Properties

Label 224.3.d
Level $224$
Weight $3$
Character orbit 224.d
Rep. character $\chi_{224}(127,\cdot)$
Character field $\Q$
Dimension $12$
Newform subspaces $2$
Sturm bound $96$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 224 = 2^{5} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 224.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 4 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(96\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(224, [\chi])\).

Total New Old
Modular forms 72 12 60
Cusp forms 56 12 44
Eisenstein series 16 0 16

Trace form

\( 12 q - 8 q^{5} - 20 q^{9} + O(q^{10}) \) \( 12 q - 8 q^{5} - 20 q^{9} + 24 q^{13} - 72 q^{17} + 132 q^{25} - 40 q^{29} + 32 q^{33} - 40 q^{37} + 24 q^{41} + 216 q^{45} - 84 q^{49} - 232 q^{53} - 320 q^{57} - 200 q^{61} + 48 q^{65} + 480 q^{69} + 120 q^{73} + 460 q^{81} + 176 q^{85} + 56 q^{89} - 576 q^{93} - 72 q^{97} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(224, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
224.3.d.a 224.d 4.b $4$ $6.104$ \(\Q(i, \sqrt{7})\) None \(0\) \(0\) \(-8\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}+(-2+\beta _{2})q^{5}-\beta _{3}q^{7}+5q^{9}+\cdots\)
224.3.d.b 224.d 4.b $8$ $6.104$ 8.0.1997017344.2 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}-\beta _{4}q^{5}-\beta _{3}q^{7}+(-5+\beta _{2}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(224, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(224, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 2}\)