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Properties

Label 185.2.b
Level $185$
Weight $2$
Character orbit 185.b
Rep. character $\chi_{185}(149,\cdot)$
Character field $\Q$
Dimension $18$
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.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
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 22 18 4
Cusp forms 18 18 0
Eisenstein series 4 0 4

Trace form

\( 18 q - 22 q^{4} + 2 q^{5} + 4 q^{6} - 26 q^{9} + 6 q^{10} + 8 q^{14} - 2 q^{15} + 22 q^{16} + 8 q^{19} - 4 q^{20} + 8 q^{21} - 12 q^{24} - 18 q^{25} - 12 q^{26} + 4 q^{29} - 12 q^{31} - 12 q^{34} - 2 q^{35}+ \cdots - 16 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
185.2.b.a 185.b 5.b $18$ $1.477$ \(\mathbb{Q}[x]/(x^{18} + \cdots)\) None 185.2.b.a \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\beta _{1}+\beta _{13})q^{2}+(\beta _{12}-\beta _{13})q^{3}+(-2+\cdots)q^{4}+\cdots\)