Properties

Label 288.2.d
Level $288$
Weight $2$
Character orbit 288.d
Rep. character $\chi_{288}(145,\cdot)$
Character field $\Q$
Dimension $4$
Newform subspaces $2$
Sturm bound $96$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 288 = 2^{5} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 288.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 8 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(96\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(5\)

Dimensions

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

Total New Old
Modular forms 64 6 58
Cusp forms 32 4 28
Eisenstein series 32 2 30

Trace form

\( 4q + O(q^{10}) \) \( 4q + 4q^{17} + 8q^{23} - 4q^{25} + 16q^{31} - 4q^{41} - 24q^{47} - 12q^{49} - 32q^{55} - 16q^{65} + 24q^{71} + 16q^{73} + 20q^{89} - 16q^{95} + O(q^{100}) \)

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.d.a \(2\) \(2.300\) \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{-6}) \) \(0\) \(0\) \(0\) \(-4\) \(q+\beta q^{5}-2q^{7}+2\beta q^{11}-3q^{25}+\beta q^{29}+\cdots\)
288.2.d.b \(2\) \(2.300\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(4\) \(q+iq^{5}+2q^{7}+2iq^{13}+2q^{17}+2iq^{19}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(288, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 2}\)