Properties

Label 570.2.f
Level $570$
Weight $2$
Character orbit 570.f
Rep. character $\chi_{570}(341,\cdot)$
Character field $\Q$
Dimension $24$
Newform subspaces $4$
Sturm bound $240$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 570.f (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 57 \)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(240\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(7\), \(29\)

Dimensions

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

Total New Old
Modular forms 128 24 104
Cusp forms 112 24 88
Eisenstein series 16 0 16

Trace form

\( 24q + 24q^{4} + 4q^{6} + 24q^{7} - 4q^{9} + O(q^{10}) \) \( 24q + 24q^{4} + 4q^{6} + 24q^{7} - 4q^{9} + 24q^{16} + 24q^{19} + 4q^{24} - 24q^{25} + 24q^{28} - 4q^{36} + 4q^{39} + 12q^{42} - 16q^{43} - 16q^{45} - 8q^{54} - 4q^{57} - 24q^{58} + 64q^{61} - 84q^{63} + 24q^{64} - 16q^{66} - 56q^{73} + 24q^{76} + 12q^{81} + 36q^{87} - 16q^{93} + 4q^{96} - 64q^{99} + O(q^{100}) \)

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.f.a \(4\) \(4.551\) \(\Q(\zeta_{8})\) None \(-4\) \(-4\) \(0\) \(8\) \(q-q^{2}+(-1-\zeta_{8}^{2})q^{3}+q^{4}+\zeta_{8}q^{5}+\cdots\)
570.2.f.b \(4\) \(4.551\) \(\Q(\zeta_{8})\) None \(4\) \(4\) \(0\) \(8\) \(q+q^{2}+(1+\zeta_{8}^{2})q^{3}+q^{4}+\zeta_{8}q^{5}+\cdots\)
570.2.f.c \(8\) \(4.551\) 8.0.7278137344.1 None \(-8\) \(2\) \(0\) \(4\) \(q-q^{2}+\beta _{1}q^{3}+q^{4}+\beta _{2}q^{5}-\beta _{1}q^{6}+\cdots\)
570.2.f.d \(8\) \(4.551\) 8.0.7278137344.1 None \(8\) \(-2\) \(0\) \(4\) \(q+q^{2}-\beta _{1}q^{3}+q^{4}+\beta _{2}q^{5}-\beta _{1}q^{6}+\cdots\)

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

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