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Properties

Label 126.16.e
Level $126$
Weight $16$
Character orbit 126.e
Rep. character $\chi_{126}(25,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $240$
Sturm bound $384$

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Defining parameters

Level: \( N \) \(=\) \( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 16 \)
Character orbit: \([\chi]\) \(=\) 126.e (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 63 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(384\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{16}(126, [\chi])\).

Total New Old
Modular forms 728 240 488
Cusp forms 712 240 472
Eisenstein series 16 0 16

Trace form

\( 240 q + 3932160 q^{4} + 312500 q^{5} + 1226240 q^{6} - 1607412 q^{7} - 16953980 q^{9} + O(q^{10}) \) \( 240 q + 3932160 q^{4} + 312500 q^{5} + 1226240 q^{6} - 1607412 q^{7} - 16953980 q^{9} - 63565640 q^{11} - 83018184 q^{13} - 64218880 q^{14} + 979327948 q^{15} + 64424509440 q^{16} + 5307761272 q^{17} - 3277515264 q^{18} + 917891400 q^{19} + 5120000000 q^{20} - 13823186264 q^{21} + 14481956728 q^{23} + 20090716160 q^{24} - 732421875000 q^{25} + 56652326912 q^{26} + 54576496890 q^{27} - 26335838208 q^{28} - 197388524950 q^{29} + 15622935040 q^{30} + 84504114300 q^{31} - 118982948920 q^{33} + 1493469456376 q^{35} - 277774008320 q^{36} + 146736661512 q^{37} + 1372986991104 q^{38} - 2192311498202 q^{39} + 1910588191266 q^{41} - 5086168478208 q^{42} + 627540675258 q^{43} - 1041459445760 q^{44} + 3731674259006 q^{45} - 1597730077440 q^{46} - 5898654858228 q^{47} + 3521213880810 q^{49} + 11769803084288 q^{50} + 1481104353272 q^{51} - 1360169926656 q^{52} + 31571665956996 q^{53} - 28369343653120 q^{54} - 8152001579628 q^{55} - 1052162129920 q^{56} - 61684760412564 q^{57} + 9119633580288 q^{58} - 9923641340656 q^{59} + 16045309100032 q^{60} + 59711764116180 q^{61} - 172019991112192 q^{62} - 8633671385238 q^{63} + 1055531162664960 q^{64} + 232191583769064 q^{65} - 143948986415104 q^{66} - 10088738690856 q^{67} + 86962360680448 q^{68} - 272799242105176 q^{69} - 100498333457664 q^{70} + 342531349194688 q^{71} - 53698810085376 q^{72} + 338696410207008 q^{73} + 55983767750400 q^{74} - 1203959621343218 q^{75} + 15038732697600 q^{76} + 630142443592436 q^{77} + 14923429253120 q^{78} + 311016025353468 q^{79} + 83886080000000 q^{80} + 278104757612248 q^{81} + 234249991644748 q^{83} - 226479083749376 q^{84} + 223477323750000 q^{85} - 349152694448640 q^{86} + 45469218209476 q^{87} + 1326204950047866 q^{89} + 1556157094492928 q^{90} - 1000529822838750 q^{91} + 237272379031552 q^{92} + 836303011701856 q^{93} + 2009385080386560 q^{94} + 1395311233958620 q^{95} + 329166293565440 q^{96} - 465327769722288 q^{97} + 350397333654528 q^{98} + 273465124662604 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{16}^{\mathrm{new}}(126, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{16}^{\mathrm{old}}(126, [\chi])\) into lower level spaces

\( S_{16}^{\mathrm{old}}(126, [\chi]) \simeq \) \(S_{16}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 2}\)