Properties

Label 592.2.bq
Level $592$
Weight $2$
Character orbit 592.bq
Rep. character $\chi_{592}(65,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $108$
Newform subspaces $5$
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.bq (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 37 \)
Character field: \(\Q(\zeta_{18})\)
Newform subspaces: \( 5 \)
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

\( 108 q + 6 q^{3} - 9 q^{5} - 6 q^{9} + O(q^{10}) \) \( 108 q + 6 q^{3} - 9 q^{5} - 6 q^{9} + 21 q^{11} - 6 q^{13} - 12 q^{15} - 9 q^{17} + 6 q^{19} - 6 q^{21} + 9 q^{23} - 3 q^{25} + 45 q^{27} - 9 q^{29} + 3 q^{33} + 6 q^{35} + 18 q^{37} + 12 q^{39} - 9 q^{41} - 9 q^{45} + 33 q^{47} + 6 q^{49} - 81 q^{51} - 18 q^{53} - 9 q^{55} - 6 q^{57} + 6 q^{59} - 36 q^{61} + 33 q^{63} + 3 q^{65} - 15 q^{69} + 24 q^{71} - 42 q^{73} + 96 q^{75} + 27 q^{77} - 66 q^{79} + 3 q^{81} + 36 q^{83} - 18 q^{85} - 27 q^{87} + 36 q^{89} + 48 q^{91} - 12 q^{93} + 6 q^{95} - 9 q^{97} - 141 q^{99} + O(q^{100}) \)

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.bq.a 592.bq 37.h $6$ $4.727$ \(\Q(\zeta_{18})\) None \(0\) \(-9\) \(0\) \(-3\) $\mathrm{SU}(2)[C_{18}]$ \(q+(-1+\zeta_{18}^{2}-\zeta_{18}^{3}-\zeta_{18}^{4}-2\zeta_{18}^{5})q^{3}+\cdots\)
592.2.bq.b 592.bq 37.h $12$ $4.727$ \(\Q(\zeta_{36})\) None \(0\) \(-6\) \(0\) \(12\) $\mathrm{SU}(2)[C_{18}]$ \(q+(\zeta_{36}-\zeta_{36}^{3}-\zeta_{36}^{5})q^{3}+(-\zeta_{36}^{2}+\cdots)q^{5}+\cdots\)
592.2.bq.c 592.bq 37.h $12$ $4.727$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(12\) \(0\) \(-6\) $\mathrm{SU}(2)[C_{18}]$ \(q+(1-\beta _{1}+\beta _{6})q^{3}+(\beta _{4}+\beta _{10})q^{5}+\cdots\)
592.2.bq.d 592.bq 37.h $18$ $4.727$ \(\mathbb{Q}[x]/(x^{18} + \cdots)\) None \(0\) \(9\) \(-3\) \(3\) $\mathrm{SU}(2)[C_{18}]$ \(q+(1+\beta _{12}-\beta _{16})q^{3}+(-1-\beta _{3}-\beta _{4}+\cdots)q^{5}+\cdots\)
592.2.bq.e 592.bq 37.h $60$ $4.727$ None \(0\) \(0\) \(-6\) \(-6\) $\mathrm{SU}(2)[C_{18}]$

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

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