Properties

Label 570.2.c
Level $570$
Weight $2$
Character orbit 570.c
Rep. character $\chi_{570}(569,\cdot)$
Character field $\Q$
Dimension $40$
Newform subspaces $6$
Sturm bound $240$
Trace bound $15$

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Defining parameters

Level: \( N \) \(=\) \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 570.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 285 \)
Character field: \(\Q\)
Newform subspaces: \( 6 \)
Sturm bound: \(240\)
Trace bound: \(15\)
Distinguishing \(T_p\): \(7\), \(11\), \(29\), \(37\)

Dimensions

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

Total New Old
Modular forms 128 40 88
Cusp forms 112 40 72
Eisenstein series 16 0 16

Trace form

\( 40q - 40q^{4} + O(q^{10}) \) \( 40q - 40q^{4} + 40q^{16} + 16q^{19} + 16q^{25} + 4q^{30} + 60q^{45} - 88q^{49} - 48q^{61} - 40q^{64} + 8q^{66} - 16q^{76} + 16q^{81} + 56q^{85} - 120q^{99} + O(q^{100}) \)

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.c.a \(4\) \(4.551\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}^{2}q^{2}+(\zeta_{8}+\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}-q^{4}+\cdots\)
570.2.c.b \(4\) \(4.551\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}^{2}q^{2}+(\zeta_{8}+\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}-q^{4}+\cdots\)
570.2.c.c \(8\) \(4.551\) 8.0.1499238400.2 None \(0\) \(-4\) \(0\) \(0\) \(q+\beta _{6}q^{2}+(-1-\beta _{3}+\beta _{4}+\beta _{6}+\beta _{7})q^{3}+\cdots\)
570.2.c.d \(8\) \(4.551\) \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}q^{2}-\zeta_{24}^{4}q^{3}-q^{4}+(-\zeta_{24}^{2}+\cdots)q^{5}+\cdots\)
570.2.c.e \(8\) \(4.551\) \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{24}q^{2}+(-\zeta_{24}-\zeta_{24}^{6})q^{3}-q^{4}+\cdots\)
570.2.c.f \(8\) \(4.551\) 8.0.1499238400.2 None \(0\) \(4\) \(0\) \(0\) \(q+\beta _{6}q^{2}+(-\beta _{3}+\beta _{4}+\beta _{6}+\beta _{7})q^{3}+\cdots\)

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

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