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Properties

Label 289.2.d
Level $289$
Weight $2$
Character orbit 289.d
Rep. character $\chi_{289}(110,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $60$
Newform subspaces $6$
Sturm bound $51$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 289 = 17^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 289.d (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 17 \)
Character field: \(\Q(\zeta_{8})\)
Newform subspaces: \( 6 \)
Sturm bound: \(51\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(2\), \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(289, [\chi])\).

Total New Old
Modular forms 140 116 24
Cusp forms 68 60 8
Eisenstein series 72 56 16

Trace form

\( 60 q + 4 q^{2} + 4 q^{3} - 4 q^{6} + 4 q^{7} - 4 q^{8} - 8 q^{9} + O(q^{10}) \) \( 60 q + 4 q^{2} + 4 q^{3} - 4 q^{6} + 4 q^{7} - 4 q^{8} - 8 q^{9} - 4 q^{10} + 4 q^{11} + 4 q^{12} - 4 q^{14} + 8 q^{15} + 44 q^{16} - 36 q^{18} - 8 q^{19} - 4 q^{20} - 12 q^{22} - 4 q^{23} - 12 q^{24} + 4 q^{25} + 4 q^{26} - 8 q^{27} - 4 q^{28} + 4 q^{29} + 12 q^{31} - 4 q^{32} - 24 q^{33} - 56 q^{35} + 8 q^{40} + 4 q^{41} + 8 q^{42} + 8 q^{43} + 20 q^{44} - 12 q^{45} - 20 q^{46} - 12 q^{48} - 8 q^{49} - 76 q^{50} - 48 q^{52} + 4 q^{53} + 8 q^{54} + 20 q^{56} + 24 q^{57} + 8 q^{60} + 12 q^{62} + 12 q^{63} + 4 q^{65} - 8 q^{66} - 56 q^{67} + 24 q^{69} + 8 q^{70} - 20 q^{71} + 28 q^{73} - 20 q^{74} + 12 q^{75} - 8 q^{76} - 8 q^{77} + 8 q^{78} + 4 q^{79} - 4 q^{82} - 16 q^{83} + 128 q^{84} - 16 q^{86} - 16 q^{87} - 12 q^{88} - 4 q^{90} + 28 q^{92} - 24 q^{93} + 24 q^{94} + 8 q^{95} + 20 q^{96} - 24 q^{97} + 4 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(289, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
289.2.d.a 289.d 17.d $4$ $2.308$ \(\Q(\zeta_{8})\) None \(-4\) \(4\) \(0\) \(4\) $\mathrm{SU}(2)[C_{8}]$ \(q+(-1+\zeta_{8}^{2}-\zeta_{8}^{3})q^{2}+(1+\zeta_{8}+\zeta_{8}^{2}+\cdots)q^{3}+\cdots\)
289.2.d.b 289.d 17.d $4$ $2.308$ \(\Q(\zeta_{8})\) None \(4\) \(-4\) \(-4\) \(-4\) $\mathrm{SU}(2)[C_{8}]$ \(q+(1-\zeta_{8}^{2}-\zeta_{8}^{3})q^{2}+(-1-\zeta_{8}+\zeta_{8}^{2}+\cdots)q^{3}+\cdots\)
289.2.d.c 289.d 17.d $4$ $2.308$ \(\Q(\zeta_{8})\) None \(4\) \(4\) \(4\) \(4\) $\mathrm{SU}(2)[C_{8}]$ \(q+(1-\zeta_{8}^{2}-\zeta_{8}^{3})q^{2}+(1+\zeta_{8}-\zeta_{8}^{2}+\cdots)q^{3}+\cdots\)
289.2.d.d 289.d 17.d $8$ $2.308$ \(\Q(\zeta_{16})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{8}]$ \(q+\zeta_{16}^{2}q^{2}-\zeta_{16}^{4}q^{4}-\zeta_{16}^{7}q^{5}+\cdots\)
289.2.d.e 289.d 17.d $16$ $2.308$ 16.0.\(\cdots\).1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{8}]$ \(q+(\beta _{3}+\beta _{5})q^{2}+(-\beta _{6}-\beta _{7})q^{3}+(-2\beta _{8}+\cdots)q^{4}+\cdots\)
289.2.d.f 289.d 17.d $24$ $2.308$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{8}]$

Decomposition of \(S_{2}^{\mathrm{old}}(289, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(289, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(17, [\chi])\)\(^{\oplus 2}\)