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Properties

Label 561.2.j
Level $561$
Weight $2$
Character orbit 561.j
Rep. character $\chi_{561}(166,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $56$
Newform subspaces $4$
Sturm bound $144$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 561 = 3 \cdot 11 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 561.j (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 17 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 4 \)
Sturm bound: \(144\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(2\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(561, [\chi])\).

Total New Old
Modular forms 152 56 96
Cusp forms 136 56 80
Eisenstein series 16 0 16

Trace form

\( 56 q - 48 q^{4} + 16 q^{5} - 8 q^{6} + O(q^{10}) \) \( 56 q - 48 q^{4} + 16 q^{5} - 8 q^{6} - 16 q^{14} + 48 q^{16} + 24 q^{17} + 8 q^{18} - 24 q^{20} + 8 q^{23} + 8 q^{24} + 72 q^{28} - 24 q^{29} - 64 q^{30} + 32 q^{31} - 8 q^{33} + 16 q^{34} - 32 q^{35} + 32 q^{38} - 16 q^{40} - 64 q^{41} - 16 q^{44} - 16 q^{45} + 8 q^{46} + 8 q^{47} + 32 q^{48} + 8 q^{50} - 8 q^{54} + 32 q^{55} - 48 q^{56} + 104 q^{58} - 8 q^{62} - 128 q^{64} - 8 q^{67} - 80 q^{68} + 32 q^{69} - 48 q^{71} - 24 q^{72} - 40 q^{73} - 72 q^{74} + 32 q^{75} - 16 q^{78} - 32 q^{79} + 96 q^{80} - 56 q^{81} + 64 q^{82} + 8 q^{85} + 80 q^{86} - 24 q^{89} - 8 q^{91} - 24 q^{92} + 88 q^{95} + 32 q^{96} + 40 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(561, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
561.2.j.a 561.j 17.c $4$ $4.480$ \(\Q(\zeta_{8})\) None \(0\) \(0\) \(-4\) \(-8\) $\mathrm{SU}(2)[C_{4}]$ \(q+\zeta_{8}^{2}q^{2}+\zeta_{8}q^{3}+q^{4}+(-1+2\zeta_{8}+\cdots)q^{5}+\cdots\)
561.2.j.b 561.j 17.c $4$ $4.480$ \(\Q(\zeta_{8})\) None \(0\) \(0\) \(4\) \(8\) $\mathrm{SU}(2)[C_{4}]$ \(q+\zeta_{8}^{2}q^{2}+\zeta_{8}q^{3}+q^{4}+(1+2\zeta_{8}+\cdots)q^{5}+\cdots\)
561.2.j.c 561.j 17.c $20$ $4.480$ \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None \(0\) \(0\) \(12\) \(8\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{1}q^{2}+\beta _{13}q^{3}+(-\beta _{5}+\beta _{6}-\beta _{8}+\cdots)q^{4}+\cdots\)
561.2.j.d 561.j 17.c $28$ $4.480$ None \(0\) \(0\) \(4\) \(-8\) $\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{2}^{\mathrm{old}}(561, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(561, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(51, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(187, [\chi])\)\(^{\oplus 2}\)