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Properties

Label 288.3.t
Level $288$
Weight $3$
Character orbit 288.t
Rep. character $\chi_{288}(79,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $44$
Newform subspaces $2$
Sturm bound $144$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 288 = 2^{5} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 288.t (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 72 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(144\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(5\)

Dimensions

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

Total New Old
Modular forms 208 52 156
Cusp forms 176 44 132
Eisenstein series 32 8 24

Trace form

\( 44 q + 4 q^{3} - 4 q^{9} + 2 q^{11} - 8 q^{17} + 8 q^{19} + 68 q^{25} + 52 q^{27} - 2 q^{33} + 108 q^{35} - 26 q^{41} + 2 q^{43} + 68 q^{49} - 40 q^{51} - 80 q^{57} + 146 q^{59} - 102 q^{65} + 2 q^{67}+ \cdots - 286 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
288.3.t.a 288.t 72.p $4$ $7.847$ \(\Q(\sqrt{-2}, \sqrt{-3})\) \(\Q(\sqrt{-2}) \) 72.3.p.a \(0\) \(-2\) \(0\) \(0\) $\mathrm{U}(1)[D_{6}]$ \(q+(-\beta _{1}-\beta _{2}+\beta _{3})q^{3}+(7+2\beta _{1}-7\beta _{2}+\cdots)q^{9}+\cdots\)
288.3.t.b 288.t 72.p $40$ $7.847$ None 72.3.p.b \(0\) \(6\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$

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

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