Properties

Label 1805.1.m
Level $1805$
Weight $1$
Character orbit 1805.m
Rep. character $\chi_{1805}(68,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $4$
Newform subspaces $1$
Sturm bound $190$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 1805 = 5 \cdot 19^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1805.m (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 95 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 1 \)
Sturm bound: \(190\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1805, [\chi])\).

Total New Old
Modular forms 84 68 16
Cusp forms 4 4 0
Eisenstein series 80 64 16

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 4 0 0 0

Trace form

\( 4 q + 2 q^{5} + 4 q^{7} + O(q^{10}) \) \( 4 q + 2 q^{5} + 4 q^{7} + 2 q^{16} - 2 q^{17} + 2 q^{23} - 2 q^{25} - 2 q^{28} + 2 q^{35} - 2 q^{36} - 2 q^{43} - 2 q^{47} + 2 q^{63} + 4 q^{68} - 2 q^{73} - 2 q^{80} + 2 q^{81} + 4 q^{83} + 2 q^{85} - 2 q^{92} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1805, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1805.1.m.a 1805.m 95.m $4$ $0.901$ \(\Q(\zeta_{12})\) $D_{4}$ \(\Q(\sqrt{-19}) \) None 1805.1.f.a \(0\) \(0\) \(2\) \(4\) \(q-\zeta_{12}^{5}q^{4}-\zeta_{12}^{4}q^{5}+(1-\zeta_{12}^{3}+\cdots)q^{7}+\cdots\)