↑

Properties

Label 224.3.w
Level $224$
Weight $3$
Character orbit 224.w
Rep. character $\chi_{224}(43,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $192$
Newform subspaces $1$
Sturm bound $96$
Trace bound $0$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 224 = 2^{5} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 224.w (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 32 \)
Character field: \(\Q(\zeta_{8})\)
Newform subspaces: \( 1 \)
Sturm bound: \(96\)
Trace bound: \(0\)

Dimensions

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

Total New Old
Modular forms 264 192 72
Cusp forms 248 192 56
Eisenstein series 16 0 16

Trace form

\( 192 q + O(q^{10}) \) \( 192 q + 80 q^{10} + 96 q^{12} - 20 q^{16} - 60 q^{18} - 260 q^{22} + 64 q^{23} - 144 q^{24} - 200 q^{26} + 192 q^{27} - 40 q^{30} + 40 q^{32} + 120 q^{34} + 464 q^{36} + 504 q^{38} - 384 q^{39} + 360 q^{40} - 96 q^{43} + 52 q^{44} + 64 q^{46} - 104 q^{48} - 312 q^{50} - 384 q^{51} - 320 q^{52} + 160 q^{53} - 576 q^{54} - 512 q^{55} - 196 q^{56} - 360 q^{58} - 872 q^{60} + 128 q^{61} - 408 q^{62} + 832 q^{66} + 160 q^{67} + 856 q^{68} - 384 q^{69} + 336 q^{70} + 1488 q^{72} + 308 q^{74} + 768 q^{75} + 1024 q^{76} - 224 q^{77} - 408 q^{78} + 1024 q^{79} - 1040 q^{80} - 240 q^{82} - 1384 q^{86} + 896 q^{87} - 560 q^{88} - 1320 q^{90} - 380 q^{92} - 936 q^{94} - 1088 q^{96} - 512 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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.w.a 224.w 32.h $192$ $6.104$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{8}]$

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

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