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

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

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
570.2.u.a \(6\) \(4.551\) \(\Q(\zeta_{18})\) None \(0\) \(0\) \(0\) \(-6\) \(q+(-\zeta_{18}+\zeta_{18}^{4})q^{2}+\zeta_{18}q^{3}-\zeta_{18}^{5}q^{4}+\cdots\)
570.2.u.b \(6\) \(4.551\) \(\Q(\zeta_{18})\) None \(0\) \(0\) \(0\) \(-6\) \(q+(-\zeta_{18}+\zeta_{18}^{4})q^{2}-\zeta_{18}q^{3}-\zeta_{18}^{5}q^{4}+\cdots\)
570.2.u.c \(6\) \(4.551\) \(\Q(\zeta_{18})\) None \(0\) \(0\) \(0\) \(-3\) \(q+(-\zeta_{18}+\zeta_{18}^{4})q^{2}-\zeta_{18}q^{3}-\zeta_{18}^{5}q^{4}+\cdots\)
570.2.u.d \(6\) \(4.551\) \(\Q(\zeta_{18})\) None \(0\) \(0\) \(0\) \(-3\) \(q+(-\zeta_{18}+\zeta_{18}^{4})q^{2}+\zeta_{18}q^{3}-\zeta_{18}^{5}q^{4}+\cdots\)
570.2.u.e \(6\) \(4.551\) \(\Q(\zeta_{18})\) None \(0\) \(0\) \(0\) \(3\) \(q+(\zeta_{18}-\zeta_{18}^{4})q^{2}+\zeta_{18}q^{3}-\zeta_{18}^{5}q^{4}+\cdots\)
570.2.u.f \(6\) \(4.551\) \(\Q(\zeta_{18})\) None \(0\) \(0\) \(0\) \(3\) \(q+(-\zeta_{18}+\zeta_{18}^{4})q^{2}-\zeta_{18}q^{3}-\zeta_{18}^{5}q^{4}+\cdots\)
570.2.u.g \(6\) \(4.551\) \(\Q(\zeta_{18})\) None \(0\) \(0\) \(0\) \(3\) \(q+(-\zeta_{18}+\zeta_{18}^{4})q^{2}+\zeta_{18}q^{3}-\zeta_{18}^{5}q^{4}+\cdots\)
570.2.u.h \(6\) \(4.551\) \(\Q(\zeta_{18})\) None \(0\) \(0\) \(0\) \(9\) \(q+(\zeta_{18}-\zeta_{18}^{4})q^{2}-\zeta_{18}q^{3}-\zeta_{18}^{5}q^{4}+\cdots\)
570.2.u.i \(12\) \(4.551\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(0\) \(0\) \(-3\) \(q+(-\beta _{1}+\beta _{4})q^{2}-\beta _{4}q^{3}-\beta _{2}q^{4}+\cdots\)
570.2.u.j \(12\) \(4.551\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(0\) \(3\) \(q+(-\beta _{4}+\beta _{6})q^{2}-\beta _{4}q^{3}+\beta _{3}q^{4}+\cdots\)

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

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