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Properties

Label 6.17.b
Level $6$
Weight $17$
Character orbit 6.b
Rep. character $\chi_{6}(5,\cdot)$
Character field $\Q$
Dimension $6$
Newform subspaces $1$
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: \(\Q\)
Newform subspaces: \( 1 \)
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

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

Display 100 coefficients 10 coefficients

Decomposition of \(S_{17}^{\mathrm{new}}(6, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
6.17.b.a 6.b 3.b $6$ $9.739$ \(\mathbb{Q}[x]/(x^{6} + \cdots)\) None \(0\) \(6006\) \(0\) \(-167892\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{2}+(1001+\beta _{1}-\beta _{2})q^{3}-2^{15}q^{4}+\cdots\)

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

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