Properties

Label 570.2.u
Level $570$
Weight $2$
Character orbit 570.u
Rep. character $\chi_{570}(61,\cdot)$
Character field $\Q(\zeta_{9})$
Dimension $72$
Newform subspaces $10$
Sturm bound $240$
Trace bound $12$

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Defining parameters

Level: \( N \) \(=\) \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 570.u (of order \(9\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
Character field: \(\Q(\zeta_{9})\)
Newform subspaces: \( 10 \)
Sturm bound: \(240\)
Trace bound: \(12\)
Distinguishing \(T_p\): \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(570, [\chi])\).

Total New Old
Modular forms 768 72 696
Cusp forms 672 72 600
Eisenstein series 96 0 96

Trace form

\( 72 q + O(q^{10}) \) \( 72 q + 24 q^{14} + 24 q^{17} - 24 q^{22} + 48 q^{23} + 12 q^{26} + 48 q^{29} + 24 q^{31} - 24 q^{34} - 12 q^{35} - 24 q^{38} + 36 q^{41} - 24 q^{42} - 24 q^{43} - 12 q^{44} + 24 q^{47} + 12 q^{49} - 24 q^{53} - 48 q^{56} + 48 q^{58} - 24 q^{59} - 24 q^{61} - 24 q^{62} - 36 q^{64} + 12 q^{65} + 48 q^{67} + 24 q^{71} - 24 q^{73} - 36 q^{74} - 12 q^{76} - 144 q^{77} - 72 q^{79} - 24 q^{82} + 24 q^{83} - 24 q^{88} - 96 q^{89} + 24 q^{91} - 24 q^{92} - 72 q^{93} - 24 q^{94} - 48 q^{97} - 48 q^{98} - 12 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(570, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
570.2.u.a 570.u 19.e $6$ $4.551$ \(\Q(\zeta_{18})\) None \(0\) \(0\) \(0\) \(-6\) $\mathrm{SU}(2)[C_{9}]$ \(q+(-\zeta_{18}+\zeta_{18}^{4})q^{2}+\zeta_{18}q^{3}-\zeta_{18}^{5}q^{4}+\cdots\)
570.2.u.b 570.u 19.e $6$ $4.551$ \(\Q(\zeta_{18})\) None \(0\) \(0\) \(0\) \(-6\) $\mathrm{SU}(2)[C_{9}]$ \(q+(-\zeta_{18}+\zeta_{18}^{4})q^{2}-\zeta_{18}q^{3}-\zeta_{18}^{5}q^{4}+\cdots\)
570.2.u.c 570.u 19.e $6$ $4.551$ \(\Q(\zeta_{18})\) None \(0\) \(0\) \(0\) \(-3\) $\mathrm{SU}(2)[C_{9}]$ \(q+(-\zeta_{18}+\zeta_{18}^{4})q^{2}-\zeta_{18}q^{3}-\zeta_{18}^{5}q^{4}+\cdots\)
570.2.u.d 570.u 19.e $6$ $4.551$ \(\Q(\zeta_{18})\) None \(0\) \(0\) \(0\) \(-3\) $\mathrm{SU}(2)[C_{9}]$ \(q+(-\zeta_{18}+\zeta_{18}^{4})q^{2}+\zeta_{18}q^{3}-\zeta_{18}^{5}q^{4}+\cdots\)
570.2.u.e 570.u 19.e $6$ $4.551$ \(\Q(\zeta_{18})\) None \(0\) \(0\) \(0\) \(3\) $\mathrm{SU}(2)[C_{9}]$ \(q+(\zeta_{18}-\zeta_{18}^{4})q^{2}+\zeta_{18}q^{3}-\zeta_{18}^{5}q^{4}+\cdots\)
570.2.u.f 570.u 19.e $6$ $4.551$ \(\Q(\zeta_{18})\) None \(0\) \(0\) \(0\) \(3\) $\mathrm{SU}(2)[C_{9}]$ \(q+(-\zeta_{18}+\zeta_{18}^{4})q^{2}-\zeta_{18}q^{3}-\zeta_{18}^{5}q^{4}+\cdots\)
570.2.u.g 570.u 19.e $6$ $4.551$ \(\Q(\zeta_{18})\) None \(0\) \(0\) \(0\) \(3\) $\mathrm{SU}(2)[C_{9}]$ \(q+(-\zeta_{18}+\zeta_{18}^{4})q^{2}+\zeta_{18}q^{3}-\zeta_{18}^{5}q^{4}+\cdots\)
570.2.u.h 570.u 19.e $6$ $4.551$ \(\Q(\zeta_{18})\) None \(0\) \(0\) \(0\) \(9\) $\mathrm{SU}(2)[C_{9}]$ \(q+(\zeta_{18}-\zeta_{18}^{4})q^{2}-\zeta_{18}q^{3}-\zeta_{18}^{5}q^{4}+\cdots\)
570.2.u.i 570.u 19.e $12$ $4.551$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(0\) \(0\) \(-3\) $\mathrm{SU}(2)[C_{9}]$ \(q+(-\beta _{1}+\beta _{4})q^{2}-\beta _{4}q^{3}-\beta _{2}q^{4}+\cdots\)
570.2.u.j 570.u 19.e $12$ $4.551$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(0\) \(3\) $\mathrm{SU}(2)[C_{9}]$ \(q+(-\beta _{4}+\beta _{6})q^{2}-\beta _{4}q^{3}+\beta _{3}q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(570, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(570, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(190, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(19, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(38, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(57, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(95, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(114, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(285, [\chi])\)\(^{\oplus 2}\)