Properties

Label 288.2.w
Level $288$
Weight $2$
Character orbit 288.w
Rep. character $\chi_{288}(35,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $64$
Newform subspaces $2$
Sturm bound $96$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 288 = 2^{5} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 288.w (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 96 \)
Character field: \(\Q(\zeta_{8})\)
Newform subspaces: \( 2 \)
Sturm bound: \(96\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(288, [\chi])\).

Total New Old
Modular forms 208 64 144
Cusp forms 176 64 112
Eisenstein series 32 0 32

Trace form

\( 64 q + O(q^{10}) \) \( 64 q + 16 q^{10} + 16 q^{16} + 32 q^{22} - 64 q^{40} - 64 q^{46} - 112 q^{52} - 64 q^{55} - 64 q^{58} + 64 q^{61} - 96 q^{64} - 32 q^{67} - 96 q^{70} - 16 q^{76} - 64 q^{79} + 80 q^{82} + 80 q^{88} - 96 q^{91} + 144 q^{94} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(288, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
288.2.w.a 288.w 96.o $32$ $2.300$ None \(-4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{8}]$
288.2.w.b 288.w 96.o $32$ $2.300$ None \(4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{8}]$

Decomposition of \(S_{2}^{\mathrm{old}}(288, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(288, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 2}\)