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Properties

Label 18.6.c
Level $18$
Weight $6$
Character orbit 18.c
Rep. character $\chi_{18}(7,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $10$
Newform subspaces $2$
Sturm bound $18$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 18 = 2 \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 18.c (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 2 \)
Sturm bound: \(18\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(18, [\chi])\).

Total New Old
Modular forms 34 10 24
Cusp forms 26 10 16
Eisenstein series 8 0 8

Trace form

\( 10 q - 4 q^{2} + 9 q^{3} - 80 q^{4} - 108 q^{5} - 84 q^{6} - 58 q^{7} + 128 q^{8} + 579 q^{9} + O(q^{10}) \) \( 10 q - 4 q^{2} + 9 q^{3} - 80 q^{4} - 108 q^{5} - 84 q^{6} - 58 q^{7} + 128 q^{8} + 579 q^{9} - 393 q^{11} - 384 q^{12} + 362 q^{13} - 824 q^{14} + 2664 q^{15} - 1280 q^{16} + 3882 q^{17} + 2568 q^{18} - 1018 q^{19} - 1728 q^{20} - 11310 q^{21} - 948 q^{22} - 8706 q^{23} + 576 q^{24} + 181 q^{25} + 14800 q^{26} + 18144 q^{27} + 1856 q^{28} - 9042 q^{29} - 7488 q^{30} - 3892 q^{31} - 1024 q^{32} - 405 q^{33} - 3828 q^{34} + 432 q^{35} - 7440 q^{36} + 30344 q^{37} - 11084 q^{38} - 30432 q^{39} + 20403 q^{41} + 36960 q^{42} + 1469 q^{43} + 12576 q^{44} + 7884 q^{45} - 18960 q^{46} + 37878 q^{47} + 3840 q^{48} - 22413 q^{49} - 23788 q^{50} - 44379 q^{51} + 5792 q^{52} - 128712 q^{53} - 116604 q^{54} + 56160 q^{55} - 13184 q^{56} + 89667 q^{57} - 5016 q^{58} + 84921 q^{59} + 42624 q^{60} - 72916 q^{61} + 106624 q^{62} + 55788 q^{63} + 40960 q^{64} + 121284 q^{65} + 80064 q^{66} + 3767 q^{67} - 31056 q^{68} - 68292 q^{69} - 9936 q^{70} - 277368 q^{71} - 59712 q^{72} - 110842 q^{73} - 99056 q^{74} - 86403 q^{75} + 8144 q^{76} + 110202 q^{77} + 240840 q^{78} + 74276 q^{79} + 55296 q^{80} + 173007 q^{81} + 82440 q^{82} + 123396 q^{83} - 2016 q^{84} - 23112 q^{85} - 256988 q^{86} - 170046 q^{87} - 15168 q^{88} + 47532 q^{89} - 344736 q^{90} - 202712 q^{91} - 139296 q^{92} - 87780 q^{93} - 48120 q^{94} + 68472 q^{95} + 12288 q^{96} + 15983 q^{97} + 666408 q^{98} + 601794 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(18, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
18.6.c.a 18.c 9.c $4$ $2.887$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(8\) \(0\) \(-54\) \(74\) $\mathrm{SU}(2)[C_{3}]$ \(q+4\beta _{1}q^{2}+(-3+6\beta _{1}+\beta _{3})q^{3}+(-2^{4}+\cdots)q^{4}+\cdots\)
18.6.c.b 18.c 9.c $6$ $2.887$ 6.0.\(\cdots\).3 None \(-12\) \(9\) \(-54\) \(-132\) $\mathrm{SU}(2)[C_{3}]$ \(q-4\beta _{1}q^{2}+(1+\beta _{1}+\beta _{2}-\beta _{3})q^{3}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(18, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(18, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 2}\)