Properties

Label 224.2.p
Level $224$
Weight $2$
Character orbit 224.p
Rep. character $\chi_{224}(31,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $16$
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.p (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 28 \)
Character field: \(\Q(\zeta_{6})\)
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 80 16 64
Cusp forms 48 16 32
Eisenstein series 32 0 32

Trace form

\( 16 q - 8 q^{9} + O(q^{10}) \) \( 16 q - 8 q^{9} - 24 q^{21} + 16 q^{25} + 16 q^{29} + 24 q^{33} - 8 q^{37} - 24 q^{45} - 32 q^{49} - 8 q^{53} - 16 q^{57} - 24 q^{61} + 8 q^{65} - 24 q^{73} + 64 q^{77} - 48 q^{81} - 16 q^{85} - 72 q^{89} + 8 q^{93} + O(q^{100}) \)

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
224.2.p.a \(16\) \(1.789\) 16.0.\(\cdots\).2 None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{14}q^{3}-\beta _{13}q^{5}-\beta _{9}q^{7}+(-\beta _{3}+\cdots)q^{9}+\cdots\)

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

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