - 28q^{51} - 42q^{54} + 4q^{55} + 18q^{56} - 28q^{59} + 44q^{60} + 20q^{61} + 36q^{64} + 10q^{65} - 148q^{66} + 70q^{69} - 10q^{70} - 46q^{71} + 56q^{74} + 32q^{75} + 24q^{76} + 2q^{79} + 132q^{80} - 2q^{81} - 168q^{84} - 28q^{85} - 22q^{86} + 8q^{89} - 28q^{90} - 48q^{91} + 32q^{94} - 10q^{95} + 106q^{96} + 64q^{99} + O(q^{100}) \)

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
185.2.n.a \(36\) \(1.477\) None \(0\) \(0\) \(-2\) \(0\)