Properties

Label 224.2.u
Level $224$
Weight $2$
Character orbit 224.u
Rep. character $\chi_{224}(29,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $96$
Newform subspaces $3$
Sturm bound $64$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 224 = 2^{5} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 224.u (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 32 \)
Character field: \(\Q(\zeta_{8})\)
Newform subspaces: \( 3 \)
Sturm bound: \(64\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(224, [\chi])\).

Total New Old
Modular forms 136 96 40
Cusp forms 120 96 24
Eisenstein series 16 0 16

Trace form

\( 96 q + O(q^{10}) \) \( 96 q - 16 q^{10} - 32 q^{12} - 20 q^{16} - 20 q^{18} - 28 q^{22} - 8 q^{23} - 16 q^{24} + 40 q^{26} - 48 q^{27} + 40 q^{30} + 40 q^{32} + 40 q^{34} + 16 q^{36} - 56 q^{38} - 48 q^{39} + 40 q^{40} - 8 q^{43} + 4 q^{44} - 64 q^{46} - 104 q^{48} - 104 q^{50} + 32 q^{51} - 64 q^{52} - 16 q^{53} + 64 q^{54} + 64 q^{55} + 28 q^{56} + 72 q^{58} - 8 q^{60} - 64 q^{61} + 24 q^{62} + 40 q^{63} - 64 q^{66} + 40 q^{67} - 8 q^{68} - 64 q^{69} + 48 q^{70} - 48 q^{72} + 28 q^{74} + 64 q^{75} - 16 q^{77} + 24 q^{78} - 16 q^{80} - 80 q^{82} + 40 q^{86} - 112 q^{87} + 80 q^{88} - 120 q^{90} + 148 q^{92} + 40 q^{94} - 128 q^{95} - 64 q^{96} - 128 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(224, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
224.2.u.a \(4\) \(1.789\) \(\Q(\zeta_{8})\) None \(-4\) \(-4\) \(-8\) \(0\) \(q+(-1+\zeta_{8}^{2})q^{2}+(-1-\zeta_{8}-\zeta_{8}^{2}+\cdots)q^{3}+\cdots\)
224.2.u.b \(40\) \(1.789\) None \(4\) \(4\) \(8\) \(0\)
224.2.u.c \(52\) \(1.789\) None \(0\) \(0\) \(0\) \(0\)

Decomposition of \(S_{2}^{\mathrm{old}}(224, [\chi])\) into lower level spaces

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