Properties

Label 1805.1.h
Level $1805$
Weight $1$
Character orbit 1805.h
Rep. character $\chi_{1805}(69,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $6$
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.h (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 95 \)
Character field: \(\Q(\zeta_{6})\)
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 46 38 8
Cusp forms 6 6 0
Eisenstein series 40 32 8

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 6 0 0 0

Trace form

\( 6 q - q^{4} + q^{5} + 4 q^{6} - q^{9} + O(q^{10}) \) \( 6 q - q^{4} + q^{5} + 4 q^{6} - q^{9} - 4 q^{11} + q^{16} - 6 q^{20} - 3 q^{25} + 8 q^{26} + 8 q^{30} - 3 q^{36} - 8 q^{39} - 2 q^{44} - 6 q^{45} + 6 q^{49} + 2 q^{55} + 2 q^{61} - 6 q^{64} + 4 q^{74} - 3 q^{80} + q^{81} + 8 q^{96} - 2 q^{99} + O(q^{100}) \)

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.h.a 1805.h 95.h $2$ $0.901$ \(\Q(\sqrt{-3}) \) $D_{2}$ \(\Q(\sqrt{-19}) \), \(\Q(\sqrt{-95}) \) \(\Q(\sqrt{5}) \) 95.1.d.a \(0\) \(0\) \(-1\) \(0\) \(q+\zeta_{6}q^{4}+\zeta_{6}^{2}q^{5}+\zeta_{6}q^{9}-q^{11}+\cdots\)
1805.1.h.b 1805.h 95.h $4$ $0.901$ \(\Q(\sqrt{2}, \sqrt{-3})\) $D_{4}$ \(\Q(\sqrt{-95}) \) None 95.1.d.b \(0\) \(0\) \(2\) \(0\) \(q-\beta _{1}q^{2}+\beta _{1}q^{3}+\beta _{2}q^{4}+(1+\beta _{2}+\cdots)q^{5}+\cdots\)