Properties

Label 224.1.v
Level $224$
Weight $1$
Character orbit 224.v
Rep. character $\chi_{224}(13,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $4$
Newform subspaces $1$
Sturm bound $32$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 224 = 2^{5} \cdot 7 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 224.v (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 224 \)
Character field: \(\Q(\zeta_{8})\)
Newform subspaces: \( 1 \)
Sturm bound: \(32\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(224, [\chi])\).

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

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

\( 4 q + O(q^{10}) \) \( 4 q - 4 q^{16} - 4 q^{18} + 4 q^{22} - 4 q^{23} - 4 q^{43} + 4 q^{44} - 4 q^{53} + 4 q^{56} + 4 q^{63} + 4 q^{67} + 4 q^{74} - 4 q^{77} - 4 q^{92} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(224, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
224.1.v.a \(4\) \(0.112\) \(\Q(\zeta_{8})\) \(D_{8}\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}-\zeta_{8}q^{7}+\zeta_{8}^{3}q^{8}+\cdots\)