Properties

Label 184.1.e
Level $184$
Weight $1$
Character orbit 184.e
Rep. character $\chi_{184}(45,\cdot)$
Character field $\Q$
Dimension $3$
Newform subspaces $2$
Sturm bound $24$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 184 = 2^{3} \cdot 23 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 184.e (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 184 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(24\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(184, [\chi])\).

Total New Old
Modular forms 5 5 0
Cusp forms 3 3 0
Eisenstein series 2 2 0

The following table gives the dimensions of subspaces with specified projective image type.

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 3 0 0 0

Trace form

\( 3 q + 3 q^{6} - 3 q^{8} - 3 q^{9} + O(q^{10}) \) \( 3 q + 3 q^{6} - 3 q^{8} - 3 q^{9} + 3 q^{12} - 3 q^{18} - 3 q^{23} - 3 q^{25} - 3 q^{26} + 3 q^{36} + 6 q^{39} - 3 q^{48} + 3 q^{49} - 3 q^{52} - 3 q^{54} + 3 q^{58} + 3 q^{62} + 3 q^{64} + 3 q^{72} + 3 q^{78} + 3 q^{81} + 3 q^{82} - 6 q^{87} - 3 q^{94} - 3 q^{96} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(184, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
184.1.e.a 184.e 184.e $1$ $0.092$ \(\Q\) $D_{2}$ \(\Q(\sqrt{-23}) \), \(\Q(\sqrt{-46}) \) \(\Q(\sqrt{2}) \) \(-1\) \(0\) \(0\) \(0\) \(q-q^{2}+q^{4}-q^{8}+q^{9}+q^{16}-q^{18}+\cdots\)
184.1.e.b 184.e 184.e $2$ $0.092$ \(\Q(\sqrt{-3}) \) $D_{6}$ \(\Q(\sqrt{-23}) \) None \(1\) \(0\) \(0\) \(0\) \(q-\zeta_{6}^{2}q^{2}+(\zeta_{6}+\zeta_{6}^{2})q^{3}-\zeta_{6}q^{4}+\cdots\)