Properties

Label 570.2.bh
Level $570$
Weight $2$
Character orbit 570.bh
Rep. character $\chi_{570}(13,\cdot)$
Character field $\Q(\zeta_{36})$
Dimension $240$
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.bh (of order \(36\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 95 \)
Character field: \(\Q(\zeta_{36})\)
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 1536 240 1296
Cusp forms 1344 240 1104
Eisenstein series 192 0 192

Trace form

\( 240q + 24q^{7} + O(q^{10}) \) \( 240q + 24q^{7} + 96q^{21} - 24q^{22} - 48q^{23} + 24q^{25} + 24q^{26} + 24q^{33} + 24q^{41} + 120q^{43} + 48q^{47} - 72q^{53} + 72q^{55} + 24q^{57} - 24q^{60} - 48q^{61} + 48q^{62} + 144q^{67} + 24q^{68} + 48q^{70} + 72q^{73} - 24q^{76} - 48q^{78} - 96q^{82} - 48q^{83} - 144q^{85} - 96q^{86} + 24q^{87} - 192q^{91} - 96q^{92} - 48q^{95} - 192q^{97} - 192q^{98} + O(q^{100}) \)

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.bh.a \(120\) \(4.551\) None \(0\) \(0\) \(-12\) \(12\)
570.2.bh.b \(120\) \(4.551\) None \(0\) \(0\) \(12\) \(12\)

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

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