Properties

Label 693.1.h
Level $693$
Weight $1$
Character orbit 693.h
Rep. character $\chi_{693}(692,\cdot)$
Character field $\Q$
Dimension $4$
Newform subspaces $1$
Sturm bound $96$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 693 = 3^{2} \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 693.h (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 231 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(96\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(693, [\chi])\).

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

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

\( 4 q + 4 q^{4} + O(q^{10}) \) \( 4 q + 4 q^{4} - 4 q^{16} + 4 q^{22} - 4 q^{25} - 4 q^{49} - 8 q^{58} - 4 q^{64} + 8 q^{67} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(693, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
693.1.h.a 693.h 231.h $4$ $0.346$ \(\Q(\zeta_{8})\) $D_{4}$ \(\Q(\sqrt{-7}) \) None 693.1.h.a \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{8}-\zeta_{8}^{3})q^{2}+q^{4}+\zeta_{8}^{2}q^{7}-\zeta_{8}^{3}q^{11}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(693, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(693, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(231, [\chi])\)\(^{\oplus 2}\)