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Properties

Label 570.2.d
Level $570$
Weight $2$
Character orbit 570.d
Rep. character $\chi_{570}(229,\cdot)$
Character field $\Q$
Dimension $16$
Newform subspaces $4$
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.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(240\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(7\), \(11\), \(13\)

Dimensions

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

Total New Old
Modular forms 128 16 112
Cusp forms 112 16 96
Eisenstein series 16 0 16

Trace form

\( 16 q - 16 q^{4} + 4 q^{5} - 4 q^{6} - 16 q^{9} + O(q^{10}) \) \( 16 q - 16 q^{4} + 4 q^{5} - 4 q^{6} - 16 q^{9} + 4 q^{10} - 8 q^{11} + 4 q^{15} + 16 q^{16} + 4 q^{19} - 4 q^{20} + 4 q^{24} + 16 q^{26} - 32 q^{29} + 16 q^{31} - 24 q^{34} + 24 q^{35} + 16 q^{36} - 8 q^{39} - 4 q^{40} - 16 q^{41} + 8 q^{44} - 4 q^{45} + 8 q^{46} - 16 q^{49} - 16 q^{50} + 16 q^{51} + 4 q^{54} + 16 q^{55} - 32 q^{59} - 4 q^{60} + 16 q^{61} - 16 q^{64} + 32 q^{65} - 8 q^{66} - 16 q^{69} + 40 q^{70} + 32 q^{71} + 16 q^{74} - 4 q^{76} + 4 q^{80} + 16 q^{81} - 8 q^{85} - 32 q^{86} - 48 q^{89} - 4 q^{90} - 112 q^{91} - 24 q^{94} + 4 q^{95} - 4 q^{96} + 8 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(570, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
570.2.d.a 570.d 5.b $2$ $4.551$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}+iq^{3}-q^{4}+(-1-2i)q^{5}+\cdots\)
570.2.d.b 570.d 5.b $2$ $4.551$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}+iq^{3}-q^{4}+(2+i)q^{5}-q^{6}+\cdots\)
570.2.d.c 570.d 5.b $6$ $4.551$ 6.0.350464.1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+\beta _{1}q^{3}-q^{4}+\beta _{3}q^{5}-q^{6}+\cdots\)
570.2.d.d 570.d 5.b $6$ $4.551$ 6.0.350464.1 None \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}-\beta _{1}q^{3}-q^{4}-\beta _{5}q^{5}+q^{6}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(570, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(95, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(190, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(285, [\chi])\)\(^{\oplus 2}\)