Properties

Label 185.2.d
Level $185$
Weight $2$
Character orbit 185.d
Rep. character $\chi_{185}(184,\cdot)$
Character field $\Q$
Dimension $16$
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.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 185 \)
Character field: \(\Q\)
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 20 20 0
Cusp forms 16 16 0
Eisenstein series 4 4 0

Trace form

\( 16q + 8q^{4} - 16q^{9} + O(q^{10}) \) \( 16q + 8q^{4} - 16q^{9} - 12q^{10} - 8q^{16} + 24q^{21} - 12q^{25} - 4q^{30} + 8q^{34} - 8q^{36} - 16q^{40} + 24q^{46} - 16q^{49} - 88q^{64} + 12q^{65} + 44q^{70} - 24q^{71} + 48q^{74} + 12q^{75} - 56q^{81} + 80q^{84} + 60q^{85} - 72q^{86} + 12q^{95} + 24q^{99} + O(q^{100}) \)

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.d.a \(16\) \(1.477\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{7}q^{2}-\beta _{9}q^{3}+(1-\beta _{2})q^{4}-\beta _{1}q^{5}+\cdots\)