Properties

Label 570.2.bb
Level $570$
Weight $2$
Character orbit 570.bb
Rep. character $\chi_{570}(41,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $168$
Newform subspaces $2$
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.bb (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 57 \)
Character field: \(\Q(\zeta_{18})\)
Newform subspaces: \( 2 \)
Sturm bound: \(240\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(11\)

Dimensions

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

Total New Old
Modular forms 768 168 600
Cusp forms 672 168 504
Eisenstein series 96 0 96

Trace form

\( 168q - 6q^{3} - 6q^{6} + 6q^{9} + O(q^{10}) \) \( 168q - 6q^{3} - 6q^{6} + 6q^{9} + 48q^{13} - 24q^{19} + 72q^{22} - 6q^{24} + 18q^{27} - 24q^{28} + 30q^{33} + 24q^{34} + 6q^{36} + 24q^{39} + 48q^{43} - 12q^{48} - 108q^{49} + 42q^{51} + 24q^{52} - 72q^{54} - 156q^{57} - 48q^{58} - 96q^{61} - 96q^{63} - 84q^{64} + 30q^{66} + 12q^{67} - 108q^{69} - 12q^{72} + 168q^{73} + 36q^{78} - 24q^{79} + 78q^{81} - 12q^{82} + 12q^{87} - 24q^{90} + 48q^{91} - 84q^{97} + 96q^{99} + O(q^{100}) \)

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.bb.a \(84\) \(4.551\) None \(0\) \(-6\) \(0\) \(0\)
570.2.bb.b \(84\) \(4.551\) None \(0\) \(0\) \(0\) \(0\)

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

\( S_{2}^{\mathrm{old}}(570, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(57, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(114, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(285, [\chi])\)\(^{\oplus 2}\)