Properties

Label 784.1.y
Level $784$
Weight $1$
Character orbit 784.y
Rep. character $\chi_{784}(117,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $4$
Newform subspaces $1$
Sturm bound $112$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 784 = 2^{4} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 784.y (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 112 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 1 \)
Sturm bound: \(112\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(784, [\chi])\).

Total New Old
Modular forms 36 20 16
Cusp forms 4 4 0
Eisenstein series 32 16 16

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

\( 4 q + 2 q^{4} + O(q^{10}) \) \( 4 q + 2 q^{4} + 2 q^{11} - 2 q^{16} - 2 q^{18} + 4 q^{22} - 4 q^{29} + 2 q^{37} + 4 q^{43} - 2 q^{44} - 4 q^{50} - 2 q^{53} + 2 q^{58} - 4 q^{64} - 2 q^{67} + 2 q^{72} - 2 q^{74} + 2 q^{81} + 2 q^{86} + 2 q^{88} - 4 q^{99} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(784, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
784.1.y.a 784.y 112.x $4$ $0.391$ \(\Q(\zeta_{12})\) $D_{4}$ \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}^{5}q^{2}-\zeta_{12}^{4}q^{4}-\zeta_{12}^{3}q^{8}+\cdots\)