Properties

Label 570.2.x
Level $570$
Weight $2$
Character orbit 570.x
Rep. character $\chi_{570}(103,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $80$
Newform subspaces $2$
Sturm bound $240$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 570.x (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 95 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 2 \)
Sturm bound: \(240\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(7\)

Dimensions

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

Total New Old
Modular forms 512 80 432
Cusp forms 448 80 368
Eisenstein series 64 0 64

Trace form

\( 80q - 8q^{5} - 16q^{7} + O(q^{10}) \) \( 80q - 8q^{5} - 16q^{7} + 16q^{11} + 40q^{16} + 8q^{17} + 48q^{21} + 24q^{22} + 8q^{23} + 32q^{26} + 8q^{28} + 16q^{30} - 24q^{33} - 8q^{35} - 40q^{36} + 16q^{38} - 24q^{41} - 16q^{43} - 8q^{47} + 72q^{53} - 8q^{55} - 32q^{57} + 24q^{60} + 16q^{61} - 16q^{62} - 8q^{63} - 72q^{67} - 16q^{68} + 24q^{70} - 48q^{73} - 64q^{77} + 48q^{78} + 8q^{80} + 40q^{81} - 16q^{82} - 128q^{83} - 72q^{85} - 48q^{86} + 32q^{87} - 96q^{91} - 8q^{92} + 16q^{93} - 112q^{95} - 24q^{97} - 96q^{98} + O(q^{100}) \)

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.x.a \(40\) \(4.551\) None \(0\) \(0\) \(-8\) \(-8\)
570.2.x.b \(40\) \(4.551\) None \(0\) \(0\) \(0\) \(-8\)

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

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