Properties

Label 1620.1.p
Level $1620$
Weight $1$
Character orbit 1620.p
Rep. character $\chi_{1620}(379,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $20$
Newform subspaces $5$
Sturm bound $324$
Trace bound $13$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1620 = 2^{2} \cdot 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1620.p (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 180 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 5 \)
Sturm bound: \(324\)
Trace bound: \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1620, [\chi])\).

Total New Old
Modular forms 88 28 60
Cusp forms 40 20 20
Eisenstein series 48 8 40

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 20 0 0 0

Trace form

\( 20 q + 4 q^{4} + O(q^{10}) \) \( 20 q + 4 q^{4} + 4 q^{10} - 4 q^{16} + 4 q^{25} - 2 q^{34} - 4 q^{40} - 12 q^{46} + 10 q^{49} - 4 q^{61} - 20 q^{64} + 6 q^{76} - 2 q^{85} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1620, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1620.1.p.a \(4\) \(0.808\) \(\Q(\zeta_{12})\) \(D_{6}\) \(\Q(\sqrt{-15}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}^{3}q^{2}-q^{4}+\zeta_{12}^{5}q^{5}+\zeta_{12}^{3}q^{8}+\cdots\)
1620.1.p.b \(4\) \(0.808\) \(\Q(\zeta_{12})\) \(D_{2}\) \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-15}) \) \(\Q(\sqrt{15}) \) \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+\zeta_{12}^{5}q^{5}+\zeta_{12}^{3}q^{8}+\cdots\)
1620.1.p.c \(4\) \(0.808\) \(\Q(\zeta_{12})\) \(D_{6}\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}-\zeta_{12}q^{5}-\zeta_{12}^{3}q^{8}+\cdots\)
1620.1.p.d \(4\) \(0.808\) \(\Q(\zeta_{12})\) \(D_{6}\) \(\Q(\sqrt{-15}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}^{5}q^{2}-\zeta_{12}^{4}q^{4}+\zeta_{12}^{5}q^{5}+\cdots\)
1620.1.p.e \(4\) \(0.808\) \(\Q(\zeta_{12})\) \(D_{6}\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}-\zeta_{12}^{3}q^{5}+\zeta_{12}^{3}q^{8}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(1620, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(1620, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(540, [\chi])\)\(^{\oplus 2}\)