Properties

Label 720.1.r
Level $720$
Weight $1$
Character orbit 720.r
Rep. character $\chi_{720}(19,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $4$
Newform subspaces $1$
Sturm bound $144$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 720 = 2^{4} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 720.r (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 80 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 1 \)
Sturm bound: \(144\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(720, [\chi])\).

Total New Old
Modular forms 20 8 12
Cusp forms 4 4 0
Eisenstein series 16 4 12

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

\( 4q + O(q^{10}) \) \( 4q - 4q^{10} - 4q^{16} + 4q^{19} - 4q^{34} + 4q^{46} + 4q^{49} - 4q^{61} - 4q^{76} - 4q^{85} + 4q^{94} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(720, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
720.1.r.a \(4\) \(0.359\) \(\Q(\zeta_{8})\) \(D_{4}\) \(\Q(\sqrt{-15}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}-\zeta_{8}^{3}q^{5}-\zeta_{8}^{3}q^{8}+\cdots\)