↑

Properties

Label 54.8.e
Level $54$
Weight $8$
Character orbit 54.e
Rep. character $\chi_{54}(7,\cdot)$
Character field $\Q(\zeta_{9})$
Dimension $126$
Newform subspaces $2$
Sturm bound $72$
Trace bound $1$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 54 = 2 \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 54.e (of order \(9\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 27 \)
Character field: \(\Q(\zeta_{9})\)
Newform subspaces: \( 2 \)
Sturm bound: \(72\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(54, [\chi])\).

Total New Old
Modular forms 390 126 264
Cusp forms 366 126 240
Eisenstein series 24 0 24

Trace form

\( 126 q + 426 q^{5} - 1392 q^{6} + 1536 q^{8} + 3444 q^{9} + O(q^{10}) \) \( 126 q + 426 q^{5} - 1392 q^{6} + 1536 q^{8} + 3444 q^{9} - 18267 q^{11} - 2496 q^{12} + 26832 q^{14} - 12762 q^{15} + 58956 q^{17} + 72528 q^{18} - 54528 q^{20} + 124512 q^{21} - 105768 q^{22} + 284712 q^{23} + 215982 q^{25} - 632736 q^{26} - 575721 q^{27} + 264306 q^{29} + 903456 q^{30} - 595962 q^{31} - 420039 q^{33} + 266184 q^{34} - 642162 q^{35} - 683904 q^{36} + 399264 q^{38} - 2367906 q^{39} + 1053903 q^{41} + 841152 q^{42} + 1080963 q^{43} + 511104 q^{44} + 4105404 q^{45} + 4733640 q^{47} - 319488 q^{48} - 976014 q^{49} - 1347552 q^{50} - 2704752 q^{51} - 5903952 q^{53} - 191520 q^{54} + 1717248 q^{56} + 1748997 q^{57} + 4371630 q^{59} + 2418048 q^{60} - 3865446 q^{61} + 5719872 q^{62} + 8843682 q^{63} - 16515072 q^{64} - 4923066 q^{65} - 8709120 q^{66} - 14387841 q^{67} - 7527936 q^{68} - 1636398 q^{69} + 3492000 q^{70} + 7063224 q^{71} + 9719808 q^{72} - 7541874 q^{73} + 23032272 q^{74} + 42538332 q^{75} + 402048 q^{76} - 2583966 q^{77} - 17129952 q^{78} - 32831064 q^{79} - 6144000 q^{80} - 55973592 q^{81} - 7892640 q^{83} + 10575360 q^{84} + 15813000 q^{85} + 25345656 q^{86} + 68772492 q^{87} + 13538304 q^{88} + 54045951 q^{89} + 6277680 q^{90} - 6630138 q^{91} - 9441408 q^{92} - 38380038 q^{93} - 34755552 q^{94} - 57195498 q^{95} - 8454144 q^{96} - 42777531 q^{97} + 29047800 q^{98} + 140319180 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{8}^{\mathrm{new}}(54, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
54.8.e.a 54.e 27.e $60$ $16.869$ None 54.8.e.a \(0\) \(0\) \(213\) \(1677\) $\mathrm{SU}(2)[C_{9}]$
54.8.e.b 54.e 27.e $66$ $16.869$ None 54.8.e.b \(0\) \(0\) \(213\) \(-1677\) $\mathrm{SU}(2)[C_{9}]$

Decomposition of \(S_{8}^{\mathrm{old}}(54, [\chi])\) into lower level spaces

\( S_{8}^{\mathrm{old}}(54, [\chi]) \simeq \) \(S_{8}^{\mathrm{new}}(27, [\chi])\)\(^{\oplus 2}\)