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Properties

Label 576.3.q
Level $576$
Weight $3$
Character orbit 576.q
Rep. character $\chi_{576}(65,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $92$
Newform subspaces $12$
Sturm bound $288$
Trace bound $9$

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Defining parameters

Level: \( N \) \(=\) \( 576 = 2^{6} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 576.q (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 12 \)
Sturm bound: \(288\)
Trace bound: \(9\)
Distinguishing \(T_p\): \(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(576, [\chi])\).

Total New Old
Modular forms 408 100 308
Cusp forms 360 92 268
Eisenstein series 48 8 40

Trace form

\( 92 q + 6 q^{5} - 4 q^{9} + 2 q^{13} - 14 q^{21} + 188 q^{25} + 6 q^{29} - 54 q^{33} + 8 q^{37} + 138 q^{41} + 6 q^{45} - 240 q^{49} - 120 q^{57} + 2 q^{61} - 6 q^{65} + 262 q^{69} - 8 q^{73} + 6 q^{77}+ \cdots - 2 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{3}^{\mathrm{new}}(576, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
576.3.q.a 576.q 9.d $2$ $15.695$ \(\Q(\sqrt{-3}) \) None 9.3.d.a \(0\) \(-3\) \(-6\) \(2\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-3+3\zeta_{6})q^{3}+(-4+2\zeta_{6})q^{5}+\cdots\)
576.3.q.b 576.q 9.d $2$ $15.695$ \(\Q(\sqrt{-3}) \) None 9.3.d.a \(0\) \(3\) \(-6\) \(-2\) $\mathrm{SU}(2)[C_{6}]$ \(q+(3-3\zeta_{6})q^{3}+(-4+2\zeta_{6})q^{5}+(-2+\cdots)q^{7}+\cdots\)
576.3.q.c 576.q 9.d $4$ $15.695$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None 72.3.m.a \(0\) \(-12\) \(-6\) \(6\) $\mathrm{SU}(2)[C_{6}]$ \(q-3q^{3}+(-1+\beta _{1}-\beta _{2})q^{5}+(\beta _{1}+3\beta _{2}+\cdots)q^{7}+\cdots\)
576.3.q.d 576.q 9.d $4$ $15.695$ \(\Q(\sqrt{-3}, \sqrt{-11})\) None 36.3.g.a \(0\) \(-3\) \(-9\) \(-1\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-1+\beta _{3})q^{3}+(-4+\beta _{1}-2\beta _{2}+\cdots)q^{5}+\cdots\)
576.3.q.e 576.q 9.d $4$ $15.695$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None 18.3.d.a \(0\) \(0\) \(18\) \(-2\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-1+2\beta _{1}+\beta _{3})q^{3}+(3+3\beta _{1})q^{5}+\cdots\)
576.3.q.f 576.q 9.d $4$ $15.695$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None 18.3.d.a \(0\) \(0\) \(18\) \(2\) $\mathrm{SU}(2)[C_{6}]$ \(q+(1-2\beta _{1}+\beta _{3})q^{3}+(3+3\beta _{1})q^{5}+\cdots\)
576.3.q.g 576.q 9.d $4$ $15.695$ \(\Q(\sqrt{-3}, \sqrt{-11})\) None 36.3.g.a \(0\) \(3\) \(-9\) \(1\) $\mathrm{SU}(2)[C_{6}]$ \(q+(1-\beta _{3})q^{3}+(-4+\beta _{1}-2\beta _{2}+\beta _{3})q^{5}+\cdots\)
576.3.q.h 576.q 9.d $4$ $15.695$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None 72.3.m.a \(0\) \(12\) \(-6\) \(-6\) $\mathrm{SU}(2)[C_{6}]$ \(q+3q^{3}+(-1+\beta _{1}-\beta _{2})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
576.3.q.i 576.q 9.d $8$ $15.695$ 8.0.\(\cdots\).9 None 72.3.m.b \(0\) \(-10\) \(6\) \(6\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-1+\beta _{2}+\beta _{7})q^{3}+(1+\beta _{2}+\beta _{3}+\cdots)q^{5}+\cdots\)
576.3.q.j 576.q 9.d $8$ $15.695$ 8.0.\(\cdots\).9 None 72.3.m.b \(0\) \(10\) \(6\) \(-6\) $\mathrm{SU}(2)[C_{6}]$ \(q+(1-\beta _{2}-\beta _{7})q^{3}+(1+\beta _{2}+\beta _{3}+\beta _{5}+\cdots)q^{5}+\cdots\)
576.3.q.k 576.q 9.d $24$ $15.695$ None 288.3.q.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$
576.3.q.l 576.q 9.d $24$ $15.695$ None 288.3.q.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{3}^{\mathrm{old}}(576, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(576, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 7}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 2}\)