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Properties

Label 561.2.o
Level $561$
Weight $2$
Character orbit 561.o
Rep. character $\chi_{561}(100,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $128$
Newform subspaces $2$
Sturm bound $144$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 561 = 3 \cdot 11 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 561.o (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 17 \)
Character field: \(\Q(\zeta_{8})\)
Newform subspaces: \( 2 \)
Sturm bound: \(144\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

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

Total New Old
Modular forms 304 128 176
Cusp forms 272 128 144
Eisenstein series 32 0 32

Trace form

\( 128 q + 16 q^{6} + O(q^{10}) \) \( 128 q + 16 q^{6} + 32 q^{14} - 176 q^{16} - 16 q^{17} + 16 q^{19} - 32 q^{20} - 16 q^{24} + 48 q^{25} + 80 q^{32} - 16 q^{33} - 16 q^{34} - 64 q^{35} - 16 q^{36} - 96 q^{40} + 48 q^{41} + 16 q^{42} + 32 q^{43} - 32 q^{44} + 16 q^{45} - 32 q^{46} + 64 q^{50} + 48 q^{53} + 16 q^{54} + 32 q^{56} - 16 q^{58} + 32 q^{59} + 16 q^{60} + 64 q^{61} - 112 q^{62} - 112 q^{65} - 48 q^{67} + 176 q^{68} + 64 q^{69} + 96 q^{70} - 32 q^{71} - 80 q^{73} - 128 q^{74} - 112 q^{76} - 64 q^{78} + 32 q^{79} + 64 q^{80} - 80 q^{82} - 48 q^{83} - 64 q^{85} + 64 q^{86} - 48 q^{87} + 64 q^{91} + 144 q^{92} - 32 q^{93} - 16 q^{94} - 64 q^{96} + 16 q^{97} + O(q^{100}) \)

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.o.a 561.o 17.d $56$ $4.480$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{8}]$
561.2.o.b 561.o 17.d $72$ $4.480$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{8}]$

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

\( S_{2}^{\mathrm{old}}(561, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(17, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(51, [\chi])\)\(^{\oplus 2}\)