Properties

Label 712.1.y
Level $712$
Weight $1$
Character orbit 712.y
Rep. character $\chi_{712}(99,\cdot)$
Character field $\Q(\zeta_{44})$
Dimension $20$
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.y (of order \(44\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 712 \)
Character field: \(\Q(\zeta_{44})\)
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 60 60 0
Cusp forms 20 20 0
Eisenstein series 40 40 0

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 20 0 0 0

Trace form

\( 20q + 2q^{2} - 2q^{3} - 2q^{4} + 2q^{6} + 2q^{8} + O(q^{10}) \) \( 20q + 2q^{2} - 2q^{3} - 2q^{4} + 2q^{6} + 2q^{8} - 2q^{12} - 2q^{16} - 2q^{19} + 2q^{24} + 2q^{25} - 22q^{27} + 2q^{32} - 20q^{38} + 2q^{41} + 2q^{43} - 2q^{48} - 2q^{50} + 4q^{51} - 4q^{57} - 2q^{59} - 2q^{64} + 22q^{72} + 2q^{75} - 2q^{76} - 2q^{81} - 2q^{82} + 2q^{83} - 2q^{86} + 2q^{89} + 2q^{96} - 4q^{97} + O(q^{100}) \)

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.y.a \(20\) \(0.355\) \(\Q(\zeta_{44})\) \(D_{44}\) \(\Q(\sqrt{-2}) \) None \(2\) \(-2\) \(0\) \(0\) \(q-\zeta_{44}^{20}q^{2}+(-\zeta_{44}^{3}+\zeta_{44}^{16})q^{3}+\cdots\)