Properties

Label 570.2.i
Level $570$
Weight $2$
Character orbit 570.i
Rep. character $\chi_{570}(121,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $32$
Newform subspaces $10$
Sturm bound $240$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 570.i (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 10 \)
Sturm bound: \(240\)
Trace bound: \(11\)
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 256 32 224
Cusp forms 224 32 192
Eisenstein series 32 0 32

Trace form

\( 32q - 4q^{3} - 16q^{4} - 8q^{7} - 16q^{9} + O(q^{10}) \) \( 32q - 4q^{3} - 16q^{4} - 8q^{7} - 16q^{9} - 4q^{10} - 8q^{11} + 8q^{12} - 4q^{13} - 12q^{14} - 16q^{16} + 16q^{17} - 4q^{19} + 4q^{21} - 8q^{23} - 16q^{25} + 8q^{27} + 4q^{28} - 8q^{29} + 24q^{31} - 8q^{33} + 8q^{34} + 4q^{35} - 16q^{36} + 8q^{37} - 24q^{39} - 4q^{40} + 12q^{41} + 8q^{42} + 12q^{43} + 4q^{44} - 24q^{46} + 16q^{47} - 4q^{48} + 64q^{49} - 4q^{52} - 8q^{53} + 24q^{56} - 12q^{57} - 16q^{58} + 4q^{61} - 8q^{62} + 4q^{63} + 32q^{64} + 16q^{65} - 8q^{66} + 4q^{67} - 32q^{68} - 16q^{69} - 8q^{70} - 12q^{73} + 12q^{74} + 8q^{75} - 4q^{76} + 64q^{77} - 8q^{78} - 20q^{79} - 16q^{81} - 16q^{82} - 16q^{83} - 8q^{84} + 24q^{86} - 16q^{87} + 12q^{89} - 4q^{90} + 36q^{91} - 8q^{92} + 20q^{93} - 16q^{94} - 24q^{95} - 16q^{97} + 16q^{98} + 4q^{99} + O(q^{100}) \)

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.i.a \(2\) \(4.551\) \(\Q(\sqrt{-3}) \) None \(-1\) \(-1\) \(1\) \(-2\) \(q+(-1+\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
570.2.i.b \(2\) \(4.551\) \(\Q(\sqrt{-3}) \) None \(-1\) \(-1\) \(1\) \(-2\) \(q+(-1+\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
570.2.i.c \(2\) \(4.551\) \(\Q(\sqrt{-3}) \) None \(-1\) \(1\) \(1\) \(6\) \(q+(-1+\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
570.2.i.d \(2\) \(4.551\) \(\Q(\sqrt{-3}) \) None \(1\) \(-1\) \(1\) \(-2\) \(q+(1-\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
570.2.i.e \(2\) \(4.551\) \(\Q(\sqrt{-3}) \) None \(1\) \(1\) \(-1\) \(-10\) \(q+(1-\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
570.2.i.f \(4\) \(4.551\) \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(-2\) \(2\) \(-2\) \(4\) \(q+(-1+\beta _{1})q^{2}+(1-\beta _{1})q^{3}-\beta _{1}q^{4}+\cdots\)
570.2.i.g \(4\) \(4.551\) \(\Q(\sqrt{-3}, \sqrt{73})\) None \(2\) \(-2\) \(-2\) \(-4\) \(q+(1-\beta _{2})q^{2}+(-1+\beta _{2})q^{3}-\beta _{2}q^{4}+\cdots\)
570.2.i.h \(4\) \(4.551\) \(\Q(\sqrt{-3}, \sqrt{19})\) None \(2\) \(-2\) \(2\) \(0\) \(q+(1+\beta _{2})q^{2}+(-1-\beta _{2})q^{3}+\beta _{2}q^{4}+\cdots\)
570.2.i.i \(4\) \(4.551\) \(\Q(\sqrt{-3}, \sqrt{7})\) None \(2\) \(2\) \(2\) \(0\) \(q+(1+\beta _{2})q^{2}+(1+\beta _{2})q^{3}+\beta _{2}q^{4}+\cdots\)
570.2.i.j \(6\) \(4.551\) 6.0.29654208.1 None \(-3\) \(-3\) \(-3\) \(2\) \(q+(-1+\beta _{1})q^{2}+(-1+\beta _{1})q^{3}-\beta _{1}q^{4}+\cdots\)

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

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