Properties

Label 570.2.s
Level $570$
Weight $2$
Character orbit 570.s
Rep. character $\chi_{570}(221,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $48$
Newform subspaces $2$
Sturm bound $240$
Trace bound $2$

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) \(=\) \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 570.s (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 57 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(240\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(17\)

Dimensions

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

Total New Old
Modular forms 256 48 208
Cusp forms 224 48 176
Eisenstein series 32 0 32

Trace form

\( 48q + 6q^{3} - 24q^{4} + 2q^{6} - 24q^{7} - 2q^{9} + O(q^{10}) \) \( 48q + 6q^{3} - 24q^{4} + 2q^{6} - 24q^{7} - 2q^{9} + 36q^{13} - 24q^{16} + 12q^{19} + 36q^{22} + 2q^{24} + 24q^{25} + 12q^{28} - 30q^{33} - 24q^{34} - 2q^{36} + 80q^{39} - 12q^{42} - 44q^{43} + 16q^{45} - 6q^{48} + 24q^{49} - 24q^{51} - 36q^{52} - 28q^{54} - 20q^{57} + 44q^{61} + 36q^{63} + 48q^{64} - 14q^{66} - 96q^{67} - 6q^{72} - 16q^{73} - 24q^{76} - 36q^{78} + 36q^{79} - 18q^{81} + 12q^{82} - 48q^{87} + 24q^{90} + 36q^{91} + 16q^{93} - 4q^{96} + 12q^{97} - 50q^{99} + O(q^{100}) \)

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.s.a \(24\) \(4.551\) None \(-12\) \(4\) \(0\) \(-12\)
570.2.s.b \(24\) \(4.551\) None \(12\) \(2\) \(0\) \(-12\)

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

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