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

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

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

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