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Properties

Label 54.10.c
Level $54$
Weight $10$
Character orbit 54.c
Rep. character $\chi_{54}(19,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $18$
Newform subspaces $2$
Sturm bound $90$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 54 = 2 \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 54.c (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 2 \)
Sturm bound: \(90\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(54, [\chi])\).

Total New Old
Modular forms 174 18 156
Cusp forms 150 18 132
Eisenstein series 24 0 24

Trace form

\( 18 q + 16 q^{2} - 2304 q^{4} - 342 q^{5} + 684 q^{7} - 8192 q^{8} + O(q^{10}) \) \( 18 q + 16 q^{2} - 2304 q^{4} - 342 q^{5} + 684 q^{7} - 8192 q^{8} + 85281 q^{11} - 64872 q^{13} + 217376 q^{14} - 589824 q^{16} - 1599510 q^{17} - 52830 q^{19} - 87552 q^{20} - 528336 q^{22} + 176952 q^{23} - 2054169 q^{25} - 1809472 q^{26} - 350208 q^{28} - 2014500 q^{29} - 1136934 q^{31} + 1048576 q^{32} + 4780080 q^{34} - 35472852 q^{35} - 32783040 q^{37} + 6559472 q^{38} + 72541053 q^{41} - 7232103 q^{43} - 43663872 q^{44} - 12858048 q^{46} + 135983676 q^{47} - 74350035 q^{49} + 127200688 q^{50} - 16607232 q^{52} - 629342016 q^{53} - 15394860 q^{55} + 55648256 q^{56} + 51486624 q^{58} + 265737135 q^{59} - 150612066 q^{61} - 399346048 q^{62} + 301989888 q^{64} + 493100046 q^{65} + 85842891 q^{67} + 204737280 q^{68} + 192824064 q^{70} - 1199069256 q^{71} - 774704214 q^{73} + 357530048 q^{74} + 6762240 q^{76} + 584715396 q^{77} + 113851422 q^{79} + 44826624 q^{80} + 1142535456 q^{82} + 1635631410 q^{83} - 261786492 q^{85} + 1238790128 q^{86} - 135254016 q^{88} - 1115256108 q^{89} + 2985456924 q^{91} + 45299712 q^{92} + 378847584 q^{94} - 1759629672 q^{95} - 533004129 q^{97} + 215378016 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{10}^{\mathrm{new}}(54, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
54.10.c.a 54.c 9.c $8$ $27.812$ \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None 18.10.c.a \(-64\) \(0\) \(-171\) \(7135\) $\mathrm{SU}(2)[C_{3}]$ \(q-2^{4}\beta _{1}q^{2}+(-2^{8}+2^{8}\beta _{1})q^{4}+(-43+\cdots)q^{5}+\cdots\)
54.10.c.b 54.c 9.c $10$ $27.812$ \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None 18.10.c.b \(80\) \(0\) \(-171\) \(-6451\) $\mathrm{SU}(2)[C_{3}]$ \(q+(2^{4}+2^{4}\beta _{1})q^{2}+2^{8}\beta _{1}q^{4}+(34\beta _{1}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{10}^{\mathrm{old}}(54, [\chi])\) into lower level spaces

\( S_{10}^{\mathrm{old}}(54, [\chi]) \simeq \) \(S_{10}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(27, [\chi])\)\(^{\oplus 2}\)