Properties

Label 712.1.w
Level $712$
Weight $1$
Character orbit 712.w
Rep. character $\chi_{712}(11,\cdot)$
Character field $\Q(\zeta_{22})$
Dimension $10$
Newform subspaces $1$
Sturm bound $90$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 712 = 2^{3} \cdot 89 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 712.w (of order \(22\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 712 \)
Character field: \(\Q(\zeta_{22})\)
Newform subspaces: \( 1 \)
Sturm bound: \(90\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(712, [\chi])\).

Total New Old
Modular forms 30 30 0
Cusp forms 10 10 0
Eisenstein series 20 20 0

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 10 0 0 0

Trace form

\( 10 q - q^{2} - q^{4} - q^{8} - q^{9} + O(q^{10}) \) \( 10 q - q^{2} - q^{4} - q^{8} - q^{9} - 9 q^{11} - q^{16} - 9 q^{17} - q^{18} + 2 q^{22} - q^{25} + 11 q^{27} - q^{32} + 2 q^{34} - q^{36} + 11 q^{38} + 2 q^{44} + q^{49} - q^{50} - 11 q^{54} - q^{64} + 2 q^{67} - 9 q^{68} + 10 q^{72} + 2 q^{73} - q^{81} + 2 q^{88} - q^{89} - 2 q^{97} + q^{98} - 9 q^{99} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(712, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
712.1.w.a 712.w 712.w $10$ $0.355$ \(\Q(\zeta_{22})\) $D_{22}$ \(\Q(\sqrt{-2}) \) None \(-1\) \(0\) \(0\) \(0\) \(q-\zeta_{22}^{9}q^{2}+(\zeta_{22}^{3}-\zeta_{22}^{5})q^{3}-\zeta_{22}^{7}q^{4}+\cdots\)