Properties

Label 1620.1.f
Level $1620$
Weight $1$
Character orbit 1620.f
Rep. character $\chi_{1620}(1459,\cdot)$
Character field $\Q$
Dimension $8$
Newform subspaces $5$
Sturm bound $324$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 1620 = 2^{2} \cdot 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1620.f (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 20 \)
Character field: \(\Q\)
Newform subspaces: \( 5 \)
Sturm bound: \(324\)
Trace bound: \(5\)

Dimensions

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

Total New Old
Modular forms 46 16 30
Cusp forms 22 8 14
Eisenstein series 24 8 16

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 8 0 0 0

Trace form

\( 8q + O(q^{10}) \) \( 8q + 2q^{10} + 8q^{16} + 6q^{25} - 4q^{34} - 2q^{40} - 4q^{46} - 4q^{49} - 4q^{70} + 2q^{85} - 4q^{94} + O(q^{100}) \)

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.f.a \(1\) \(0.808\) \(\Q\) \(D_{3}\) \(\Q(\sqrt{-5}) \) None \(-1\) \(0\) \(-1\) \(-1\) \(q-q^{2}+q^{4}-q^{5}-q^{7}-q^{8}+q^{10}+\cdots\)
1620.1.f.b \(1\) \(0.808\) \(\Q\) \(D_{3}\) \(\Q(\sqrt{-5}) \) None \(-1\) \(0\) \(1\) \(1\) \(q-q^{2}+q^{4}+q^{5}+q^{7}-q^{8}-q^{10}+\cdots\)
1620.1.f.c \(1\) \(0.808\) \(\Q\) \(D_{3}\) \(\Q(\sqrt{-5}) \) None \(1\) \(0\) \(-1\) \(1\) \(q+q^{2}+q^{4}-q^{5}+q^{7}+q^{8}-q^{10}+\cdots\)
1620.1.f.d \(1\) \(0.808\) \(\Q\) \(D_{3}\) \(\Q(\sqrt{-5}) \) None \(1\) \(0\) \(1\) \(-1\) \(q+q^{2}+q^{4}+q^{5}-q^{7}+q^{8}+q^{10}+\cdots\)
1620.1.f.e \(4\) \(0.808\) \(\Q(\zeta_{12})\) \(D_{6}\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}^{3}q^{2}-q^{4}-\zeta_{12}q^{5}-\zeta_{12}^{3}q^{8}+\cdots\)

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

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