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Properties

Label 570.2.k
Level $570$
Weight $2$
Character orbit 570.k
Rep. character $\chi_{570}(77,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $72$
Newform subspaces $2$
Sturm bound $240$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 570.k (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 15 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 2 \)
Sturm bound: \(240\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(7\)

Dimensions

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

Total New Old
Modular forms 256 72 184
Cusp forms 224 72 152
Eisenstein series 32 0 32

Trace form

\( 72 q + 8 q^{3} + 8 q^{6} + 8 q^{7} + O(q^{10}) \) \( 72 q + 8 q^{3} + 8 q^{6} + 8 q^{7} - 8 q^{10} - 8 q^{12} + 16 q^{13} + 8 q^{15} - 72 q^{16} - 16 q^{21} - 8 q^{22} + 48 q^{25} - 16 q^{27} + 8 q^{28} + 24 q^{30} - 16 q^{31} + 32 q^{33} + 8 q^{36} - 32 q^{37} - 16 q^{40} + 24 q^{42} - 32 q^{43} - 32 q^{46} - 8 q^{48} - 16 q^{52} - 40 q^{55} + 40 q^{58} - 8 q^{60} + 80 q^{61} + 16 q^{63} + 80 q^{67} - 24 q^{70} - 24 q^{73} - 32 q^{75} - 40 q^{78} - 56 q^{81} + 32 q^{82} - 8 q^{88} - 24 q^{90} + 64 q^{91} - 56 q^{93} - 8 q^{96} - 56 q^{97} + O(q^{100}) \)

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.k.a 570.k 15.e $36$ $4.551$ None \(0\) \(4\) \(0\) \(-12\) $\mathrm{SU}(2)[C_{4}]$
570.2.k.b 570.k 15.e $36$ $4.551$ None \(0\) \(4\) \(0\) \(20\) $\mathrm{SU}(2)[C_{4}]$

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

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