Properties

Label 570.2.m
Level $570$
Weight $2$
Character orbit 570.m
Rep. character $\chi_{570}(37,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $40$
Newform subspaces $2$
Sturm bound $240$
Trace bound $5$

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.m (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 95 \)
Character field: \(\Q(i)\)
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 256 40 216
Cusp forms 224 40 184
Eisenstein series 32 0 32

Trace form

\( 40q + 8q^{5} - 8q^{7} + O(q^{10}) \) \( 40q + 8q^{5} - 8q^{7} - 16q^{11} - 40q^{16} - 8q^{17} + 40q^{23} - 24q^{25} + 16q^{26} - 8q^{28} - 16q^{30} + 8q^{35} + 40q^{36} - 16q^{38} + 40q^{43} - 40q^{47} + 80q^{55} + 8q^{57} + 32q^{61} - 32q^{62} + 8q^{63} - 8q^{68} - 24q^{73} + 24q^{76} + 64q^{77} - 8q^{80} - 40q^{81} - 32q^{82} - 40q^{83} - 72q^{85} + 16q^{87} - 40q^{92} - 16q^{93} - 56q^{95} + O(q^{100}) \)

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.m.a \(20\) \(4.551\) \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None \(0\) \(0\) \(-4\) \(-4\) \(q+\beta _{2}q^{2}+\beta _{11}q^{3}+\beta _{4}q^{4}+\beta _{6}q^{5}+\cdots\)
570.2.m.b \(20\) \(4.551\) \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None \(0\) \(0\) \(12\) \(-4\) \(q+\beta _{7}q^{2}-\beta _{10}q^{3}+\beta _{2}q^{4}+(1+\beta _{6}+\cdots)q^{5}+\cdots\)

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

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