Properties

Label 224.4.u
Level $224$
Weight $4$
Character orbit 224.u
Rep. character $\chi_{224}(29,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $288$
Newform subspaces $2$
Sturm bound $128$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 224 = 2^{5} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 224.u (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 32 \)
Character field: \(\Q(\zeta_{8})\)
Newform subspaces: \( 2 \)
Sturm bound: \(128\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

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

Total New Old
Modular forms 392 288 104
Cusp forms 376 288 88
Eisenstein series 16 0 16

Trace form

\( 288q + O(q^{10}) \) \( 288q - 240q^{10} + 96q^{12} + 300q^{16} + 180q^{18} - 628q^{22} - 328q^{23} - 912q^{24} - 40q^{26} + 528q^{27} - 1160q^{30} - 1240q^{32} - 1000q^{34} - 2480q^{36} - 2408q^{38} - 1200q^{39} + 1640q^{40} - 808q^{43} + 500q^{44} + 2880q^{46} + 4888q^{48} + 4264q^{50} + 2976q^{51} + 1728q^{52} - 752q^{53} + 1728q^{54} + 576q^{55} - 196q^{56} - 2376q^{58} - 8552q^{60} + 3648q^{61} - 6840q^{62} - 2520q^{63} - 6592q^{66} - 2040q^{67} - 5032q^{68} + 2112q^{69} - 1008q^{70} + 3408q^{72} + 1316q^{74} + 4416q^{75} + 10240q^{76} - 1904q^{77} + 5064q^{78} + 15600q^{80} + 5840q^{82} + 1848q^{86} + 2576q^{87} - 3120q^{88} - 3720q^{90} - 13692q^{92} - 16264q^{94} + 12160q^{95} - 12352q^{96} + 10624q^{99} + O(q^{100}) \)

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
224.4.u.a \(140\) \(13.216\) None \(0\) \(0\) \(0\) \(0\)
224.4.u.b \(148\) \(13.216\) None \(0\) \(0\) \(0\) \(0\)

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

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