Properties

Label 224.1.h
Level $224$
Weight $1$
Character orbit 224.h
Rep. character $\chi_{224}(209,\cdot)$
Character field $\Q$
Dimension $1$
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.h (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 56 \)
Character field: \(\Q\)
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 3 9
Cusp forms 4 1 3
Eisenstein series 8 2 6

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 1 0 0 0

Trace form

\( q + q^{7} - q^{9} + O(q^{10}) \) \( q + q^{7} - q^{9} - 2 q^{23} - q^{25} + q^{49} - q^{63} + 2 q^{71} + 2 q^{79} + q^{81} + O(q^{100}) \)

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

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
224.1.h.a 224.h 56.h $1$ $0.112$ \(\Q\) $D_{2}$ \(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-14}) \) \(\Q(\sqrt{2}) \) \(0\) \(0\) \(0\) \(1\) \(q+q^{7}-q^{9}-2q^{23}-q^{25}+q^{49}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(224, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(224, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 3}\)