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

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

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

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 17
17.10.a.a \(5\) \(8.756\) \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(-33\) \(-236\) \(1480\) \(-13202\) \(+\) \(q+(-7+\beta _{1})q^{2}+(-48+2\beta _{1}+\beta _{4})q^{3}+\cdots\)
17.10.a.b \(7\) \(8.756\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(-1\) \(88\) \(1362\) \(9388\) \(-\) \(q-\beta _{1}q^{2}+(12+2\beta _{1}-\beta _{4})q^{3}+(341+\cdots)q^{4}+\cdots\)