Properties

Label 224.2.b
Level $224$
Weight $2$
Character orbit 224.b
Rep. character $\chi_{224}(113,\cdot)$
Character field $\Q$
Dimension $6$
Newform subspaces $2$
Sturm bound $64$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 224 = 2^{5} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 224.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 8 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(64\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

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

Total New Old
Modular forms 40 6 34
Cusp forms 24 6 18
Eisenstein series 16 0 16

Trace form

\( 6q + 2q^{7} - 6q^{9} + O(q^{10}) \) \( 6q + 2q^{7} - 6q^{9} - 8q^{15} - 4q^{17} + 8q^{23} - 2q^{25} + 16q^{31} + 8q^{33} - 8q^{39} - 4q^{41} + 6q^{49} - 32q^{55} - 8q^{57} - 10q^{63} + 16q^{65} + 32q^{71} - 20q^{73} - 16q^{79} + 14q^{81} - 32q^{87} - 20q^{89} + 8q^{95} - 4q^{97} + O(q^{100}) \)

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.b.a \(2\) \(1.789\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(-2\) \(q+\beta q^{3}+\beta q^{5}-q^{7}+q^{9}+2\beta q^{11}+\cdots\)
224.2.b.b \(4\) \(1.789\) 4.0.2312.1 None \(0\) \(0\) \(0\) \(4\) \(q+\beta _{1}q^{3}+\beta _{2}q^{5}+q^{7}+(-2+\beta _{3})q^{9}+\cdots\)

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

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