↑

Properties

Label 570.2.q
Level $570$
Weight $2$
Character orbit 570.q
Rep. character $\chi_{570}(49,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $40$
Newform subspaces $3$
Sturm bound $240$
Trace bound $1$

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.q (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 95 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 3 \)
Sturm bound: \(240\)
Trace bound: \(1\)
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

\( 40q + 20q^{4} + 4q^{5} + 20q^{9} + O(q^{10}) \) \( 40q + 20q^{4} + 4q^{5} + 20q^{9} + 24q^{11} + 4q^{14} + 4q^{15} - 20q^{16} + 20q^{19} + 8q^{20} - 16q^{21} + 12q^{25} - 16q^{26} - 16q^{29} + 8q^{30} + 16q^{31} + 16q^{34} + 16q^{35} - 20q^{36} - 16q^{39} - 4q^{41} + 12q^{44} + 8q^{45} + 72q^{46} - 80q^{49} - 8q^{51} + 8q^{56} + 24q^{59} - 4q^{60} - 40q^{64} - 8q^{65} - 16q^{69} + 12q^{70} + 64q^{71} + 12q^{74} + 16q^{75} - 8q^{76} + 4q^{80} - 20q^{81} - 32q^{84} - 24q^{85} - 8q^{86} - 52q^{89} - 32q^{91} - 16q^{94} - 52q^{95} + 12q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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.q.a \(8\) \(4.551\) \(\Q(\zeta_{24})\) None \(0\) \(0\) \(4\) \(0\) \(q+(\zeta_{24}-\zeta_{24}^{4})q^{2}+(\zeta_{24}-\zeta_{24}^{4})q^{3}+\cdots\)
570.2.q.b \(12\) \(4.551\) 12.0.\(\cdots\).1 None \(0\) \(0\) \(0\) \(0\) \(q+(-\beta _{3}-\beta _{4})q^{2}+(-\beta _{3}-\beta _{4})q^{3}+\cdots\)
570.2.q.c \(20\) \(4.551\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{11}q^{2}+\beta _{11}q^{3}+(1-\beta _{12})q^{4}+\cdots\)

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

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