Properties

Label 288.2.i
Level $288$
Weight $2$
Character orbit 288.i
Rep. character $\chi_{288}(97,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $24$
Newform subspaces $6$
Sturm bound $96$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 288 = 2^{5} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 288.i (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 6 \)
Sturm bound: \(96\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(5\), \(7\)

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

\( 24q + 4q^{9} + O(q^{10}) \) \( 24q + 4q^{9} + 8q^{17} + 8q^{21} - 12q^{25} - 8q^{29} + 28q^{33} + 12q^{41} - 40q^{45} - 12q^{49} - 48q^{53} - 4q^{57} - 16q^{65} - 48q^{69} + 24q^{73} - 16q^{77} - 68q^{81} - 64q^{89} + 64q^{93} - 12q^{97} + O(q^{100}) \)

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.i.a \(2\) \(2.300\) \(\Q(\sqrt{-3}) \) None \(0\) \(-3\) \(-4\) \(-2\) \(q+(-1-\zeta_{6})q^{3}-4\zeta_{6}q^{5}+(-2+2\zeta_{6})q^{7}+\cdots\)
288.2.i.b \(2\) \(2.300\) \(\Q(\sqrt{-3}) \) None \(0\) \(3\) \(-4\) \(2\) \(q+(1+\zeta_{6})q^{3}-4\zeta_{6}q^{5}+(2-2\zeta_{6})q^{7}+\cdots\)
288.2.i.c \(4\) \(2.300\) \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(0\) \(-4\) \(2\) \(2\) \(q+(-1+\beta _{3})q^{3}+\beta _{2}q^{5}+(1-\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots\)
288.2.i.d \(4\) \(2.300\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(2\) \(0\) \(q-\zeta_{12}^{3}q^{3}+(1-\zeta_{12})q^{5}+\zeta_{12}^{2}q^{7}+\cdots\)
288.2.i.e \(4\) \(2.300\) \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(0\) \(4\) \(2\) \(-2\) \(q+(1-\beta _{3})q^{3}+(1-\beta _{2})q^{5}+(-\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots\)
288.2.i.f \(8\) \(2.300\) 8.0.170772624.1 None \(0\) \(0\) \(2\) \(0\) \(q+(-\beta _{1}+\beta _{5})q^{3}+(1-\beta _{4}+\beta _{7})q^{5}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(288, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 2}\)