Properties

Label 6.17.b
Level 6
Weight 17
Character orbit b
Rep. character \(\chi_{6}(5,\cdot)\)
Character field \(\Q\)
Dimension 6
Newforms 1
Sturm bound 17
Trace bound 0

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Defining parameters

Level: \( N \) = \( 6 = 2 \cdot 3 \)
Weight: \( k \) = \( 17 \)
Character orbit: \([\chi]\) = 6.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 3 \)
Character field: \(\Q\)
Newforms: \( 1 \)
Sturm bound: \(17\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{17}(6, [\chi])\).

Total New Old
Modular forms 18 6 12
Cusp forms 14 6 8
Eisenstein series 4 0 4

Trace form

\( 6q + 6006q^{3} - 196608q^{4} + 159744q^{6} - 167892q^{7} - 10215738q^{9} + O(q^{10}) \) \( 6q + 6006q^{3} - 196608q^{4} + 159744q^{6} - 167892q^{7} - 10215738q^{9} + 39297024q^{10} - 196804608q^{12} + 1763152140q^{13} - 8080218432q^{15} + 6442450944q^{16} - 12549169152q^{18} + 60306979692q^{19} - 155770661748q^{21} + 94233305088q^{22} - 5234491392q^{24} - 75722441466q^{25} + 330190979958q^{27} + 5501485056q^{28} + 987679531008q^{30} - 2846203650132q^{31} + 3282289396416q^{33} - 1812957659136q^{34} + 334749302784q^{36} + 2483836081932q^{37} - 8759076866580q^{39} - 1287684882432q^{40} - 3652917731328q^{42} + 46155081190764q^{43} - 46496752783488q^{45} - 17111605395456q^{46} + 6448893394944q^{48} + 42155513811090q^{49} - 3055668993792q^{51} - 57774969323520q^{52} + 240022278328320q^{54} - 155561818958208q^{55} + 27052692784332q^{57} - 366644114104320q^{58} + 264772597579776q^{60} + 306036501898764q^{61} - 801652315914324q^{63} - 211106232532992q^{64} + 1157574327017472q^{66} + 1979846570008812q^{67} - 2345782552693632q^{69} - 2197723307360256q^{70} + 411211174772736q^{72} + 3864207384753420q^{73} - 3376263465802122q^{75} - 1976139110547456q^{76} + 5837442492456960q^{78} + 1835806484101548q^{79} - 703356001465338q^{81} - 9913023387353088q^{82} + 5104293044158464q^{84} + 2872972366990848q^{85} - 3000080900606400q^{87} - 3087836941123584q^{88} + 12789804912058368q^{90} - 1824281133603240q^{91} - 11156835457641972q^{93} - 4579876939530240q^{94} + 171523813933056q^{96} + 31097493125645196q^{97} - 28794216850745472q^{99} + O(q^{100}) \)

Decomposition of \(S_{17}^{\mathrm{new}}(6, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
6.17.b.a \(6\) \(9.739\) \(\mathbb{Q}[x]/(x^{6} + \cdots)\) None \(0\) \(6006\) \(0\) \(-167892\) \(q-\beta _{1}q^{2}+(1001+\beta _{1}-\beta _{2})q^{3}-2^{15}q^{4}+\cdots\)

Decomposition of \(S_{17}^{\mathrm{old}}(6, [\chi])\) into lower level spaces

\( S_{17}^{\mathrm{old}}(6, [\chi]) \cong \) \(S_{17}^{\mathrm{new}}(3, [\chi])\)\(^{\oplus 2}\)