Properties

Label 712.1.s
Level $712$
Weight $1$
Character orbit 712.s
Rep. character $\chi_{712}(67,\cdot)$
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.s (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

\( 10q - q^{2} - 2q^{3} - q^{4} - 2q^{6} - q^{8} - 3q^{9} + O(q^{10}) \) \( 10q - q^{2} - 2q^{3} - q^{4} - 2q^{6} - q^{8} - 3q^{9} + 9q^{11} - 2q^{12} - q^{16} + 9q^{17} - 3q^{18} - 2q^{19} - 2q^{22} - 2q^{24} - q^{25} + 7q^{27} - q^{32} - 4q^{33} - 2q^{34} - 3q^{36} + 9q^{38} - 2q^{41} - 2q^{43} - 2q^{44} - 2q^{48} - q^{49} - q^{50} - 4q^{51} + 7q^{54} - 4q^{57} - 2q^{59} - q^{64} - 4q^{66} - 2q^{67} + 9q^{68} + 8q^{72} - 2q^{73} - 2q^{75} - 2q^{76} - 5q^{81} - 2q^{82} - 2q^{83} - 2q^{86} - 2q^{88} - q^{89} - 2q^{96} - 2q^{97} - q^{98} + 5q^{99} + O(q^{100}) \)

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

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
712.1.s.a \(10\) \(0.355\) \(\Q(\zeta_{22})\) \(D_{11}\) \(\Q(\sqrt{-2}) \) None \(-1\) \(-2\) \(0\) \(0\) \(q-\zeta_{22}^{5}q^{2}+(\zeta_{22}^{4}-\zeta_{22}^{9})q^{3}+\zeta_{22}^{10}q^{4}+\cdots\)