Properties

Label 840.1.bp
Level $840$
Weight $1$
Character orbit 840.bp
Rep. character $\chi_{840}(293,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $24$
Newform subspaces $4$
Sturm bound $192$
Trace bound $14$

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Defining parameters

Level: \( N \) \(=\) \( 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 840.bp (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 840 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 4 \)
Sturm bound: \(192\)
Trace bound: \(14\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(840, [\chi])\).

Total New Old
Modular forms 40 40 0
Cusp forms 24 24 0
Eisenstein series 16 16 0

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 24 0 0 0

Trace form

\( 24q - 4q^{7} + O(q^{10}) \) \( 24q - 4q^{7} + 8q^{15} - 24q^{16} + 8q^{18} - 8q^{22} + 4q^{28} - 8q^{36} + 4q^{42} + 8q^{57} - 8q^{58} - 8q^{60} - 4q^{63} + 4q^{70} - 8q^{72} - 8q^{78} - 8q^{81} + 8q^{88} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(840, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
840.1.bp.a \(4\) \(0.419\) \(\Q(\zeta_{8})\) \(D_{4}\) \(\Q(\sqrt{-6}) \) None \(0\) \(0\) \(0\) \(-4\) \(q-\zeta_{8}^{3}q^{2}+\zeta_{8}^{3}q^{3}-\zeta_{8}^{2}q^{4}-\zeta_{8}q^{5}+\cdots\)
840.1.bp.b \(4\) \(0.419\) \(\Q(\zeta_{8})\) \(D_{4}\) \(\Q(\sqrt{-6}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}^{3}q^{2}-\zeta_{8}^{3}q^{3}-\zeta_{8}^{2}q^{4}+\zeta_{8}q^{5}+\cdots\)
840.1.bp.c \(8\) \(0.419\) \(\Q(\zeta_{16})\) \(D_{8}\) \(\Q(\sqrt{-14}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{16}^{2}q^{2}+\zeta_{16}^{5}q^{3}+\zeta_{16}^{4}q^{4}+\cdots\)
840.1.bp.d \(8\) \(0.419\) \(\Q(\zeta_{16})\) \(D_{8}\) \(\Q(\sqrt{-14}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{16}^{2}q^{2}+\zeta_{16}^{3}q^{3}+\zeta_{16}^{4}q^{4}+\cdots\)