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Properties

Label 576.2.bb
Level $576$
Weight $2$
Character orbit 576.bb
Rep. character $\chi_{576}(49,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $88$
Newform subspaces $5$
Sturm bound $192$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 576 = 2^{6} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 576.bb (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 144 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 5 \)
Sturm bound: \(192\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(576, [\chi])\).

Total New Old
Modular forms 416 104 312
Cusp forms 352 88 264
Eisenstein series 64 16 48

Trace form

\( 88 q + 4 q^{3} - 2 q^{5} + O(q^{10}) \) \( 88 q + 4 q^{3} - 2 q^{5} + 2 q^{11} - 2 q^{13} + 8 q^{15} - 16 q^{17} + 8 q^{19} - 10 q^{21} - 8 q^{27} - 2 q^{29} + 4 q^{31} - 8 q^{33} + 28 q^{35} - 8 q^{37} + 2 q^{43} - 14 q^{45} + 44 q^{47} + 16 q^{49} + 36 q^{51} - 8 q^{53} - 10 q^{59} - 2 q^{61} + 36 q^{63} - 4 q^{65} + 2 q^{67} - 10 q^{69} - 56 q^{75} - 30 q^{77} + 4 q^{79} - 8 q^{81} + 22 q^{83} - 12 q^{85} + 36 q^{91} - 22 q^{93} - 60 q^{95} - 4 q^{97} - 10 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(576, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
576.2.bb.a 576.bb 144.x $4$ $4.599$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(-4\) \(-12\) $\mathrm{SU}(2)[C_{12}]$ \(q+(-2\zeta_{12}+\zeta_{12}^{3})q^{3}+(-1-\zeta_{12}+\cdots)q^{5}+\cdots\)
576.2.bb.b 576.bb 144.x $4$ $4.599$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(2\) \(12\) $\mathrm{SU}(2)[C_{12}]$ \(q+(1-2\zeta_{12}^{2})q^{3}+(\zeta_{12}^{2}-\zeta_{12}^{3})q^{5}+\cdots\)
576.2.bb.c 576.bb 144.x $4$ $4.599$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(4\) \(-6\) $\mathrm{SU}(2)[C_{12}]$ \(q+(-\zeta_{12}-\zeta_{12}^{3})q^{3}+(2\zeta_{12}^{2}-2\zeta_{12}^{3})q^{5}+\cdots\)
576.2.bb.d 576.bb 144.x $4$ $4.599$ \(\Q(\zeta_{12})\) None \(0\) \(6\) \(-8\) \(6\) $\mathrm{SU}(2)[C_{12}]$ \(q+(2-\zeta_{12}^{2})q^{3}+(-2-2\zeta_{12}+2\zeta_{12}^{3})q^{5}+\cdots\)
576.2.bb.e 576.bb 144.x $72$ $4.599$ None \(0\) \(-2\) \(4\) \(0\) $\mathrm{SU}(2)[C_{12}]$

Decomposition of \(S_{2}^{\mathrm{old}}(576, [\chi])\) into lower level spaces

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