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Properties

Label 18.11.d
Level $18$
Weight $11$
Character orbit 18.d
Rep. character $\chi_{18}(5,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $20$
Newform subspaces $1$
Sturm bound $33$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 18 = 2 \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 11 \)
Character orbit: \([\chi]\) \(=\) 18.d (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(33\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{11}(18, [\chi])\).

Total New Old
Modular forms 64 20 44
Cusp forms 56 20 36
Eisenstein series 8 0 8

Trace form

\( 20 q - 84 q^{3} + 5120 q^{4} - 9918 q^{5} + 12864 q^{6} + 12238 q^{7} + 79248 q^{9} + O(q^{10}) \) \( 20 q - 84 q^{3} + 5120 q^{4} - 9918 q^{5} + 12864 q^{6} + 12238 q^{7} + 79248 q^{9} - 327582 q^{11} + 9216 q^{12} - 280550 q^{13} + 175680 q^{14} - 2685042 q^{15} - 2621440 q^{16} + 3925632 q^{18} - 2966240 q^{19} - 5078016 q^{20} - 11895726 q^{21} + 3473472 q^{22} + 10446606 q^{23} + 2752512 q^{24} + 9609944 q^{25} + 2340576 q^{27} + 12531712 q^{28} + 32440806 q^{29} + 37556352 q^{30} - 40069958 q^{31} - 35367930 q^{33} + 30746496 q^{34} - 32695296 q^{36} - 127390400 q^{37} + 370567296 q^{38} + 153125550 q^{39} - 245419398 q^{41} - 344505600 q^{42} - 86593094 q^{43} + 394622766 q^{45} - 366913920 q^{46} + 1094979330 q^{47} + 26738688 q^{48} - 598072056 q^{49} - 456606720 q^{50} - 2329772724 q^{51} + 143641600 q^{52} + 1623484224 q^{54} - 262510308 q^{55} + 89948160 q^{56} + 311135772 q^{57} + 249515904 q^{58} - 2125085130 q^{59} - 2357738496 q^{60} + 312021586 q^{61} + 5475513858 q^{63} - 2684354560 q^{64} + 13076821350 q^{65} + 2185467264 q^{66} - 1200881210 q^{67} - 2610487296 q^{68} - 11765922354 q^{69} + 1138681152 q^{70} + 1554382848 q^{72} + 5213376328 q^{73} + 9118122624 q^{74} + 13244996208 q^{75} - 759357440 q^{76} - 33678720774 q^{77} - 14572366080 q^{78} - 3396212726 q^{79} + 14546869128 q^{81} + 3667214592 q^{82} + 16739541378 q^{83} + 1518514176 q^{84} + 7141101588 q^{85} - 11512304064 q^{86} - 32778228834 q^{87} - 1778417664 q^{88} + 16769410560 q^{90} - 10426841884 q^{91} + 5348662272 q^{92} - 4843832814 q^{93} + 6416128320 q^{94} - 26494427340 q^{95} - 1962934272 q^{96} + 6721893598 q^{97} + 41160676842 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{11}^{\mathrm{new}}(18, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
18.11.d.a 18.d 9.d $20$ $11.436$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(0\) \(-84\) \(-9918\) \(12238\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{2}q^{2}+(-2-4\beta _{1}+\beta _{3}-\beta _{4})q^{3}+\cdots\)

Decomposition of \(S_{11}^{\mathrm{old}}(18, [\chi])\) into lower level spaces

\( S_{11}^{\mathrm{old}}(18, [\chi]) \cong \) \(S_{11}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 2}\)