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Properties

Label 840.1.dh
Level $840$
Weight $1$
Character orbit 840.dh
Rep. character $\chi_{840}(173,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $16$
Newform subspaces $2$
Sturm bound $192$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 840.dh (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 840 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 2 \)
Sturm bound: \(192\)
Trace bound: \(7\)

Dimensions

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

Total New Old
Modular forms 48 48 0
Cusp forms 16 16 0
Eisenstein series 32 32 0

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 16 0 0 0

Trace form

\( 16 q + 4 q^{7} + O(q^{10}) \) \( 16 q + 4 q^{7} - 12 q^{10} - 8 q^{15} + 8 q^{16} + 8 q^{22} - 4 q^{28} - 12 q^{33} - 16 q^{36} - 4 q^{42} - 4 q^{58} + 8 q^{63} - 4 q^{70} + 8 q^{81} + 12 q^{87} + 4 q^{88} + O(q^{100}) \)

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.dh.a 840.dh 840.ch $8$ $0.419$ \(\Q(\zeta_{24})\) $D_{12}$ \(\Q(\sqrt{-6}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{5}q^{2}+\zeta_{24}q^{3}+\zeta_{24}^{10}q^{4}+\cdots\)
840.1.dh.b 840.dh 840.ch $8$ $0.419$ \(\Q(\zeta_{24})\) $D_{12}$ \(\Q(\sqrt{-6}) \) None \(0\) \(0\) \(0\) \(4\) \(q+\zeta_{24}^{5}q^{2}+\zeta_{24}q^{3}+\zeta_{24}^{10}q^{4}+\cdots\)