Properties

Label 288.2.s
Level $288$
Weight $2$
Character orbit 288.s
Rep. character $\chi_{288}(95,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $24$
Newform subspaces $1$
Sturm bound $96$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 288 = 2^{5} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 288.s (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 36 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(96\)
Trace bound: \(0\)

Dimensions

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

Total New Old
Modular forms 112 24 88
Cusp forms 80 24 56
Eisenstein series 32 0 32

Trace form

\( 24q - 4q^{9} + O(q^{10}) \) \( 24q - 4q^{9} + 8q^{21} + 12q^{25} + 24q^{29} - 20q^{33} - 36q^{41} - 8q^{45} + 12q^{49} - 36q^{57} - 48q^{65} - 16q^{69} + 24q^{73} - 48q^{77} - 20q^{81} - 64q^{93} + 12q^{97} + O(q^{100}) \)

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
288.2.s.a \(24\) \(2.300\) None \(0\) \(0\) \(0\) \(0\)

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

\( S_{2}^{\mathrm{old}}(288, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 2}\)