Properties

Label 288.4.d
Level $288$
Weight $4$
Character orbit 288.d
Rep. character $\chi_{288}(145,\cdot)$
Character field $\Q$
Dimension $14$
Newform subspaces $4$
Sturm bound $192$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 288 = 2^{5} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 288.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 8 \)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(192\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(288, [\chi])\).

Total New Old
Modular forms 160 16 144
Cusp forms 128 14 114
Eisenstein series 32 2 30

Trace form

\( 14 q + 16 q^{7} + O(q^{10}) \) \( 14 q + 16 q^{7} - 24 q^{17} + 24 q^{23} - 274 q^{25} + 80 q^{31} - 96 q^{41} + 264 q^{47} + 750 q^{49} + 48 q^{55} + 624 q^{65} - 1848 q^{71} - 156 q^{73} - 2144 q^{79} - 312 q^{89} + 4320 q^{95} - 1084 q^{97} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(288, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
288.4.d.a 288.d 8.b $2$ $16.993$ \(\Q(\sqrt{-7}) \) None 8.4.b.a \(0\) \(0\) \(0\) \(16\) $\mathrm{SU}(2)[C_{2}]$ \(q-2\beta q^{5}+8q^{7}+3\beta q^{11}-10\beta q^{13}+\cdots\)
288.4.d.b 288.d 8.b $2$ $16.993$ \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{-6}) \) 72.4.d.a \(0\) \(0\) \(0\) \(68\) $\mathrm{U}(1)[D_{2}]$ \(q+7\beta q^{5}+34q^{7}+2\beta q^{11}-267q^{25}+\cdots\)
288.4.d.c 288.d 8.b $4$ $16.993$ \(\Q(\sqrt{-10}, \sqrt{22})\) None 72.4.d.c \(0\) \(0\) \(0\) \(-40\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{5}-10q^{7}-6\beta _{1}q^{11}+\beta _{3}q^{13}+\cdots\)
288.4.d.d 288.d 8.b $6$ $16.993$ 6.0.8248384.1 None 24.4.d.a \(0\) \(0\) \(0\) \(-28\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{5}+(-5-\beta _{1})q^{7}+(-2\beta _{2}-2\beta _{3}+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(288, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(288, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(8, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 2}\)