Properties

Label 570.2.bi
Level $570$
Weight $2$
Character orbit 570.bi
Rep. character $\chi_{570}(17,\cdot)$
Character field $\Q(\zeta_{36})$
Dimension $480$
Newform subspaces $1$
Sturm bound $240$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 570.bi (of order \(36\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 285 \)
Character field: \(\Q(\zeta_{36})\)
Newform subspaces: \( 1 \)
Sturm bound: \(240\)
Trace bound: \(0\)

Dimensions

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

Total New Old
Modular forms 1536 480 1056
Cusp forms 1344 480 864
Eisenstein series 192 0 192

Trace form

\( 480q + O(q^{10}) \) \( 480q - 36q^{15} - 48q^{18} + 24q^{22} - 24q^{25} + 72q^{33} + 24q^{43} - 36q^{45} + 24q^{51} - 120q^{55} + 108q^{57} - 48q^{60} - 48q^{61} - 36q^{63} - 24q^{66} + 48q^{67} - 48q^{70} - 48q^{78} - 144q^{81} - 48q^{85} - 96q^{87} - 168q^{90} - 144q^{91} - 228q^{93} + 48q^{97} + O(q^{100}) \)

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.bi.a \(480\) \(4.551\) None \(0\) \(0\) \(0\) \(0\)

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

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