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Properties

Label 17.3.e
Level $17$
Weight $3$
Character orbit 17.e
Rep. character $\chi_{17}(3,\cdot)$
Character field $\Q(\zeta_{16})$
Dimension $16$
Newform subspaces $2$
Sturm bound $4$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 17 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 17.e (of order \(16\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 17 \)
Character field: \(\Q(\zeta_{16})\)
Newform subspaces: \( 2 \)
Sturm bound: \(4\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(17, [\chi])\).

Total New Old
Modular forms 32 32 0
Cusp forms 16 16 0
Eisenstein series 16 16 0

Trace form

\( 16 q - 8 q^{2} - 8 q^{3} - 8 q^{4} - 8 q^{5} - 8 q^{6} - 8 q^{7} - 8 q^{8} - 8 q^{9} + O(q^{10}) \) \( 16 q - 8 q^{2} - 8 q^{3} - 8 q^{4} - 8 q^{5} - 8 q^{6} - 8 q^{7} - 8 q^{8} - 8 q^{9} + 16 q^{10} + 32 q^{11} + 88 q^{12} + 16 q^{13} + 24 q^{14} + 16 q^{15} - 16 q^{17} - 80 q^{18} - 32 q^{19} - 120 q^{20} - 128 q^{21} - 104 q^{22} - 64 q^{23} - 56 q^{24} + 80 q^{25} + 176 q^{26} + 136 q^{27} + 232 q^{28} + 72 q^{29} + 184 q^{30} + 56 q^{31} + 64 q^{32} - 72 q^{34} - 80 q^{35} - 232 q^{36} - 136 q^{37} - 112 q^{38} - 24 q^{39} - 136 q^{40} + 48 q^{41} - 56 q^{42} - 136 q^{43} + 24 q^{44} - 88 q^{45} - 88 q^{46} + 112 q^{47} + 224 q^{48} + 24 q^{49} - 40 q^{51} - 144 q^{52} + 64 q^{53} + 216 q^{54} + 216 q^{55} - 48 q^{56} + 272 q^{57} + 240 q^{58} - 40 q^{59} + 80 q^{60} + 104 q^{61} - 304 q^{62} + 64 q^{63} - 184 q^{64} - 128 q^{65} + 96 q^{68} + 32 q^{69} + 144 q^{70} + 72 q^{71} + 64 q^{72} + 72 q^{73} + 16 q^{74} - 488 q^{75} - 264 q^{77} - 768 q^{78} - 232 q^{79} - 216 q^{80} - 648 q^{81} - 472 q^{82} - 352 q^{83} + 240 q^{85} + 1120 q^{86} + 520 q^{87} + 440 q^{88} + 448 q^{89} + 704 q^{90} + 296 q^{91} + 360 q^{92} + 216 q^{93} + 24 q^{94} + 120 q^{95} + 272 q^{96} - 296 q^{97} - 104 q^{98} - 88 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(17, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
17.3.e.a 17.e 17.e $8$ $0.463$ \(\Q(\zeta_{16})\) None \(-8\) \(-8\) \(16\) \(8\) $\mathrm{SU}(2)[C_{16}]$ \(q+(-1+\zeta_{16}+\zeta_{16}^{2}-\zeta_{16}^{4}-\zeta_{16}^{5}+\cdots)q^{2}+\cdots\)
17.3.e.b 17.e 17.e $8$ $0.463$ \(\Q(\zeta_{16})\) None \(0\) \(0\) \(-24\) \(-16\) $\mathrm{SU}(2)[C_{16}]$ \(q+(-\zeta_{16}^{2}+\zeta_{16}^{4}+\zeta_{16}^{7})q^{2}+(2\zeta_{16}^{2}+\cdots)q^{3}+\cdots\)