Properties

Label 224.2.i
Level $224$
Weight $2$
Character orbit 224.i
Rep. character $\chi_{224}(65,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $16$
Newform subspaces $4$
Sturm bound $64$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 224 = 2^{5} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 224.i (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 4 \)
Sturm bound: \(64\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(3\)

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

\( 16q - 8q^{9} + O(q^{10}) \) \( 16q - 8q^{9} - 16q^{13} + 24q^{21} - 16q^{25} + 16q^{29} - 8q^{33} + 8q^{37} + 16q^{41} - 8q^{45} - 16q^{49} - 8q^{53} - 48q^{57} - 24q^{61} + 8q^{65} + 24q^{73} - 48q^{77} + 32q^{81} - 80q^{85} + 40q^{89} + 8q^{93} - 16q^{97} + O(q^{100}) \)

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.i.a \(4\) \(1.789\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(-2\) \(-2\) \(-4\) \(q+(-1+\beta _{1}-\beta _{2})q^{3}+(-2\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
224.2.i.b \(4\) \(1.789\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(-2\) \(0\) \(q+(-\zeta_{12}-\zeta_{12}^{3})q^{3}+(-1+\zeta_{12}^{2}+\cdots)q^{5}+\cdots\)
224.2.i.c \(4\) \(1.789\) \(\Q(\sqrt{-3}, \sqrt{7})\) None \(0\) \(0\) \(6\) \(0\) \(q+\beta _{1}q^{3}-3\beta _{2}q^{5}-\beta _{3}q^{7}+4\beta _{2}q^{9}+\cdots\)
224.2.i.d \(4\) \(1.789\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(2\) \(-2\) \(4\) \(q+(1+\beta _{1}+\beta _{2})q^{3}+(2\beta _{1}+\beta _{2}+2\beta _{3})q^{5}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(224, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 2}\)