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Properties

Label 17.10.a
Level $17$
Weight $10$
Character orbit 17.a
Rep. character $\chi_{17}(1,\cdot)$
Character field $\Q$
Dimension $12$
Newform subspaces $2$
Sturm bound $15$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 17 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 17.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(15\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_0(17))\).

Total New Old
Modular forms 14 12 2
Cusp forms 12 12 0
Eisenstein series 2 0 2

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(17\)Dim
\(+\)\(5\)
\(-\)\(7\)

Trace form

\( 12 q - 34 q^{2} - 148 q^{3} + 3242 q^{4} + 2842 q^{5} - 4142 q^{6} - 3814 q^{7} - 25602 q^{8} + 92400 q^{9} + O(q^{10}) \) \( 12 q - 34 q^{2} - 148 q^{3} + 3242 q^{4} + 2842 q^{5} - 4142 q^{6} - 3814 q^{7} - 25602 q^{8} + 92400 q^{9} + 64898 q^{10} + 67500 q^{11} - 207850 q^{12} + 7260 q^{13} + 362552 q^{14} - 528276 q^{15} + 1813810 q^{16} + 167042 q^{17} - 1762558 q^{18} + 406180 q^{19} + 715478 q^{20} - 1628224 q^{21} - 1100230 q^{22} + 3003634 q^{23} + 1191342 q^{24} + 4336024 q^{25} - 13645120 q^{26} - 7517332 q^{27} - 3145520 q^{28} + 4635618 q^{29} + 4489552 q^{30} - 3715622 q^{31} - 780458 q^{32} + 593116 q^{33} + 2672672 q^{34} - 27034724 q^{35} + 54317142 q^{36} - 13124210 q^{37} - 30849320 q^{38} + 43856988 q^{39} + 73224598 q^{40} + 2288748 q^{41} - 29899080 q^{42} - 34995064 q^{43} + 140019678 q^{44} + 121715946 q^{45} - 183572956 q^{46} + 39736464 q^{47} - 304192994 q^{48} + 15226292 q^{49} - 175229210 q^{50} + 27060804 q^{51} + 17392704 q^{52} + 38450580 q^{53} + 292953820 q^{54} + 47156492 q^{55} + 121233936 q^{56} + 290228864 q^{57} - 172256422 q^{58} - 8724216 q^{59} - 851802400 q^{60} - 127601298 q^{61} + 251348744 q^{62} - 194130634 q^{63} + 449545162 q^{64} - 162954956 q^{65} - 326848468 q^{66} - 2640180 q^{67} + 128288256 q^{68} + 46274160 q^{69} + 843528568 q^{70} + 175871018 q^{71} - 645941526 q^{72} + 16675856 q^{73} + 511462886 q^{74} + 765386140 q^{75} - 902581384 q^{76} - 245828184 q^{77} + 1015080612 q^{78} + 130907274 q^{79} + 220577342 q^{80} + 516841632 q^{81} - 63174400 q^{82} - 1318264120 q^{83} + 1059929000 q^{84} - 9855478 q^{85} + 999753908 q^{86} - 1454400972 q^{87} + 114058870 q^{88} - 1594479008 q^{89} - 4524752134 q^{90} - 866519200 q^{91} + 3407899844 q^{92} + 2696236984 q^{93} + 290020128 q^{94} - 1750951648 q^{95} - 1506989058 q^{96} + 2698561500 q^{97} - 1298895954 q^{98} - 552052864 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_0(17))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 17
17.10.a.a 17.a 1.a $5$ $8.756$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(-33\) \(-236\) \(1480\) \(-13202\) $+$ $\mathrm{SU}(2)$ \(q+(-7+\beta _{1})q^{2}+(-48+2\beta _{1}+\beta _{4})q^{3}+\cdots\)
17.10.a.b 17.a 1.a $7$ $8.756$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(-1\) \(88\) \(1362\) \(9388\) $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(12+2\beta _{1}-\beta _{4})q^{3}+(341+\cdots)q^{4}+\cdots\)