Properties

Label 1620.1.l
Level $1620$
Weight $1$
Character orbit 1620.l
Rep. character $\chi_{1620}(973,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $4$
Newform subspaces $2$
Sturm bound $324$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 1620 = 2^{2} \cdot 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1620.l (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 2 \)
Sturm bound: \(324\)
Trace bound: \(11\)

Dimensions

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

Total New Old
Modular forms 76 4 72
Cusp forms 4 4 0
Eisenstein series 72 0 72

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 0 0 4 0

Trace form

\( 4q - 4q^{7} + O(q^{10}) \) \( 4q - 4q^{7} - 4q^{25} + 4q^{31} - 4q^{67} + 4q^{73} - 4q^{85} + O(q^{100}) \)

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.l.a \(2\) \(0.808\) \(\Q(\sqrt{-1}) \) \(S_{4}\) None None \(0\) \(0\) \(0\) \(-2\) \(q+iq^{5}+(-1+i)q^{7}-q^{11}+(-1+\cdots)q^{17}+\cdots\)
1620.1.l.b \(2\) \(0.808\) \(\Q(\sqrt{-1}) \) \(S_{4}\) None None \(0\) \(0\) \(0\) \(-2\) \(q-iq^{5}+(-1+i)q^{7}+q^{11}+(1-i+\cdots)q^{17}+\cdots\)