Properties

Label 224.2.q
Level $224$
Weight $2$
Character orbit 224.q
Rep. character $\chi_{224}(47,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $12$
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.q (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 56 \)
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 20 60
Cusp forms 48 12 36
Eisenstein series 32 8 24

Trace form

\( 12q + 6q^{3} + O(q^{10}) \) \( 12q + 6q^{3} + 6q^{11} - 6q^{17} + 6q^{19} - 6q^{33} - 18q^{35} - 12q^{49} - 6q^{51} - 36q^{57} - 42q^{59} - 12q^{65} - 30q^{67} + 18q^{73} - 24q^{75} + 6q^{81} + 18q^{89} + 72q^{91} + 24q^{99} + O(q^{100}) \)

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.q.a \(12\) \(1.789\) 12.0.\(\cdots\).2 None \(0\) \(6\) \(0\) \(0\) \(q+\beta _{8}q^{3}+(-\beta _{4}-\beta _{7})q^{5}+(\beta _{5}-\beta _{7}+\cdots)q^{7}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(224, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 3}\)