Properties

Label 224.3.g
Level $224$
Weight $3$
Character orbit 224.g
Rep. character $\chi_{224}(15,\cdot)$
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.g (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 8 \)
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

\( 12 q + 36 q^{9} + O(q^{10}) \) \( 12 q + 36 q^{9} + 16 q^{11} - 8 q^{17} - 64 q^{19} - 84 q^{25} + 96 q^{27} + 16 q^{33} + 88 q^{41} + 80 q^{43} - 84 q^{49} + 192 q^{51} - 80 q^{57} - 288 q^{59} + 96 q^{65} - 80 q^{67} + 120 q^{73} - 160 q^{75} - 4 q^{81} - 160 q^{83} - 200 q^{89} - 72 q^{97} - 16 q^{99} + O(q^{100}) \)

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.g.a 224.g 8.d $4$ $6.104$ \(\Q(\sqrt{2}, \sqrt{-7})\) None \(0\) \(-8\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-2+\beta _{1})q^{3}+(-\beta _{2}+2\beta _{3})q^{5}+\cdots\)
224.3.g.b 224.g 8.d $8$ $6.104$ 8.0.\(\cdots\).3 None \(0\) \(8\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(1+\beta _{3})q^{3}+(-\beta _{1}+\beta _{2}+\beta _{4})q^{5}+\cdots\)

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

\( S_{3}^{\mathrm{old}}(224, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(8, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 3}\)