Properties

Label 76.6.e
Level $76$
Weight $6$
Character orbit 76.e
Rep. character $\chi_{76}(45,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $18$
Newform subspaces $1$
Sturm bound $60$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 76 = 2^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 76.e (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
Character field: \(\Q(\zeta_{3})\)
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 106 18 88
Cusp forms 94 18 76
Eisenstein series 12 0 12

Trace form

\( 18 q - 11 q^{3} + 11 q^{5} + 336 q^{7} - 902 q^{9} + O(q^{10}) \) \( 18 q - 11 q^{3} + 11 q^{5} + 336 q^{7} - 902 q^{9} - 320 q^{11} + 227 q^{13} - 101 q^{15} + 179 q^{17} - 868 q^{19} - 5700 q^{21} - 3425 q^{23} - 7054 q^{25} + 14722 q^{27} - 7349 q^{29} - 9960 q^{31} - 2998 q^{33} + 15888 q^{35} + 26444 q^{37} - 30246 q^{39} - 7311 q^{41} - 8283 q^{43} - 62164 q^{45} + 37603 q^{47} + 124738 q^{49} + 47227 q^{51} - 20337 q^{53} + 716 q^{55} - 57555 q^{57} - 74455 q^{59} - 7569 q^{61} - 52544 q^{63} + 188998 q^{65} - 26177 q^{67} + 116282 q^{69} - 53463 q^{71} - 14103 q^{73} + 120912 q^{75} - 31960 q^{77} + 31825 q^{79} - 21137 q^{81} + 82600 q^{83} - 50787 q^{85} - 339766 q^{87} - 155197 q^{89} - 2800 q^{91} - 46460 q^{93} + 49315 q^{95} + 111241 q^{97} - 193544 q^{99} + O(q^{100}) \)

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
76.6.e.a 76.e 19.c $18$ $12.189$ \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(0\) \(-11\) \(11\) \(336\) $\mathrm{SU}(2)[C_{3}]$ \(q+(\beta _{1}-\beta _{2}+\beta _{3})q^{3}+(\beta _{2}+\beta _{6}+\beta _{8}+\cdots)q^{5}+\cdots\)

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

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