Properties

Label 576.3.o
Level $576$
Weight $3$
Character orbit 576.o
Rep. character $\chi_{576}(319,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $92$
Newform subspaces $9$
Sturm bound $288$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 576 = 2^{6} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 576.o (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 36 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 9 \)
Sturm bound: \(288\)
Trace bound: \(3\)
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

\( 92 q + 2 q^{5} - 4 q^{9} + O(q^{10}) \) \( 92 q + 2 q^{5} - 4 q^{9} + 2 q^{13} - 8 q^{17} + 22 q^{21} - 192 q^{25} + 2 q^{29} + 10 q^{33} + 8 q^{37} - 50 q^{41} - 94 q^{45} + 236 q^{49} + 296 q^{53} - 48 q^{57} + 2 q^{61} + 98 q^{65} - 218 q^{69} - 8 q^{73} + 198 q^{77} + 76 q^{81} + 52 q^{85} + 184 q^{89} - 602 q^{93} - 2 q^{97} + O(q^{100}) \)

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
576.3.o.a 576.o 36.f $2$ $15.695$ \(\Q(\sqrt{-3}) \) None \(0\) \(-3\) \(4\) \(6\) $\mathrm{SU}(2)[C_{6}]$ \(q-3\zeta_{6}q^{3}+(4-4\zeta_{6})q^{5}+(4-2\zeta_{6})q^{7}+\cdots\)
576.3.o.b 576.o 36.f $2$ $15.695$ \(\Q(\sqrt{-3}) \) None \(0\) \(3\) \(4\) \(-6\) $\mathrm{SU}(2)[C_{6}]$ \(q+3\zeta_{6}q^{3}+(4-4\zeta_{6})q^{5}+(-4+2\zeta_{6})q^{7}+\cdots\)
576.3.o.c 576.o 36.f $4$ $15.695$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(14\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q-3\zeta_{12}^{3}q^{3}+(7-7\zeta_{12}^{2})q^{5}+(-5\zeta_{12}+\cdots)q^{7}+\cdots\)
576.3.o.d 576.o 36.f $8$ $15.695$ 8.0.856615824.2 None \(0\) \(-3\) \(-3\) \(-3\) $\mathrm{SU}(2)[C_{6}]$ \(q+(\beta _{3}-\beta _{4})q^{3}+(-1+\beta _{2}-\beta _{3}+\beta _{4}+\cdots)q^{5}+\cdots\)
576.3.o.e 576.o 36.f $8$ $15.695$ 8.0.121550625.1 None \(0\) \(0\) \(6\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q-\beta _{5}q^{3}+(-2\beta _{1}-\beta _{4}+\beta _{7})q^{5}+(2\beta _{2}+\cdots)q^{7}+\cdots\)
576.3.o.f 576.o 36.f $8$ $15.695$ 8.0.856615824.2 None \(0\) \(3\) \(-3\) \(3\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\beta _{1}-\beta _{3}+\beta _{4})q^{3}+(-1-\beta _{1}+\cdots)q^{5}+\cdots\)
576.3.o.g 576.o 36.f $16$ $15.695$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(-6\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(\beta _{3}+\beta _{6})q^{3}+(-\beta _{1}+\beta _{7})q^{5}+(\beta _{3}+\cdots)q^{7}+\cdots\)
576.3.o.h 576.o 36.f $20$ $15.695$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(0\) \(0\) \(-14\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{2}q^{3}+(-\beta _{1}+\beta _{4}-\beta _{7})q^{5}+(-\beta _{15}+\cdots)q^{7}+\cdots\)
576.3.o.i 576.o 36.f $24$ $15.695$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$

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

\( S_{3}^{\mathrm{old}}(576, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 2}\)