Properties

Label 6.16.a
Level $6$
Weight $16$
Character orbit 6.a
Rep. character $\chi_{6}(1,\cdot)$
Character field $\Q$
Dimension $3$
Newform subspaces $3$
Sturm bound $16$
Trace bound $3$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 6 = 2 \cdot 3 \)
Weight: \( k \) \(=\) \( 16 \)
Character orbit: \([\chi]\) \(=\) 6.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(16\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{16}(\Gamma_0(6))\).

Total New Old
Modular forms 17 3 14
Cusp forms 13 3 10
Eisenstein series 4 0 4

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)\(3\)FrickeDim.
\(+\)\(+\)\(+\)\(1\)
\(-\)\(+\)\(-\)\(1\)
\(-\)\(-\)\(+\)\(1\)
Plus space\(+\)\(2\)
Minus space\(-\)\(1\)

Trace form

\( 3 q + 128 q^{2} - 2187 q^{3} + 49152 q^{4} - 351654 q^{5} + 279936 q^{6} - 247368 q^{7} + 2097152 q^{8} + 14348907 q^{9} + O(q^{10}) \) \( 3 q + 128 q^{2} - 2187 q^{3} + 49152 q^{4} - 351654 q^{5} + 279936 q^{6} - 247368 q^{7} + 2097152 q^{8} + 14348907 q^{9} + 35497728 q^{10} + 54814524 q^{11} - 35831808 q^{12} + 236812146 q^{13} - 550077440 q^{14} + 1108690902 q^{15} + 805306368 q^{16} - 4106086218 q^{17} + 612220032 q^{18} + 1202087364 q^{19} - 5761499136 q^{20} + 3874436712 q^{21} - 21209034240 q^{22} + 14220884280 q^{23} + 4586471424 q^{24} + 26561463141 q^{25} + 15963702016 q^{26} - 10460353203 q^{27} - 4052877312 q^{28} + 286157354226 q^{29} - 34161709824 q^{30} - 542755745328 q^{31} + 34359738368 q^{32} + 90121502340 q^{33} - 31472305920 q^{34} - 229291374576 q^{35} + 235092492288 q^{36} - 167027835126 q^{37} - 399908991488 q^{38} + 729250972830 q^{39} + 581594775552 q^{40} - 1366519968402 q^{41} + 1629700051968 q^{42} - 489890179812 q^{43} + 898081161216 q^{44} - 1681950180726 q^{45} + 225655723008 q^{46} + 9009642578640 q^{47} - 587068342272 q^{48} - 352670037093 q^{49} - 14107046503552 q^{50} - 4901628870918 q^{51} + 3879930200064 q^{52} + 12546949293162 q^{53} + 1338925209984 q^{54} - 19068946165368 q^{55} - 9012468776960 q^{56} - 28414203586308 q^{57} + 20053749259008 q^{58} + 23389468339980 q^{59} + 18164791738368 q^{60} + 62057091114114 q^{61} - 64291906973696 q^{62} - 1183153475592 q^{63} + 13194139533312 q^{64} + 16494962423388 q^{65} + 73264268772864 q^{66} - 64428771786348 q^{67} - 67274116595712 q^{68} - 32557661374968 q^{69} + 133686828582912 q^{70} + 19829570466024 q^{71} + 10030613004288 q^{72} - 221540395581714 q^{73} - 146555267074304 q^{74} - 165203392251933 q^{75} + 19694999371776 q^{76} + 573789241106400 q^{77} + 124723753115904 q^{78} - 414153951555648 q^{79} - 94396401844224 q^{80} + 68630377364883 q^{81} + 22809377279232 q^{82} + 377513484920196 q^{83} + 63478771089408 q^{84} + 246030873170004 q^{85} - 397238123314688 q^{86} - 112819827728322 q^{87} - 347488816988160 q^{88} + 92197563215742 q^{89} + 169784532594432 q^{90} + 647499908194896 q^{91} + 232994968043520 q^{92} + 199263780625104 q^{93} + 295167948171264 q^{94} - 1704507560977800 q^{95} + 75144747810816 q^{96} - 461982087578586 q^{97} + 120415920194688 q^{98} + 262176169041756 q^{99} + O(q^{100}) \)

Decomposition of \(S_{16}^{\mathrm{new}}(\Gamma_0(6))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3
6.16.a.a \(1\) \(8.562\) \(\Q\) None \(-128\) \(-2187\) \(-314490\) \(2025056\) \(+\) \(+\) \(q-2^{7}q^{2}-3^{7}q^{3}+2^{14}q^{4}-314490q^{5}+\cdots\)
6.16.a.b \(1\) \(8.562\) \(\Q\) None \(128\) \(-2187\) \(-114810\) \(-3034528\) \(-\) \(+\) \(q+2^{7}q^{2}-3^{7}q^{3}+2^{14}q^{4}-114810q^{5}+\cdots\)
6.16.a.c \(1\) \(8.562\) \(\Q\) None \(128\) \(2187\) \(77646\) \(762104\) \(-\) \(-\) \(q+2^{7}q^{2}+3^{7}q^{3}+2^{14}q^{4}+77646q^{5}+\cdots\)

Decomposition of \(S_{16}^{\mathrm{old}}(\Gamma_0(6))\) into lower level spaces

\( S_{16}^{\mathrm{old}}(\Gamma_0(6)) \cong \) \(S_{16}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 2}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 2}\)