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Properties

Label 224.4.q
Level $224$
Weight $4$
Character orbit 224.q
Rep. character $\chi_{224}(47,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $44$
Newform subspaces $1$
Sturm bound $128$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 224 = 2^{5} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
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: \(128\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(224, [\chi])\).

Total New Old
Modular forms 208 52 156
Cusp forms 176 44 132
Eisenstein series 32 8 24

Trace form

\( 44 q + 6 q^{3} + 160 q^{9} + O(q^{10}) \) \( 44 q + 6 q^{3} + 160 q^{9} + 22 q^{11} - 6 q^{17} + 6 q^{19} - 352 q^{25} - 6 q^{33} - 18 q^{35} - 800 q^{43} + 356 q^{49} + 810 q^{51} + 220 q^{57} + 2070 q^{59} - 252 q^{65} + 98 q^{67} + 642 q^{73} - 744 q^{75} + 182 q^{81} - 1278 q^{89} + 424 q^{91} - 1000 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(224, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
224.4.q.a 224.q 56.m $44$ $13.216$ None \(0\) \(6\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{4}^{\mathrm{old}}(224, [\chi])\) into lower level spaces

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