Properties

Label 570.2.v
Level $570$
Weight $2$
Character orbit 570.v
Rep. character $\chi_{570}(83,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $160$
Newform subspaces $3$
Sturm bound $240$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 570.v (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 285 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 3 \)
Sturm bound: \(240\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(7\), \(17\)

Dimensions

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

Total New Old
Modular forms 512 160 352
Cusp forms 448 160 288
Eisenstein series 64 0 64

Trace form

\( 160q + O(q^{10}) \) \( 160q - 16q^{13} + 12q^{15} + 80q^{16} + 32q^{18} - 8q^{22} + 8q^{25} + 24q^{27} + 32q^{31} + 12q^{33} - 16q^{37} - 32q^{42} - 40q^{43} - 56q^{45} - 8q^{51} + 16q^{52} - 8q^{55} - 92q^{57} - 8q^{60} + 16q^{61} + 28q^{63} + 8q^{66} - 24q^{67} - 8q^{70} + 16q^{72} + 64q^{73} - 24q^{75} - 16q^{76} + 16q^{78} + 32q^{85} - 232q^{87} + 16q^{88} - 4q^{90} + 80q^{91} - 20q^{93} - 16q^{97} + O(q^{100}) \)

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.v.a \(8\) \(4.551\) \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{24}^{7}q^{2}+(\zeta_{24}-\zeta_{24}^{2}+\zeta_{24}^{6}+\cdots)q^{3}+\cdots\)
570.2.v.b \(8\) \(4.551\) \(\Q(\zeta_{24})\) None \(0\) \(4\) \(0\) \(0\) \(q+\zeta_{24}^{7}q^{2}+(\zeta_{24}+\zeta_{24}^{4}-\zeta_{24}^{7})q^{3}+\cdots\)
570.2.v.c \(144\) \(4.551\) None \(0\) \(-4\) \(0\) \(0\)

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

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