Properties

Label 288.4.p
Level $288$
Weight $4$
Character orbit 288.p
Rep. character $\chi_{288}(47,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $68$
Newform subspaces $2$
Sturm bound $192$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 288 = 2^{5} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 4 \)
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: \(192\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(5\)

Dimensions

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

Total New Old
Modular forms 304 76 228
Cusp forms 272 68 204
Eisenstein series 32 8 24

Trace form

\( 68 q + 4 q^{3} - 4 q^{9} + 6 q^{11} + 8 q^{19} - 652 q^{25} - 128 q^{27} - 290 q^{33} + 54 q^{41} + 2 q^{43} + 1076 q^{49} + 596 q^{51} - 284 q^{57} - 3054 q^{59} - 6 q^{65} + 2 q^{67} - 8 q^{73} + 3004 q^{75}+ \cdots + 4118 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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.p.a 288.p 72.l $4$ $16.993$ \(\Q(\sqrt{-2}, \sqrt{-3})\) \(\Q(\sqrt{-2}) \) 72.4.l.a \(0\) \(10\) \(0\) \(0\) $\mathrm{U}(1)[D_{6}]$ \(q+(5-\beta _{1}-5\beta _{2})q^{3}+(-10\beta _{1}-23\beta _{2}+\cdots)q^{9}+\cdots\)
288.4.p.b 288.p 72.l $64$ $16.993$ None 72.4.l.b \(0\) \(-6\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$

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

\( S_{4}^{\mathrm{old}}(288, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 3}\)