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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

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

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
840.1.bp.a 840.bp 840.ap $4$ $0.419$ \(\Q(\zeta_{8})\) $D_{4}$ \(\Q(\sqrt{-6}) \) 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 840.bp 840.ap $4$ $0.419$ \(\Q(\zeta_{8})\) $D_{4}$ \(\Q(\sqrt{-6}) \) 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 840.bp 840.ap $8$ $0.419$ \(\Q(\zeta_{16})\) $D_{8}$ \(\Q(\sqrt{-14}) \) 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 840.bp 840.ap $8$ $0.419$ \(\Q(\zeta_{16})\) $D_{8}$ \(\Q(\sqrt{-14}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{16}^{2}q^{2}+\zeta_{16}^{3}q^{3}+\zeta_{16}^{4}q^{4}+\cdots\)