Properties

Label 288.2.p
Level $288$
Weight $2$
Character orbit 288.p
Rep. character $\chi_{288}(47,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $20$
Newform subspaces $2$
Sturm bound $96$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 288 = 2^{5} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 288.p (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 72 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(96\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(5\)

Dimensions

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

Total New Old
Modular forms 112 28 84
Cusp forms 80 20 60
Eisenstein series 32 8 24

Trace form

\( 20q + 4q^{3} - 4q^{9} + O(q^{10}) \) \( 20q + 4q^{3} - 4q^{9} + 6q^{11} + 8q^{19} - 4q^{25} + 16q^{27} - 2q^{33} - 18q^{41} + 2q^{43} - 4q^{49} - 28q^{51} - 20q^{57} - 30q^{59} - 6q^{65} + 2q^{67} - 8q^{73} - 68q^{75} + 8q^{81} - 54q^{83} + 36q^{91} - 2q^{97} - 10q^{99} + O(q^{100}) \)

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.p.a \(4\) \(2.300\) \(\Q(\sqrt{-2}, \sqrt{-3})\) \(\Q(\sqrt{-2}) \) \(0\) \(-2\) \(0\) \(0\) \(q+(\beta _{1}-\beta _{2}-\beta _{3})q^{3}+(1-2\beta _{1}-\beta _{2}+\cdots)q^{9}+\cdots\)
288.2.p.b \(16\) \(2.300\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(6\) \(0\) \(0\) \(q+(-\beta _{1}+\beta _{3}-\beta _{8})q^{3}-\beta _{9}q^{5}-\beta _{4}q^{7}+\cdots\)

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

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