Properties

Label 592.2.bc
Level $592$
Weight $2$
Character orbit 592.bc
Rep. character $\chi_{592}(33,\cdot)$
Character field $\Q(\zeta_{9})$
Dimension $108$
Newform subspaces $7$
Sturm bound $152$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 592 = 2^{4} \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 592.bc (of order \(9\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 37 \)
Character field: \(\Q(\zeta_{9})\)
Newform subspaces: \( 7 \)
Sturm bound: \(152\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(592, [\chi])\).

Total New Old
Modular forms 492 120 372
Cusp forms 420 108 312
Eisenstein series 72 12 60

Trace form

\( 108 q + 6 q^{3} - 9 q^{5} + 12 q^{7} - 6 q^{9} + O(q^{10}) \) \( 108 q + 6 q^{3} - 9 q^{5} + 12 q^{7} - 6 q^{9} + 21 q^{11} - 6 q^{13} + 24 q^{15} - 3 q^{17} + 6 q^{19} - 6 q^{21} + 3 q^{23} - 3 q^{25} + 9 q^{27} - 3 q^{29} + 12 q^{31} + 3 q^{33} + 6 q^{35} - 30 q^{37} + 12 q^{39} - 3 q^{41} - 3 q^{45} - 27 q^{47} + 6 q^{49} + 33 q^{51} + 6 q^{53} - 9 q^{55} - 6 q^{57} + 6 q^{59} + 24 q^{61} - 27 q^{63} - 9 q^{65} + 12 q^{67} + 3 q^{69} + 24 q^{71} + 18 q^{73} - 72 q^{75} + 27 q^{77} + 18 q^{79} + 3 q^{81} - 24 q^{83} + 12 q^{85} - 45 q^{87} - 48 q^{89} + 48 q^{91} - 48 q^{93} + 6 q^{95} - 3 q^{97} + 99 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(592, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
592.2.bc.a 592.bc 37.f $6$ $4.727$ \(\Q(\zeta_{18})\) None \(0\) \(-3\) \(-6\) \(-3\) $\mathrm{SU}(2)[C_{9}]$ \(q+(-\zeta_{18}+\zeta_{18}^{2}-\zeta_{18}^{3})q^{3}+(-2\zeta_{18}^{3}+\cdots)q^{5}+\cdots\)
592.2.bc.b 592.bc 37.f $6$ $4.727$ \(\Q(\zeta_{18})\) None \(0\) \(3\) \(3\) \(-6\) $\mathrm{SU}(2)[C_{9}]$ \(q+(\zeta_{18}+\zeta_{18}^{3})q^{3}+(1+\zeta_{18}+2\zeta_{18}^{2}+\cdots)q^{5}+\cdots\)
592.2.bc.c 592.bc 37.f $6$ $4.727$ \(\Q(\zeta_{18})\) None \(0\) \(6\) \(6\) \(12\) $\mathrm{SU}(2)[C_{9}]$ \(q+(1+\zeta_{18}^{4})q^{3}+(1+\zeta_{18}-\zeta_{18}^{2}+\cdots)q^{5}+\cdots\)
592.2.bc.d 592.bc 37.f $12$ $4.727$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(3\) \(-6\) \(-6\) $\mathrm{SU}(2)[C_{9}]$ \(q+(\beta _{1}+\beta _{9})q^{3}+(-1+\beta _{1}+\beta _{5})q^{5}+\cdots\)
592.2.bc.e 592.bc 37.f $24$ $4.727$ None \(0\) \(-3\) \(-3\) \(9\) $\mathrm{SU}(2)[C_{9}]$
592.2.bc.f 592.bc 37.f $24$ $4.727$ None \(0\) \(0\) \(3\) \(3\) $\mathrm{SU}(2)[C_{9}]$
592.2.bc.g 592.bc 37.f $30$ $4.727$ None \(0\) \(0\) \(-6\) \(3\) $\mathrm{SU}(2)[C_{9}]$

Decomposition of \(S_{2}^{\mathrm{old}}(592, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(592, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(37, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(74, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(148, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(296, [\chi])\)\(^{\oplus 2}\)