Properties

Label 224.2.f
Level 224
Weight 2
Character orbit f
Rep. character \(\chi_{224}(223,\cdot)\)
Character field \(\Q\)
Dimension 8
Newforms 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: \(\Q\)
Newforms: \( 1 \)
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

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

Decomposition of \(S_{2}^{\mathrm{new}}(224, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
224.2.f.a \(8\) \(1.789\) \(\Q(\zeta_{16})\) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{16}^{2}q^{3}-\zeta_{16}^{5}q^{5}-\zeta_{16}^{6}q^{7}+\cdots\)

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

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