Properties

Label 224.2.f
Level $224$
Weight $2$
Character orbit 224.f
Rep. character $\chi_{224}(223,\cdot)$
Character field $\Q$
Dimension $8$
Newform subspaces $1$
Sturm bound $64$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 224 = 2^{5} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 224.f (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 28 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(64\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(224, [\chi])\).

Total New Old
Modular forms 40 8 32
Cusp forms 24 8 16
Eisenstein series 16 0 16

Trace form

\( 8 q + 8 q^{9} + O(q^{10}) \) \( 8 q + 8 q^{9} + 8 q^{25} - 16 q^{29} - 16 q^{37} + 8 q^{49} - 16 q^{53} - 32 q^{57} - 32 q^{65} - 16 q^{77} - 24 q^{81} + 64 q^{85} + 64 q^{93} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(224, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
224.2.f.a 224.f 28.d $8$ $1.789$ \(\Q(\zeta_{16})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{16}^{2}q^{3}-\zeta_{16}^{5}q^{5}-\zeta_{16}^{6}q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(224, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(224, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 2}\)