Properties

Label 570.2.bc
Level $570$
Weight $2$
Character orbit 570.bc
Rep. character $\chi_{570}(139,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $120$
Newform subspaces $2$
Sturm bound $240$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 570.bc (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 95 \)
Character field: \(\Q(\zeta_{18})\)
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 768 120 648
Cusp forms 672 120 552
Eisenstein series 96 0 96

Trace form

\( 120q + O(q^{10}) \) \( 120q - 24q^{11} + 24q^{14} + 24q^{15} + 48q^{19} + 24q^{20} - 48q^{21} + 12q^{25} - 12q^{26} + 48q^{29} + 24q^{35} + 12q^{41} - 12q^{44} - 12q^{45} - 24q^{46} + 84q^{49} - 72q^{55} + 48q^{59} + 12q^{60} + 120q^{61} + 60q^{64} + 48q^{69} - 72q^{70} - 144q^{71} - 36q^{74} + 12q^{76} - 72q^{79} + 24q^{84} - 120q^{85} - 48q^{86} - 120q^{89} - 48q^{91} - 216q^{94} - 60q^{95} - 12q^{99} + O(q^{100}) \)

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.bc.a \(60\) \(4.551\) None \(0\) \(0\) \(-6\) \(0\)
570.2.bc.b \(60\) \(4.551\) None \(0\) \(0\) \(6\) \(0\)

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

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