Properties

Label 76.6.i
Level $76$
Weight $6$
Character orbit 76.i
Rep. character $\chi_{76}(5,\cdot)$
Character field $\Q(\zeta_{9})$
Dimension $48$
Newform subspaces $1$
Sturm bound $60$
Trace bound $0$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 76 = 2^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 76.i (of order \(9\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
Character field: \(\Q(\zeta_{9})\)
Newform subspaces: \( 1 \)
Sturm bound: \(60\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(76, [\chi])\).

Total New Old
Modular forms 318 48 270
Cusp forms 282 48 234
Eisenstein series 36 0 36

Trace form

\( 48q + 33q^{3} - 177q^{7} + 33q^{9} + O(q^{10}) \) \( 48q + 33q^{3} - 177q^{7} + 33q^{9} - 237q^{11} + 2049q^{13} + 2085q^{15} - 609q^{17} - 6012q^{19} + 3591q^{21} + 14100q^{23} + 11802q^{25} - 861q^{27} - 10575q^{29} - 6546q^{31} - 21234q^{33} - 231q^{35} + 20052q^{37} + 72204q^{39} - 3249q^{41} - 34677q^{43} - 34956q^{45} + 4461q^{47} - 41139q^{49} + 12099q^{51} - 24291q^{53} - 61767q^{55} - 64470q^{57} - 20100q^{59} + 95490q^{61} + 86403q^{63} - 57915q^{65} - 64452q^{67} - 99315q^{69} - 115536q^{71} - 16362q^{73} + 236250q^{75} + 26688q^{77} + 29799q^{79} + 180327q^{81} + 52347q^{83} + 204618q^{85} + 69414q^{87} + 47394q^{89} - 249384q^{91} - 462126q^{93} + 412869q^{95} - 229974q^{97} - 692274q^{99} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(76, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
76.6.i.a \(48\) \(12.189\) None \(0\) \(33\) \(0\) \(-177\)

Decomposition of \(S_{6}^{\mathrm{old}}(76, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(76, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(19, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(38, [\chi])\)\(^{\oplus 2}\)