Properties

Label 1805.1.o
Level $1805$
Weight $1$
Character orbit 1805.o
Rep. character $\chi_{1805}(299,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $18$
Newform subspaces $2$
Sturm bound $190$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 1805 = 5 \cdot 19^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1805.o (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 95 \)
Character field: \(\Q(\zeta_{18})\)
Newform subspaces: \( 2 \)
Sturm bound: \(190\)
Trace bound: \(1\)

Dimensions

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

Total New Old
Modular forms 138 114 24
Cusp forms 18 18 0
Eisenstein series 120 96 24

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 18 0 0 0

Trace form

\( 18 q + O(q^{10}) \) \( 18 q + 6 q^{11} - 18 q^{20} - 12 q^{26} - 12 q^{30} - 24 q^{39} + 9 q^{45} - 9 q^{49} + 9 q^{64} + 24 q^{96} + O(q^{100}) \)

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

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1805.1.o.a $6$ $0.901$ \(\Q(\zeta_{18})\) $D_{2}$ \(\Q(\sqrt{-19}) \), \(\Q(\sqrt{-95}) \) \(\Q(\sqrt{5}) \) \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{18}^{2}q^{4}-\zeta_{18}^{7}q^{5}-\zeta_{18}^{8}q^{9}+\cdots\)
1805.1.o.b $12$ $0.901$ 12.0.\(\cdots\).2 $D_{4}$ \(\Q(\sqrt{-95}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{5}+\beta _{11})q^{2}+\beta _{5}q^{3}+(-\beta _{4}-\beta _{10}+\cdots)q^{4}+\cdots\)