Properties

Label 17.10.b
Level $17$
Weight $10$
Character orbit 17.b
Rep. character $\chi_{17}(16,\cdot)$
Character field $\Q$
Dimension $12$
Newform subspaces $1$
Sturm bound $15$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 17 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 17.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 17 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(15\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(17, [\chi])\).

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

Trace form

\( 12q + 30q^{2} + 1874q^{4} + 23550q^{8} - 9184q^{9} + O(q^{10}) \) \( 12q + 30q^{2} + 1874q^{4} + 23550q^{8} - 9184q^{9} - 63204q^{13} - 243480q^{15} + 38978q^{16} - 105960q^{17} + 547706q^{18} + 1110672q^{19} - 172580q^{21} - 4441796q^{25} + 1336332q^{26} - 500496q^{30} - 1934850q^{32} - 6557404q^{33} - 15085546q^{34} + 3519864q^{35} + 30244102q^{36} + 28748136q^{38} - 11901296q^{42} + 10004616q^{43} - 112552440q^{47} + 121354720q^{49} - 164889018q^{50} - 52506472q^{51} - 59093180q^{52} + 76804272q^{53} + 300732568q^{55} + 11618904q^{59} + 101609232q^{60} - 260062974q^{64} + 18429632q^{66} - 304208752q^{67} - 444301206q^{68} - 211308236q^{69} + 460311456q^{70} + 493218954q^{72} + 416024248q^{76} + 138357828q^{77} - 363335792q^{81} - 845042136q^{83} + 958037984q^{84} - 388949632q^{85} + 127952904q^{86} + 610860648q^{87} - 938223804q^{89} + 1635779524q^{93} - 238629952q^{94} - 152046078q^{98} + O(q^{100}) \)

Decomposition of \(S_{10}^{\mathrm{new}}(17, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
17.10.b.a \(12\) \(8.756\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(30\) \(0\) \(0\) \(0\) \(q+(2+\beta _{2})q^{2}+\beta _{1}q^{3}+(154+4\beta _{2}+\cdots)q^{4}+\cdots\)