Properties

Label 1412.1.r
Level $1412$
Weight $1$
Character orbit 1412.r
Rep. character $\chi_{1412}(35,\cdot)$
Character field $\Q(\zeta_{44})$
Dimension $20$
Newform subspaces $1$
Sturm bound $177$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 1412 = 2^{2} \cdot 353 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1412.r (of order \(44\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1412 \)
Character field: \(\Q(\zeta_{44})\)
Newform subspaces: \( 1 \)
Sturm bound: \(177\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1412, [\chi])\).

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

\( 20 q + 2 q^{2} - 2 q^{4} - 2 q^{5} + 2 q^{8} + O(q^{10}) \) \( 20 q + 2 q^{2} - 2 q^{4} - 2 q^{5} + 2 q^{8} + 2 q^{10} - 2 q^{13} - 2 q^{16} + 4 q^{17} - 2 q^{20} + 2 q^{26} + 2 q^{32} - 4 q^{34} - 20 q^{37} + 2 q^{40} + 2 q^{45} - 22 q^{50} - 2 q^{52} - 2 q^{53} - 2 q^{64} + 4 q^{68} - 2 q^{74} - 2 q^{80} + 2 q^{81} + 4 q^{85} - 2 q^{89} - 2 q^{90} - 4 q^{97} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1412, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1412.1.r.a 1412.r 1412.r $20$ $0.705$ \(\Q(\zeta_{44})\) $D_{44}$ \(\Q(\sqrt{-1}) \) None \(2\) \(0\) \(-2\) \(0\) \(q+\zeta_{44}^{14}q^{2}-\zeta_{44}^{6}q^{4}+(-\zeta_{44}+\zeta_{44}^{4}+\cdots)q^{5}+\cdots\)