Properties

Label 288.3.e
Level $288$
Weight $3$
Character orbit 288.e
Rep. character $\chi_{288}(161,\cdot)$
Character field $\Q$
Dimension $8$
Newform subspaces $4$
Sturm bound $144$
Trace bound $13$

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Defining parameters

Level: \( N \) \(=\) \( 288 = 2^{5} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 288.e (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3 \)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(144\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(288, [\chi])\).

Total New Old
Modular forms 112 8 104
Cusp forms 80 8 72
Eisenstein series 32 0 32

Trace form

\( 8q + O(q^{10}) \) \( 8q - 32q^{13} - 8q^{25} + 176q^{37} - 136q^{49} - 304q^{61} + 384q^{73} + 176q^{85} - 320q^{97} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(288, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
288.3.e.a \(2\) \(7.847\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(-16\) \(q+\beta q^{5}-8q^{7}-8\beta q^{11}-8q^{13}-9\beta q^{17}+\cdots\)
288.3.e.b \(2\) \(7.847\) \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(0\) \(0\) \(q+7\beta q^{5}-24q^{13}-7\beta q^{17}-73q^{25}+\cdots\)
288.3.e.c \(2\) \(7.847\) \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(0\) \(0\) \(q+\beta q^{5}+24q^{13}+23\beta q^{17}+23q^{25}+\cdots\)
288.3.e.d \(2\) \(7.847\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(16\) \(q+\beta q^{5}+8q^{7}+8\beta q^{11}-8q^{13}-9\beta q^{17}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(288, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(288, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 2}\)