Properties

Label 405.1.h
Level $405$
Weight $1$
Character orbit 405.h
Rep. character $\chi_{405}(134,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $4$
Newform subspaces $2$
Sturm bound $54$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 405 = 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 405.h (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 45 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(54\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(405, [\chi])\).

Total New Old
Modular forms 28 8 20
Cusp forms 4 4 0
Eisenstein series 24 4 20

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

\( 4 q + O(q^{10}) \) \( 4 q - 4 q^{10} + 2 q^{16} - 4 q^{19} - 2 q^{25} + 2 q^{31} - 2 q^{34} - 2 q^{40} + 4 q^{46} - 2 q^{49} + 2 q^{61} + 4 q^{64} + 2 q^{79} + 2 q^{85} + 4 q^{94} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(405, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
405.1.h.a 405.h 45.h $2$ $0.202$ \(\Q(\sqrt{-3}) \) $D_{3}$ \(\Q(\sqrt{-15}) \) None 135.1.d.a \(-1\) \(0\) \(1\) \(0\) \(q-\zeta_{6}q^{2}-\zeta_{6}^{2}q^{5}-q^{8}-q^{10}+\zeta_{6}q^{16}+\cdots\)
405.1.h.b 405.h 45.h $2$ $0.202$ \(\Q(\sqrt{-3}) \) $D_{3}$ \(\Q(\sqrt{-15}) \) None 135.1.d.a \(1\) \(0\) \(-1\) \(0\) \(q+\zeta_{6}q^{2}+\zeta_{6}^{2}q^{5}+q^{8}-q^{10}+\zeta_{6}q^{16}+\cdots\)