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Properties

Label 76.11.j
Level $76$
Weight $11$
Character orbit 76.j
Rep. character $\chi_{76}(13,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $102$
Newform subspaces $1$
Sturm bound $110$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 76 = 2^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 11 \)
Character orbit: \([\chi]\) \(=\) 76.j (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
Character field: \(\Q(\zeta_{18})\)
Newform subspaces: \( 1 \)
Sturm bound: \(110\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{11}(76, [\chi])\).

Total New Old
Modular forms 618 102 516
Cusp forms 582 102 480
Eisenstein series 36 0 36

Trace form

\( 102 q + 66 q^{3} - 5841 q^{7} - 15906 q^{9} + O(q^{10}) \) \( 102 q + 66 q^{3} - 5841 q^{7} - 15906 q^{9} - 171825 q^{11} + 1473309 q^{13} - 1411629 q^{15} + 5998221 q^{17} - 9233214 q^{19} - 3704049 q^{21} + 23209248 q^{23} - 54962154 q^{25} + 23087178 q^{27} - 73746561 q^{29} + 61388388 q^{31} + 161401485 q^{33} - 190639659 q^{35} + 276639168 q^{39} - 178537266 q^{41} - 331682859 q^{43} + 312367968 q^{45} + 1593394629 q^{47} - 2343473676 q^{49} + 1083649356 q^{51} + 1220659179 q^{53} + 124667979 q^{55} - 2895950478 q^{57} - 1708977921 q^{59} + 1084976412 q^{61} + 447362211 q^{63} + 1455423345 q^{65} + 2655900315 q^{67} - 3462502329 q^{69} + 5553232434 q^{71} - 8858405196 q^{73} + 4786871364 q^{77} + 553784781 q^{79} + 23900123202 q^{81} - 1860259239 q^{83} - 24359347674 q^{85} - 18031919976 q^{87} + 17688671088 q^{89} + 751347186 q^{91} - 15239864472 q^{93} + 27558802671 q^{95} - 8973304659 q^{97} - 74993247177 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{11}^{\mathrm{new}}(76, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
76.11.j.a 76.j 19.f $102$ $48.287$ None 76.11.j.a \(0\) \(66\) \(0\) \(-5841\) $\mathrm{SU}(2)[C_{18}]$

Decomposition of \(S_{11}^{\mathrm{old}}(76, [\chi])\) into lower level spaces

\( S_{11}^{\mathrm{old}}(76, [\chi]) \simeq \) \(S_{11}^{\mathrm{new}}(19, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(38, [\chi])\)\(^{\oplus 2}\)